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Bug in example in documentation at page "Nonlinear Least-Squares Fitting"
- To: gsl-discuss at sources dot redhat dot com
- Subject: Bug in example in documentation at page "Nonlinear Least-Squares Fitting"
- From: Erik-Jan Vlieger <E dot J dot Vlieger at amc dot uva dot nl>
- Date: Wed, 5 Sep 2001 16:13:44 +0200
Hi,
I tried to compile the example from "Nonlinear Least-Squares Fitting", but it
gave compilation errors. I created a different version that does compile, but
I'm not sure I did it right. The calculated results are correct though.
The source in included below.
Thanks,
Erik-Jan Vlieger
-------------------------------
#include <stdlib.h>
#include <stdio.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_multifit_nlin.h>
struct data
{
size_t n;
double *y;
double *sigma;
};
int
print_state (size_t iter, gsl_multifit_fdfsolver * s)
{
printf ("iter: %3u x = % 15.8f % 15.8f % 15.8f |f(x)| = %g\n",
iter,
gsl_vector_get (s->x, 0), gsl_vector_get (s->x, 1),
gsl_vector_get (s->x, 2), gsl_blas_dnrm2 (s->f));
}
int
expb_f (const gsl_vector * x, void *params, gsl_vector * f)
{
size_t n = ((struct data *) params)->n;
double *y = ((struct data *) params)->y;
double *sigma = ((struct data *) params)->sigma;
double b = gsl_vector_get (x, 0);
double A = gsl_vector_get (x, 1);
double lambda = gsl_vector_get (x, 2);
size_t i;
for (i = 0; i < n; i++)
{
double t = i;
double Yi = b + A * exp (lambda * t);
gsl_vector_set (f, i, (y[i] - Yi) / sigma[i]);
}
return GSL_SUCCESS;
}
int
expb_df (const gsl_vector * x, void *params, gsl_matrix * df)
{
size_t n = ((struct data *) params)->n;
double *sigma = ((struct data *) params)->sigma;
double A = gsl_vector_get (x, 1);
double lambda = gsl_vector_get (x, 2);
size_t i;
for (i = 0; i < n; i++)
{
/* Yi = b + A * exp(lambda * i) */
double t = i;
double s = sigma[i];
gsl_matrix_set (df, i, 0, -1 / s);
gsl_matrix_set (df, i, 1, -exp (lambda * t) / s);
gsl_matrix_set (df, i, 2, -t * A * exp (lambda * t) / s);
}
return GSL_SUCCESS;
}
int
expb_fdf (const gsl_vector * x, void *params, gsl_vector * f, gsl_matrix * df)
{
expb_f (x, params, f);
expb_df (x, params, df);
return GSL_SUCCESS;
}
int
main (void)
{
const gsl_multifit_fdfsolver_type *Ts;
gsl_multifit_fdfsolver *s;
int status;
size_t i, iter = 0;
const size_t n = 40;
const size_t p = 3;
gsl_matrix *covar = gsl_matrix_alloc (p, p);
double y[n], sigma[n];
struct data d = { n, y, sigma };
gsl_multifit_function_fdf f =
{ &expb_f, &expb_df, &expb_fdf, n, p, (void *) &d };
double x_init[3] = { 0.0, 1.0, -0.0 };
gsl_vector_view x = gsl_vector_view_array (x_init, p);
const gsl_rng_type *Tr;
gsl_rng *r;
gsl_rng_env_setup ();
Tr = gsl_rng_default;
r = gsl_rng_alloc (Tr); /* This is the data to be fitted */
for (i = 0; i < n; i++)
{
double t = i;
y[i] = 1.0 + 5 * exp (-0.1 * t) + gsl_ran_gaussian (r, 0.1);
sigma[i] = 0.1;
printf ("data: %d %g %g\n", i, y[i], sigma[i]);
};
Ts = gsl_multifit_fdfsolver_lmsder;
s = gsl_multifit_fdfsolver_alloc (Ts, n, p);
gsl_multifit_fdfsolver_set (s, &f, &x.vector);
print_state (iter, s);
do
{
iter++;
status = gsl_multifit_fdfsolver_iterate (s);
printf ("status = %s\n", gsl_strerror (status));
print_state (iter, s);
if (status)
break;
status = gsl_multifit_test_delta (s->dx, s->x, 0.0001, 0.0001);
}
while (status == GSL_CONTINUE && iter < 500);
gsl_multifit_covar (s->J, 0.0, covar);
gsl_matrix_fprintf (stdout, covar, "%g");
#define FIT(i) gsl_vector_get(s->x, i)
#define ERR(i) sqrt(gsl_matrix_get(covar,i,i))
printf("b = %g +/- %g\n", FIT(0), ERR(0));
printf ("A = %g +/- %g\n", FIT (1), ERR (1));
printf ("lambda = %g +/- %g\n", FIT (2), ERR (2));
printf ("status = %s\n", gsl_strerror (status));
gsl_multifit_fdfsolver_free (s);
}