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Title "lmcurve 3" For nroff, turn off justification. Always turn off hyphenation; it makes
way too many mistakes in technical documents.
lmcurve - Levenberg-Marquardt least-squares fit of a curve (t,y) Header "SYNOPSIS" \fB#include <lmcurve.h>

\fBvoid lmcurve( const int n_par, double *par, const int m_dat, const double *t, const double *y, double (*f)( const double ti, const double *par ), const lm_control_struct *control, lm_status_struct *status);

\fBvoid lmcurve_tyd( const int n_par, double *par, const int m_dat, const double *t, const double *y, const double *dy, double (*f)( const double ti, const double *par ), const lm_control_struct *control, lm_status_struct *status);

\fBextern const lm_control_struct lm_control_double;

\fBextern const lm_control_struct lm_control_float;

\fBextern const char *lm_infmsg[];

\fBextern const char *lm_shortmsg[];

Header "DESCRIPTION" \fB\f(BIlmcurve() and \f(BIlmcurve_tyd() wrap the more generic minimization function \f(BIlmmin(), for use in curve fitting.

\fB\f(BIlmcurve() determines a vector par that minimizes the sum of squared elements of a residue vector r[i] := y[i] - f(t[i];par). Typically, \f(BIlmcurve() is used to approximate a data set t,y by a parametric function f(ti;par). On success, par represents a local minimum, not necessarily a global one; it may depend on its starting value.

\fB\f(BIlmcurve_tyd() does the same for a data set t,y,dy, where dy represents the standard deviation of empirical data y. Residues are computed as r[i] := (y[i] - f(t[i];par))/dy[i]. Users must ensure that all dy[i] are positive.

Function arguments:

Item "n_par" Number of free variables. Length of parameter vector par. Item "par" Parameter vector. On input, it must contain a reasonable guess. On output, it contains the solution found to minimize ||r||. Item "m_dat" Number of data points. Length of vectors t and y. Must statisfy n_par <= m_dat. Item "t" Array of length m_dat. Contains the abcissae (time, or \*(L"x\*(R") for which function f will be evaluated. Item "y" Array of length m_dat. Contains the ordinate values that shall be fitted. Item "dy" Only in \f(BIlmcurve_tyd(). Array of length m_dat. Contains the standard deviations of the values y. Item "f" A user-supplied parametric function f(ti;par). Item "control" Parameter collection for tuning the fit procedure. In most cases, the default &lm_control_double is adequate. If f is only computed with single-precision accuracy, \fI&lm_control_float should be used. Parameters are explained in \f(BIlmmin\|(3). Item "status" A record used to return information about the minimization process: For details, see \f(BIlmmin\|(3). Header "EXAMPLE" Fit a data set y(x) by a curve f(x;p):

.Vb 2 #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 ...\en" ); lmcurve( n, par, m, t, y, f, &control, &status ); \& printf( "Results:\en" ); printf( "status after %d function evaluations:\en %s\en", status.nfev, lm_infmsg[status.outcome] ); \& printf("obtained parameters:\en"); for ( i = 0; i < n; ++i) printf(" par[%i] = %12g\en", i, par[i]); printf("obtained norm:\en %12g\en", status.fnorm ); \& printf("fitting data as follows:\en"); for ( i = 0; i < m; ++i) printf( " t[%2d]=%4g y=%6g fit=%10g residue=%12g\en", i, t[i], y[i], f(t[i],par), y[i] - f(t[i],par) ); \& return 0; } .Ve

Header "COPYING" Copyright (C) 2009-2015 Joachim Wuttke, Forschungszentrum Juelich GmbH

Software: FreeBSD License

Documentation: Creative Commons Attribution Share Alike

Header "SEE ALSO" lmmin(3)

Homepage: http://apps.jcns.fz-juelich.de/lmfit

Header "BUGS" Please send bug reports and suggestions to the author <j.wuttke@fz-juelich.de>.