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<link rel="stylesheet" href="podstyle.css" type="text/css" />
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=head1 NAME
lmcurve - Levenberg-Marquardt least-squares fit of a curve (t,y)
B<#include <lmcurve.h>>
B<void lmcurve( const int> I<n_par>B<, double *>I<par>B<, const int> I<m_dat>B<,
constS< >double *>I<t>B<, constS< >double *>I<y>B<,
double (*>I<f>B<)( const double >I<ti>B<, const double *>I<par>B< ),
constS< >lm_control_struct *>I<control>B<,
lm_status_struct *>I<status>B<);>
B<void lmcurve_tyd(
const int> I<n_par>B<, double *>I<par>B<, const int> I<m_dat>B<,
constS< >double *>I<t>B<, constS< >double *>I<y>B<, constS< >double *>I<dy>B<,
double (*>I<f>B<)( const double >I<ti>B<, const double *>I<par>B< ),
constS< >lm_control_struct *>I<control>B<,
lm_status_struct *>I<status>B<);>
B<extern const lm_control_struct lm_control_double;>
B<extern const lm_control_struct lm_control_float;>
B<extern const char *lm_infmsg[];>
B<extern const char *lm_shortmsg[];>
B<lmcurve()> and B<lmcurve_tyd()> wrap the more generic minimization function B<lmmin()>, for use in curve fitting.
B<lmcurve()> determines a vector I<par> that minimizes the sum of squared elements of a residue vector I<r>[i] := I<y>[i] - I<f>(I<t>[i];I<par>). Typically, B<lmcurve()> is used to approximate a data set I<t>,I<y> by a parametric function I<f>(I<ti>;I<par>). On success, I<par> represents a local minimum, not necessarily a global one; it may depend on its starting value.
B<lmcurve_tyd()> does the same for a data set I<t>,I<y>,I<dy>, where I<dy> represents the standard deviation of empirical data I<y>. Residues are computed as I<r>[i] := (I<y>[i] - I<f>(I<t>[i];I<par>))/I<dy>[i]. Users must ensure that all I<dy>[i] are positive.
Function arguments:
=item I<n_par>
Number of free variables.
Length of parameter vector I<par>.
=item I<par>
Parameter vector.
On input, it must contain a reasonable guess.
On output, it contains the solution found to minimize ||I<r>||.
=item I<m_dat>
Number of data points.
Length of vectors I<t> and I<y>.
Must statisfy I<n_par> <= I<m_dat>.
=item I<t>
Array of length I<m_dat>.
Contains the abcissae (time, or "x") for which function I<f> will be evaluated.
=item I<y>
Array of length I<m_dat>.
Contains the ordinate values that shall be fitted.
=item I<dy>
Only in B<lmcurve_tyd()>.
Array of length I<m_dat>.
Contains the standard deviations of the values I<y>.
=item I<f>
A user-supplied parametric function I<f>(ti;I<par>).
=item I<control>
Parameter collection for tuning the fit procedure.
In most cases, the default &I<lm_control_double> is adequate.
If I<f> is only computed with single-precision accuracy,
I<&lm_control_float> should be used.
Parameters are explained in B<lmmin(3)>.
=item I<status>
A record used to return information about the minimization process:
For details, see B<lmmin(3)>.
=head1 EXAMPLE
Fit a data set y(x) by a curve f(x;p):
#include "lmcurve.h"
#include <stdio.h>
/* model function: a parabola */
double f( double t, const double *p )
return p[0] + p[1]*t + p[2]*t*t;
int main()
int n = 3; /* number of parameters in model function f */
double par[3] = { 100, 0, -10 }; /* really bad starting value */
/* data points: a slightly distorted standard parabola */
int m = 9;
int i;
double t[9] = { -4., -3., -2., -1., 0., 1., 2., 3., 4. };
double y[9] = { 16.6, 9.9, 4.4, 1.1, 0., 1.1, 4.2, 9.3, 16.4 };
lm_control_struct control = lm_control_double;
lm_status_struct status;
control.verbosity = 7;
printf( "Fitting ...\n" );
lmcurve( n, par, m, t, y, f, &control, &status );
printf( "Results:\n" );
printf( "status after %d function evaluations:\n %s\n",
status.nfev, lm_infmsg[status.outcome] );
printf("obtained parameters:\n");
for ( i = 0; i < n; ++i)
printf(" par[%i] = %12g\n", i, par[i]);
printf("obtained norm:\n %12g\n", status.fnorm );
printf("fitting data as follows:\n");
for ( i = 0; i < m; ++i)
printf( " t[%2d]=%4g y=%6g fit=%10g residue=%12g\n",
i, t[i], y[i], f(t[i],par), y[i] - f(t[i],par) );
return 0;
=head1 COPYING
Copyright (C) 2009-2015 Joachim Wuttke, Forschungszentrum Juelich GmbH
Software: FreeBSD License
Documentation: Creative Commons Attribution Share Alike
=head1 SEE ALSO
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<a href=""><b>lmmin</b>(3)</a>
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=begin man
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=head1 BUGS
Please send bug reports and suggestions to the author <>.