static void test_fdf_checksol(const char *sname, const char *pname, const double epsrel, gsl_multifit_fdfsolver *s, test_fdf_problem *problem) { gsl_multifit_function_fdf *fdf = problem->fdf; const double *sigma = problem->sigma; gsl_vector *f = gsl_multifit_fdfsolver_residual(s); gsl_vector *x = gsl_multifit_fdfsolver_position(s); double sumsq; /* check solution vector x and sumsq = ||f||^2 */ gsl_blas_ddot(f, f, &sumsq); (problem->checksol)(x->data, sumsq, epsrel, sname, pname); #if 1 /* check variances */ if (sigma) { const size_t n = fdf->n; const size_t p = fdf->p; size_t i; gsl_matrix * J = gsl_matrix_alloc(n, p); gsl_matrix * covar = gsl_matrix_alloc (p, p); gsl_multifit_fdfsolver_jac (s, J); gsl_multifit_covar(J, 0.0, covar); for (i = 0; i < p; i++) { double ei = sqrt(sumsq/(n-p))*sqrt(gsl_matrix_get(covar,i,i)); gsl_test_rel (ei, sigma[i], epsrel, "%s/%s, sigma(%d)", sname, pname, i) ; } gsl_matrix_free (J); gsl_matrix_free (covar); } #endif }
int main (void) { const gsl_multifit_fdfsolver_type *T = gsl_multifit_fdfsolver_lmsder; gsl_multifit_fdfsolver *s; int status, info; size_t i; const size_t n = N; const size_t p = 3; gsl_matrix *J = gsl_matrix_alloc(n, p); gsl_matrix *covar = gsl_matrix_alloc (p, p); double y[N], weights[N]; struct data d = { n, y }; gsl_multifit_function_fdf f; double x_init[3] = { 1.0, 0.0, 0.0 }; gsl_vector_view x = gsl_vector_view_array (x_init, p); gsl_vector_view w = gsl_vector_view_array(weights, n); const gsl_rng_type * type; gsl_rng * r; gsl_vector *res_f; double chi, chi0; const double xtol = 1e-8; const double gtol = 1e-8; const double ftol = 0.0; gsl_rng_env_setup(); type = gsl_rng_default; r = gsl_rng_alloc (type); f.f = &expb_f; f.df = &expb_df; /* set to NULL for finite-difference Jacobian */ f.n = n; f.p = p; f.params = &d; /* This is the data to be fitted */ for (i = 0; i < n; i++) { double t = i; double yi = 1.0 + 5 * exp (-0.1 * t); double si = 0.1 * yi; double dy = gsl_ran_gaussian(r, si); weights[i] = 1.0 / (si * si); y[i] = yi + dy; printf ("data: %zu %g %g\n", i, y[i], si); }; s = gsl_multifit_fdfsolver_alloc (T, n, p); /* initialize solver with starting point and weights */ gsl_multifit_fdfsolver_wset (s, &f, &x.vector, &w.vector); /* compute initial residual norm */ res_f = gsl_multifit_fdfsolver_residual(s); chi0 = gsl_blas_dnrm2(res_f); /* solve the system with a maximum of 20 iterations */ status = gsl_multifit_fdfsolver_driver(s, 20, xtol, gtol, ftol, &info); gsl_multifit_fdfsolver_jac(s, J); gsl_multifit_covar (J, 0.0, covar); /* compute final residual norm */ chi = gsl_blas_dnrm2(res_f); #define FIT(i) gsl_vector_get(s->x, i) #define ERR(i) sqrt(gsl_matrix_get(covar,i,i)) fprintf(stderr, "summary from method '%s'\n", gsl_multifit_fdfsolver_name(s)); fprintf(stderr, "number of iterations: %zu\n", gsl_multifit_fdfsolver_niter(s)); fprintf(stderr, "function evaluations: %zu\n", f.nevalf); fprintf(stderr, "Jacobian evaluations: %zu\n", f.nevaldf); fprintf(stderr, "reason for stopping: %s\n", (info == 1) ? "small step size" : "small gradient"); fprintf(stderr, "initial |f(x)| = %g\n", chi0); fprintf(stderr, "final |f(x)| = %g\n", chi); { double dof = n - p; double c = GSL_MAX_DBL(1, chi / sqrt(dof)); fprintf(stderr, "chisq/dof = %g\n", pow(chi, 2.0) / 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_fdfsolver_free (s); gsl_matrix_free (covar); gsl_matrix_free (J); gsl_rng_free (r); return 0; }
gsl_vector * gsl_multifit_fdfridge_residual (const gsl_multifit_fdfridge * w) { return gsl_multifit_fdfsolver_residual(w->s); }