Hello,
Yes this is a bug, thanks for reporting it. The problem was I had
defined the time variable to be in [0, N], where N is the number of
points to fit. Then, for some values of N, after the first iteration the
solver finds a negative value for lambda, and so exp(-lambda * N) gets
very large, resulting in nan values in the expb_f function.
I have now replaced the time variable with:
t_i = i * TMAX / (N - 1)
so that t \in [0,TMAX] and you can increase N to anything you want. I
left TMAX = 40. I will update the example program in the repository. In
the meantime I have attached the corrected source code. I tested it up
to N = 1000. Please let me know if you have any further problems.
Thanks,
Patrick
On 01/11/2018 04:50 AM, Anna Russo Russo wrote:
Hi!
I've run the "Exponential Fitting Example", from the GSL 2.4 documentation,
and I noticed that, if the number of data points is greater than 56, the
solver terminates with status "exceeded max number of iterations". It
happens even if I allow it to perform a considerably larger number of
iterations: after the first iteration the parameters are so different from
the right ones that the value of the function to be minimized is 'nan' and
they don't change in the next iterations.
What may be the cause for this behavior?
Thanks for reading,
Anna
#include <stdlib.h>
#include <stdio.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_multifit_nlinear.h>
#define N 100 /* number of data points to fit */
#define TMAX (40.0) /* time variable in [0,TMAX] */
struct data {
size_t n;
double * t;
double * y;
};
int
expb_f (const gsl_vector * x, void *data,
gsl_vector * f)
{
size_t n = ((struct data *)data)->n;
double *t = ((struct data *)data)->t;
double *y = ((struct data *)data)->y;
double A = gsl_vector_get (x, 0);
double lambda = gsl_vector_get (x, 1);
double b = gsl_vector_get (x, 2);
size_t i;
for (i = 0; i < n; i++)
{
/* Model Yi = A * exp(-lambda * t_i) + b */
double Yi = A * exp (-lambda * t[i]) + b;
gsl_vector_set (f, i, Yi - y[i]);
}
return GSL_SUCCESS;
}
int
expb_df (const gsl_vector * x, void *data,
gsl_matrix * J)
{
size_t n = ((struct data *)data)->n;
double *t = ((struct data *)data)->t;
double A = gsl_vector_get (x, 0);
double lambda = gsl_vector_get (x, 1);
size_t i;
for (i = 0; i < n; i++)
{
/* Jacobian matrix J(i,j) = dfi / dxj, */
/* where fi = (Yi - yi)/sigma[i], */
/* Yi = A * exp(-lambda * t_i) + b */
/* and the xj are the parameters (A,lambda,b) */
double e = exp(-lambda * t[i]);
gsl_matrix_set (J, i, 0, e);
gsl_matrix_set (J, i, 1, -t[i] * A * e);
gsl_matrix_set (J, i, 2, 1.0);
}
return GSL_SUCCESS;
}
void
callback(const size_t iter, void *params,
const gsl_multifit_nlinear_workspace *w)
{
gsl_vector *f = gsl_multifit_nlinear_residual(w);
gsl_vector *x = gsl_multifit_nlinear_position(w);
double rcond;
/* compute reciprocal condition number of J(x) */
gsl_multifit_nlinear_rcond(&rcond, w);
fprintf(stderr, "iter %2zu: A = %.4f, lambda = %.4f, b = %.4f, cond(J) = %8.4f, |f(x)| = %.4f\n",
iter,
gsl_vector_get(x, 0),
gsl_vector_get(x, 1),
gsl_vector_get(x, 2),
1.0 / rcond,
gsl_blas_dnrm2(f));
}
int
main (void)
{
const gsl_multifit_nlinear_type *T = gsl_multifit_nlinear_trust;
gsl_multifit_nlinear_workspace *w;
gsl_multifit_nlinear_fdf fdf;
gsl_multifit_nlinear_parameters fdf_params =
gsl_multifit_nlinear_default_parameters();
const size_t n = N;
const size_t p = 3;
gsl_vector *f;
gsl_matrix *J;
gsl_matrix *covar = gsl_matrix_alloc (p, p);
double t[N], y[N], weights[N];
struct data d = { n, t, y };
double x_init[3] = { 1.0, 1.0, 0.0 }; /* starting values */
gsl_vector_view x = gsl_vector_view_array (x_init, p);
gsl_vector_view wts = gsl_vector_view_array(weights, n);
gsl_rng * r;
double chisq, chisq0;
int status, info;
size_t i;
const double xtol = 1e-8;
const double gtol = 1e-8;
const double ftol = 0.0;
gsl_rng_env_setup();
r = gsl_rng_alloc(gsl_rng_default);
/* define the function to be minimized */
fdf.f = expb_f;
fdf.df = expb_df; /* set to NULL for finite-difference Jacobian */
fdf.fvv = NULL; /* not using geodesic acceleration */
fdf.n = n;
fdf.p = p;
fdf.params = &d;
/* this is the data to be fitted */
for (i = 0; i < n; i++)
{
double ti = i * TMAX / (n - 1.0);
double yi = 1.0 + 5 * exp (-0.1 * ti);
double si = 0.1 * yi;
double dy = gsl_ran_gaussian(r, si);
t[i] = ti;
y[i] = yi + dy;
weights[i] = 1.0 / (si * si);
printf ("data: %g %g %g\n", ti, y[i], si);
};
/* allocate workspace with default parameters */
w = gsl_multifit_nlinear_alloc (T, &fdf_params, n, p);
/* initialize solver with starting point and weights */
gsl_multifit_nlinear_winit (&x.vector, &wts.vector, &fdf, w);
/* compute initial cost function */
f = gsl_multifit_nlinear_residual(w);
gsl_blas_ddot(f, f, &chisq0);
/* solve the system with a maximum of 100 iterations */
status = gsl_multifit_nlinear_driver(100, xtol, gtol, ftol,
callback, NULL, &info, w);
/* compute covariance of best fit parameters */
J = gsl_multifit_nlinear_jac(w);
gsl_multifit_nlinear_covar (J, 0.0, covar);
/* compute final cost */
gsl_blas_ddot(f, f, &chisq);
#define FIT(i) gsl_vector_get(w->x, i)
#define ERR(i) sqrt(gsl_matrix_get(covar,i,i))
fprintf(stderr, "summary from method '%s/%s'\n",
gsl_multifit_nlinear_name(w),
gsl_multifit_nlinear_trs_name(w));
fprintf(stderr, "number of iterations: %zu\n",
gsl_multifit_nlinear_niter(w));
fprintf(stderr, "function evaluations: %zu\n", fdf.nevalf);
fprintf(stderr, "Jacobian evaluations: %zu\n", fdf.nevaldf);
fprintf(stderr, "reason for stopping: %s\n",
(info == 1) ? "small step size" : "small gradient");
fprintf(stderr, "initial |f(x)| = %f\n", sqrt(chisq0));
fprintf(stderr, "final |f(x)| = %f\n", sqrt(chisq));
{
double dof = n - p;
double c = GSL_MAX_DBL(1, sqrt(chisq / dof));
fprintf(stderr, "chisq/dof = %g\n", chisq / dof);
fprintf (stderr, "A = %.5f +/- %.5f\n", FIT(0), c*ERR(0));
fprintf (stderr, "lambda = %.5f +/- %.5f\n", FIT(1), c*ERR(1));
fprintf (stderr, "b = %.5f +/- %.5f\n", FIT(2), c*ERR(2));
}
fprintf (stderr, "status = %s\n", gsl_strerror (status));
gsl_multifit_nlinear_free (w);
gsl_matrix_free (covar);
gsl_rng_free (r);
return 0;
}
