#define gaussian_N 15
#define gaussian_P 3
#define gaussian_NTRIES 2
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);
}
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);
}
return GSL_SUCCESS;
}
static gsl_multifit_function_fdf gaussian_func =
{
&gaussian_f,
&gaussian_df,
NULL,
gaussian_N,
gaussian_P,
NULL,
0,
0
};
static test_fdf_problem gaussian_problem =
{
"gaussian",
gaussian_x0,
NULL,
&gaussian_epsrel,
gaussian_NTRIES,
&gaussian_checksol,
&gaussian_func
};