From mboxrd@z Thu Jan  1 00:00:00 1970
From: Erik-Jan Vlieger <E.J.Vlieger@amc.uva.nl>
To: gsl-discuss@sources.redhat.com
Subject: Bug in example in documentation at page "Nonlinear Least-Squares Fitting"
Date: Wed, 19 Dec 2001 13:20:00 -0000
Message-id: <200109051404.QAA16057@cube.amc.uva.nl>
X-SW-Source: 2001/msg00459.html

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);
}