gaussian_fit.c

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#include "extern.h"

struct data
{
  double *t;
  double *y;
  size_t n;
};

/* model function: a * exp( -1/2 * [ (t - b) / c ]^2 ) */
double
gaussian(const double a, const double b, const double c, const double t)
{
  const double z = (t - b) / c;
  return (a * exp(-0.5 * z * z));
}

int
func_f (const gsl_vector * x, void *params, gsl_vector * f)
{
  struct data *d = (struct data *) params;
  double a = gsl_vector_get(x, 0);
  double b = gsl_vector_get(x, 1);
  double c = gsl_vector_get(x, 2);
  size_t i;

  for (i = 0; i < d->n; ++i)
    {
      double ti = d->t[i];
      double yi = d->y[i];
      double y = gaussian(a, b, c, ti);

      gsl_vector_set(f, i, yi - y);
    }

  return GSL_SUCCESS;
}

int
func_df (const gsl_vector * x, void *params, gsl_matrix * J)
{
  struct data *d = (struct data *) params;
  double a = gsl_vector_get(x, 0);
  double b = gsl_vector_get(x, 1);
  double c = gsl_vector_get(x, 2);
  size_t i;

  for (i = 0; i < d->n; ++i)
    {
      double ti = d->t[i];
      double zi = (ti - b) / c;
      double ei = exp(-0.5 * zi * zi);

      gsl_matrix_set(J, i, 0, -ei);
      gsl_matrix_set(J, i, 1, -(a / c) * ei * zi);
      gsl_matrix_set(J, i, 2, -(a / c) * ei * zi * zi);
    }

  return GSL_SUCCESS;
}

int
func_fvv (const gsl_vector * x, const gsl_vector * v,
          void *params, gsl_vector * fvv)
{
  struct data *d = (struct data *) params;
  double a = gsl_vector_get(x, 0);
  double b = gsl_vector_get(x, 1);
  double c = gsl_vector_get(x, 2);
  double va = gsl_vector_get(v, 0);
  double vb = gsl_vector_get(v, 1);
  double vc = gsl_vector_get(v, 2);
  size_t i;

  for (i = 0; i < d->n; ++i)
    {
      double ti = d->t[i];
      double zi = (ti - b) / c;
      double ei = exp(-0.5 * zi * zi);
      double Dab = -zi * ei / c;
      double Dac = -zi * zi * ei / c;
      double Dbb = a * ei / (c * c) * (1.0 - zi*zi);
      double Dbc = a * zi * ei / (c * c) * (2.0 - zi*zi);
      double Dcc = a * zi * zi * ei / (c * c) * (3.0 - zi*zi);
      double sum;

      sum = 2.0 * va * vb * Dab +
            2.0 * va * vc * Dac +
                  vb * vb * Dbb +
            2.0 * vb * vc * Dbc +
                  vc * vc * Dcc;

      gsl_vector_set(fvv, i, sum);
    }

  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 avratio = gsl_multifit_nlinear_avratio(w);
  double rcond;

  (void) params; /* not used */

  /* compute reciprocal condition number of J(x) */
  gsl_multifit_nlinear_rcond(&rcond, w);

  if(isSet(PF_V_FLAG))
  {
    fprintf(stderr, "iter %2zu: a = %.4f, b = %.4f, c = %.4f, |a|/|v| = %.4f cond(J) = %e, |f(x)| = %.4f\n",
          iter,
          gsl_vector_get(x, 0),
          gsl_vector_get(x, 1),
          gsl_vector_get(x, 2),
          avratio,
          1.0 / rcond,
          gsl_blas_dnrm2(f));
  }
}

void
solve_system(gsl_vector *x, gsl_multifit_nlinear_fdf *fdf,
             gsl_multifit_nlinear_parameters *params)
{
  const gsl_multifit_nlinear_type *T = gsl_multifit_nlinear_trust;
  const size_t max_iter = 200;
  const double xtol = 1.0e-8;
  const double gtol = 1.0e-8;
  const double ftol = 1.0e-8;
  const size_t n = fdf->n;
  const size_t p = fdf->p;
  gsl_multifit_nlinear_workspace *work = gsl_multifit_nlinear_alloc(T, params, n, p);
  gsl_vector * f = gsl_multifit_nlinear_residual(work);
  gsl_vector * y = gsl_multifit_nlinear_position(work);
  int info;
  double chisq0, chisq, rcond;

  /* initialize solver */
  gsl_multifit_nlinear_init(x, fdf, work);

  /* store initial cost */
  gsl_blas_ddot(f, f, &chisq0);

  /* iterate until convergence */
  gsl_multifit_nlinear_driver(max_iter, xtol, gtol, ftol,
                              callback, NULL, &info, work);

  /* store final cost */
  gsl_blas_ddot(f, f, &chisq);

  /* store cond(J(x)) */
  gsl_multifit_nlinear_rcond(&rcond, work);

  gsl_vector_memcpy(x, y);

  /* print summary */

  if(isSet(PF_V_FLAG))
  {
    fprintf(stderr, "NITER         = %zu\n", gsl_multifit_nlinear_niter(work));
    fprintf(stderr, "NFEV          = %zu\n", fdf->nevalf);
    fprintf(stderr, "NJEV          = %zu\n", fdf->nevaldf);
    fprintf(stderr, "NAEV          = %zu\n", fdf->nevalfvv);
    fprintf(stderr, "chisq0        = %f\n",  chisq0);
    fprintf(stderr, "chisq         = %f\n",  chisq);
    fprintf(stderr, "final         = (%f, %f, %f)\n", gsl_vector_get(x, 0), gsl_vector_get(x, 1), gsl_vector_get(x, 2));
    fprintf(stderr, "final cond(J) = %f\n", 1.0 / rcond);
  }

  gsl_multifit_nlinear_free(work);
}



/* main entry point */
int gaussian_fit_gsl(xd, yd, n, aa)
double *xd;      /* X-data array */
double *yd;      /* Y-data array */
const size_t n;  /* number of data points to fit */
double *aa;      /* amplitude, center & width guesses; returned results here */
{
  const size_t p = 3;    /* number of model parameters */
  const gsl_rng_type * T = gsl_rng_default;
  gsl_vector *f = gsl_vector_alloc(n);
  gsl_vector *x = gsl_vector_alloc(p);
  gsl_multifit_nlinear_fdf fdf;
  gsl_multifit_nlinear_parameters fdf_params = gsl_multifit_nlinear_default_parameters();
  struct data fit_data;
  gsl_rng * r;
  size_t i;

  gsl_rng_env_setup ();
  r = gsl_rng_alloc (T);

  fit_data.t = malloc(n * sizeof(double));
  fit_data.y = malloc(n * sizeof(double));
  fit_data.n = n;

  /* load passed data into fit_data */
  for(i=0;i<n;i++)
  {
    fit_data.t[i] = xd[i];
    fit_data.y[i] = yd[i];
  }

  /* define function to be minimized */
  fdf.f = func_f;
  fdf.df = func_df;
  fdf.fvv = func_fvv;
  fdf.n = n;
  fdf.p = p;
  fdf.params = &fit_data;

  /* starting point */
  gsl_vector_set(x, 0, aa[0]);
  gsl_vector_set(x, 1, aa[1]);
  gsl_vector_set(x, 2, aa[2]);

  fdf_params.trs = gsl_multifit_nlinear_trs_lmaccel;
  solve_system(x, &fdf, &fdf_params);

  /* Return results */
  aa[0] = gsl_vector_get(x, 0);  /* A */
  aa[1] = gsl_vector_get(x, 1);  /* B */
  aa[2] = gsl_vector_get(x, 2);  /* C */

  gsl_vector_free(f);
  gsl_vector_free(x);
  gsl_rng_free(r);

  return 0;
}