#define gaussian_N         15

#define gaussian_P         3

static double gaussian_x0[gaussian_P] = { 0.4, 1.0, 0.0 };

static double gaussian_epsrel = 1.0e-10;

static double gaussian_Y[gaussian_N] = {

0.0009, 0.0044, 0.0175, 0.0540, 0.1295, 0.2420, 0.3521, 0.3989,

0.3521, 0.2420, 0.1295, 0.0540, 0.0175, 0.0044, 0.0009

};

static void

gaussian_checksol(const double x[], const double sumsq,

                  const double epsrel, const char *sname,

                  const char *pname)

{

  size_t i;

  const double sumsq_exact = 1.12793276961871985e-08;

  const double gaussian_x[gaussian_P] = { 0.398956137838762825,

                                          1.00001908448786647,

                                          0.0 };

  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",

               sname, pname);

  for (i = 0; i < gaussian_P; ++i)

    {

      gsl_test_rel(x[i], gaussian_x[i], epsrel, "%s/%s i=%zu",

                   sname, pname, i);

    }

}

static int

gaussian_f (const gsl_vector * x, void *params, gsl_vector * f)

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  size_t i;

  for (i = 0; i < gaussian_N; ++i)

    {

      double ti = (7.0 - i) / 2.0;

      double yi = gaussian_Y[i];

      double term = ti - x3;

      double fi = x1 * exp(-x2*term*term/2.0) - yi;

      gsl_vector_set(f, i, fi);

    }

  (void)params; /* avoid unused parameter warning */

  return GSL_SUCCESS;

}

static int

gaussian_df (const gsl_vector * x, void *params, gsl_matrix * J)

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  size_t i;

  for (i = 0; i < gaussian_N; ++i)

    {

      double ti = (7.0 - i) / 2.0;

      double term1 = ti - x3;

      double term2 = exp(-x2*term1*term1/2.0);

      gsl_matrix_set(J, i, 0, term2);

      gsl_matrix_set(J, i, 1, -0.5*x1*term2*term1*term1);

      gsl_matrix_set(J, i, 2, x1*x2*term1*term2);

    }

  (void)params; /* avoid unused parameter warning */

  return GSL_SUCCESS;

}

static int

gaussian_fvv (const gsl_vector * x, const gsl_vector * v,

              void *params, gsl_vector * fvv)

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  double v1 = gsl_vector_get(v, 0);

  double v2 = gsl_vector_get(v, 1);

  double v3 = gsl_vector_get(v, 2);

  size_t i;

  for (i = 0; i < gaussian_N; ++i)

    {

      double ti = (7.0 - i) / 2.0;

      double term1 = ti - x3;

      double term2 = exp(-x2*term1*term1/2.0);

      gsl_vector_set(fvv, i, 0.25 * term2 *

                             (ti*ti*ti*ti*v2*v2*x1 -

                              4*ti*ti*ti*v2*x1*(v3*x2 + v2*x3) +

                              v2*x3*x3*(v2*x1*x3*x3 - 4*v1) +

                              4*v3*v3*x1*x2*(x2*x3*x3 - 1.0) +

                              4*v3*x3*(-2*v1*x2 + v2*x1*(x2*x3*x3 - 2.0)) +

                              ti*ti*(4*v3*v3*x1*x2*x2 + 2*v2*(-2*v1 + 3*x1*x3*(2*v3*x2 + v2*x3))) -

                              4*ti*(v2*v2*x1*x3*x3*x3 + 2*v3*x2*(-v1 + v3*x1*x2*x3) +

                                    v2*(-2*v1*x3 + v3*x1*(-2.0 + 3*x2*x3*x3)))));

    }

  (void)params; /* avoid unused parameter warning */

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf gaussian_func =

{

  gaussian_f,

  gaussian_df,

  gaussian_fvv,

  gaussian_N,

  gaussian_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem gaussian_problem =

{

  "gaussian",

  gaussian_x0,

  NULL,

  NULL,

  &gaussian_epsrel,

  &gaussian_checksol,

  &gaussian_func

};