To demonstrate the use of the generic minimization function lmmin(), this example shows how to fit a surface y(t) with a parametric function f(t,p). The t two-dimensional vectors.
/* demo/surface1.c */ #include "lmmin.h" #include <stdio.h> /* fit model: a plane p0 + p1*tx + p2*tz */ double f( double tx, double tz, const double *p ) { return p[0] + p[1]*tx + p[2]*tz; } /* data structure to transmit data arrays and fit model */ typedef struct { double *tx, *tz; double *y; double (*f)( double tx, double tz, const double *p ); } data_struct; /* function evaluation, determination of residues */ void evaluate_surface( const double *par, int m_dat, const void *data, double *fvec, int *info ) { /* for readability, explicit type conversion */ data_struct *D; D = (data_struct*)data; int i; for ( i = 0; i < m_dat; i++ ) fvec[i] = D->y[i] - D->f( D->tx[i], D->tz[i], par ); } int main() { /* parameter vector */ int n_par = 3; /* number of parameters in model function f */ double par[3] = { -1, 0, 1 }; /* arbitrary starting value */ /* data points */ int m_dat = 4; double tx[4] = { -1, -1, 1, 1 }; double tz[4] = { -1, 1, -1, 1 }; double y[4] = { 0, 1, 1, 2 }; data_struct data = { tx, tz, y, f }; /* auxiliary parameters */ lm_status_struct status; lm_control_struct control = lm_control_double; lm_princon_struct princon = lm_princon_std; princon.flags = 3; /* perform the fit */ printf( "Fitting:\n" ); lmmin( n_par, par, m_dat, (const void*) &data, evaluate_surface, lm_printout_std, &control, &princon, &status ); /* print results */ printf( "\nResults:\n" ); printf( "status after %d function evaluations:\n %s\n", status.nfev, lm_infmsg[status.info] ); printf("obtained parameters:\n"); int i; for ( i=0; i<n_par; ++i ) printf(" par[%i] = %12g\n", i, par[i]); printf("obtained norm:\n %12g\n", status.fnorm ); printf("fitting data as follows:\n"); double ff; for ( i=0; i<m_dat; ++i ){ ff = f(tx[i], tz[i], par); printf( " t[%2d]=%12g,%12g y=%12g fit=%12g residue=%12g\n", i, tx[i], tz[i], y[i], ff, y[i] - ff ); } return 0; }