1*5ddc57e5SXin Li<?xml version="1.0" ?> 2*5ddc57e5SXin Li<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> 3*5ddc57e5SXin Li<html xmlns="http://www.w3.org/1999/xhtml"> 4*5ddc57e5SXin Li<head> 5*5ddc57e5SXin Li<title>lmfit: a self-contained C library for Levenberg-Marquardt least-squares minimization and curve fitting</title> 6*5ddc57e5SXin Li<meta http-equiv="content-type" content="text/html; charset=utf-8" /> 7*5ddc57e5SXin Li<link rev="made" href="mailto:root@localhost" /> 8*5ddc57e5SXin Li</head> 9*5ddc57e5SXin Li 10*5ddc57e5SXin Li<body> 11*5ddc57e5SXin Li 12*5ddc57e5SXin Li 13*5ddc57e5SXin Li 14*5ddc57e5SXin Li 15*5ddc57e5SXin Li 16*5ddc57e5SXin Li<link rel="stylesheet" href="podstyle.css" type="text/css" /> 17*5ddc57e5SXin Li 18*5ddc57e5SXin Li<h1 id="NAME">NAME</h1> 19*5ddc57e5SXin Li 20*5ddc57e5SXin Li<p>lmcurve - Levenberg-Marquardt least-squares fit of a curve (t,y)</p> 21*5ddc57e5SXin Li 22*5ddc57e5SXin Li<h1 id="SYNOPSIS">SYNOPSIS</h1> 23*5ddc57e5SXin Li 24*5ddc57e5SXin Li<p><b>#include <lmcurve.h</b>></p> 25*5ddc57e5SXin Li 26*5ddc57e5SXin Li<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*5ddc57e5SXin Li 28*5ddc57e5SXin Li<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*5ddc57e5SXin Li 30*5ddc57e5SXin Li<p><b>extern const lm_control_struct lm_control_double;</b></p> 31*5ddc57e5SXin Li 32*5ddc57e5SXin Li<p><b>extern const lm_control_struct lm_control_float;</b></p> 33*5ddc57e5SXin Li 34*5ddc57e5SXin Li<p><b>extern const char *lm_infmsg[];</b></p> 35*5ddc57e5SXin Li 36*5ddc57e5SXin Li<p><b>extern const char *lm_shortmsg[];</b></p> 37*5ddc57e5SXin Li 38*5ddc57e5SXin Li<h1 id="DESCRIPTION">DESCRIPTION</h1> 39*5ddc57e5SXin Li 40*5ddc57e5SXin Li<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*5ddc57e5SXin Li 42*5ddc57e5SXin Li<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*5ddc57e5SXin Li 44*5ddc57e5SXin Li<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*5ddc57e5SXin Li 46*5ddc57e5SXin Li<p>Function arguments:</p> 47*5ddc57e5SXin Li 48*5ddc57e5SXin Li<dl> 49*5ddc57e5SXin Li 50*5ddc57e5SXin Li<dt id="n_par"><i>n_par</i></dt> 51*5ddc57e5SXin Li<dd> 52*5ddc57e5SXin Li 53*5ddc57e5SXin Li<p>Number of free variables. Length of parameter vector <i>par</i>.</p> 54*5ddc57e5SXin Li 55*5ddc57e5SXin Li</dd> 56*5ddc57e5SXin Li<dt id="par"><i>par</i></dt> 57*5ddc57e5SXin Li<dd> 58*5ddc57e5SXin Li 59*5ddc57e5SXin Li<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*5ddc57e5SXin Li 61*5ddc57e5SXin Li</dd> 62*5ddc57e5SXin Li<dt id="m_dat"><i>m_dat</i></dt> 63*5ddc57e5SXin Li<dd> 64*5ddc57e5SXin Li 65*5ddc57e5SXin Li<p>Number of data points. Length of vectors <i>t</i> and <i>y</i>. Must statisfy <i>n_par</i> <= <i>m_dat</i>.</p> 66*5ddc57e5SXin Li 67*5ddc57e5SXin Li</dd> 68*5ddc57e5SXin Li<dt id="t"><i>t</i></dt> 69*5ddc57e5SXin Li<dd> 70*5ddc57e5SXin Li 71*5ddc57e5SXin Li<p>Array of length <i>m_dat</i>. Contains the abcissae (time, or "x") for which function <i>f</i> will be evaluated.</p> 72*5ddc57e5SXin Li 73*5ddc57e5SXin Li</dd> 74*5ddc57e5SXin Li<dt id="y"><i>y</i></dt> 75*5ddc57e5SXin Li<dd> 76*5ddc57e5SXin Li 77*5ddc57e5SXin Li<p>Array of length <i>m_dat</i>. Contains the ordinate values that shall be fitted.</p> 78*5ddc57e5SXin Li 79*5ddc57e5SXin Li</dd> 80*5ddc57e5SXin Li<dt id="dy"><i>dy</i></dt> 81*5ddc57e5SXin Li<dd> 82*5ddc57e5SXin Li 83*5ddc57e5SXin Li<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*5ddc57e5SXin Li 85*5ddc57e5SXin Li</dd> 86*5ddc57e5SXin Li<dt id="f"><i>f</i></dt> 87*5ddc57e5SXin Li<dd> 88*5ddc57e5SXin Li 89*5ddc57e5SXin Li<p>A user-supplied parametric function <i>f</i>(ti;<i>par</i>).</p> 90*5ddc57e5SXin Li 91*5ddc57e5SXin Li</dd> 92*5ddc57e5SXin Li<dt id="control"><i>control</i></dt> 93*5ddc57e5SXin Li<dd> 94*5ddc57e5SXin Li 95*5ddc57e5SXin Li<p>Parameter collection for tuning the fit procedure. In most cases, the default &<i>lm_control_double</i> is adequate. If <i>f</i> is only computed with single-precision accuracy, <i>&lm_control_float</i> should be used. Parameters are explained in <b>lmmin(3)</b>.</p> 96*5ddc57e5SXin Li 97*5ddc57e5SXin Li</dd> 98*5ddc57e5SXin Li<dt id="status"><i>status</i></dt> 99*5ddc57e5SXin Li<dd> 100*5ddc57e5SXin Li 101*5ddc57e5SXin Li<p>A record used to return information about the minimization process: For details, see <b>lmmin(3)</b>.</p> 102*5ddc57e5SXin Li 103*5ddc57e5SXin Li</dd> 104*5ddc57e5SXin Li</dl> 105*5ddc57e5SXin Li 106*5ddc57e5SXin Li<h1 id="EXAMPLE">EXAMPLE</h1> 107*5ddc57e5SXin Li 108*5ddc57e5SXin Li<p>Fit a data set y(x) by a curve f(x;p):</p> 109*5ddc57e5SXin Li 110*5ddc57e5SXin Li<pre><code> #include "lmcurve.h" 111*5ddc57e5SXin Li #include <stdio.h> 112*5ddc57e5SXin Li 113*5ddc57e5SXin Li /* model function: a parabola */ 114*5ddc57e5SXin Li 115*5ddc57e5SXin Li double f( double t, const double *p ) 116*5ddc57e5SXin Li { 117*5ddc57e5SXin Li return p[0] + p[1]*t + p[2]*t*t; 118*5ddc57e5SXin Li } 119*5ddc57e5SXin Li 120*5ddc57e5SXin Li int main() 121*5ddc57e5SXin Li { 122*5ddc57e5SXin Li int n = 3; /* number of parameters in model function f */ 123*5ddc57e5SXin Li double par[3] = { 100, 0, -10 }; /* really bad starting value */ 124*5ddc57e5SXin Li 125*5ddc57e5SXin Li /* data points: a slightly distorted standard parabola */ 126*5ddc57e5SXin Li int m = 9; 127*5ddc57e5SXin Li int i; 128*5ddc57e5SXin Li double t[9] = { -4., -3., -2., -1., 0., 1., 2., 3., 4. }; 129*5ddc57e5SXin Li double y[9] = { 16.6, 9.9, 4.4, 1.1, 0., 1.1, 4.2, 9.3, 16.4 }; 130*5ddc57e5SXin Li 131*5ddc57e5SXin Li lm_control_struct control = lm_control_double; 132*5ddc57e5SXin Li lm_status_struct status; 133*5ddc57e5SXin Li control.verbosity = 7; 134*5ddc57e5SXin Li 135*5ddc57e5SXin Li printf( "Fitting ...\n" ); 136*5ddc57e5SXin Li lmcurve( n, par, m, t, y, f, &control, &status ); 137*5ddc57e5SXin Li 138*5ddc57e5SXin Li printf( "Results:\n" ); 139*5ddc57e5SXin Li printf( "status after %d function evaluations:\n %s\n", 140*5ddc57e5SXin Li status.nfev, lm_infmsg[status.outcome] ); 141*5ddc57e5SXin Li 142*5ddc57e5SXin Li printf("obtained parameters:\n"); 143*5ddc57e5SXin Li for ( i = 0; i < n; ++i) 144*5ddc57e5SXin Li printf(" par[%i] = %12g\n", i, par[i]); 145*5ddc57e5SXin Li printf("obtained norm:\n %12g\n", status.fnorm ); 146*5ddc57e5SXin Li 147*5ddc57e5SXin Li printf("fitting data as follows:\n"); 148*5ddc57e5SXin Li for ( i = 0; i < m; ++i) 149*5ddc57e5SXin Li printf( " t[%2d]=%4g y=%6g fit=%10g residue=%12g\n", 150*5ddc57e5SXin Li i, t[i], y[i], f(t[i],par), y[i] - f(t[i],par) ); 151*5ddc57e5SXin Li 152*5ddc57e5SXin Li return 0; 153*5ddc57e5SXin Li }</code></pre> 154*5ddc57e5SXin Li 155*5ddc57e5SXin Li<h1 id="COPYING">COPYING</h1> 156*5ddc57e5SXin Li 157*5ddc57e5SXin Li<p>Copyright (C) 2009-2015 Joachim Wuttke, Forschungszentrum Juelich GmbH</p> 158*5ddc57e5SXin Li 159*5ddc57e5SXin Li<p>Software: FreeBSD License</p> 160*5ddc57e5SXin Li 161*5ddc57e5SXin Li<p>Documentation: Creative Commons Attribution Share Alike</p> 162*5ddc57e5SXin Li 163*5ddc57e5SXin Li<h1 id="SEE-ALSO">SEE ALSO</h1> 164*5ddc57e5SXin Li 165*5ddc57e5SXin Li 166*5ddc57e5SXin Li 167*5ddc57e5SXin Li<a href="http://apps.jcns.fz-juelich.de/man/lmmin.html"><b>lmmin</b>(3)</a> 168*5ddc57e5SXin Li 169*5ddc57e5SXin Li<p>Homepage: http://apps.jcns.fz-juelich.de/lmfit</p> 170*5ddc57e5SXin Li 171*5ddc57e5SXin Li<h1 id="BUGS">BUGS</h1> 172*5ddc57e5SXin Li 173*5ddc57e5SXin Li<p>Please send bug reports and suggestions to the author <[email protected]>.</p> 174*5ddc57e5SXin Li 175*5ddc57e5SXin Li 176*5ddc57e5SXin Li</body> 177*5ddc57e5SXin Li 178*5ddc57e5SXin Li</html> 179*5ddc57e5SXin Li 180*5ddc57e5SXin Li 181