#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
};