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wrkdirs::usr:...::man::lmcurve(3) lmfit manual wrkdirs::usr:...::man::lmcurve(3) NAME lmcurve - Levenberg-Marquardt least-squares fit of a curve (t,y) SYNOPSIS #include <lmcurve.h> void 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); void 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); extern const lm_control_struct lm_control_double; extern const lm_control_struct lm_control_float; extern const char *lm_infmsg[]; extern const char *lm_shortmsg[]; DESCRIPTION lmcurve() and lmcurve_tyd() wrap the more generic minimization function lm- min(), for use in curve fitting. lmcurve() determines a vector par that minimizes the sum of squared ele- ments of a residue vector r[i] := y[i] - f(t[i];par). Typically, lmcurve() 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. lmcurve_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: n_par Number of free variables. Length of parameter vector par. par Parameter vector. On input, it must contain a reasonable guess. On output, it contains the solution found to minimize ||r||. m_dat Number of data points. Length of vectors t and y. Must statisfy n_par <= m_dat. t Array of length m_dat. Contains the abcissae (time, or "x") for which function f will be evaluated. y Array of length m_dat. Contains the ordinate values that shall be fit- ted. dy Only in lmcurve_tyd(). Array of length m_dat. Contains the standard deviations of the values y. f A user-supplied parametric function f(ti;par). 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, &lm_control_float should be used. Parame- ters are explained in lmmin(3). status A record used to return information about the minimization process: For details, see lmmin(3). 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; } COPYING Copyright (C) 2009-2015 Joachim Wuttke, Forschungszentrum Juelich GmbH Software: FreeBSD License Documentation: Creative Commons Attribution Share Alike SEE ALSO lmmin(3) Homepage: https://jugit.fz-juelich.de/mlz/lmfit BUGS Please send bug reports and suggestions to the author <j.wut- tke@fz-juelich.de>. perl v5.42.2 2025-09-17 wrkdirs::usr:...::man::lmcurve(3)
NAME | SYNOPSIS | DESCRIPTION | EXAMPLE | COPYING | SEE ALSO | BUGS
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