#define biggs_N 6 /* >= p */
#define biggs_P 6
#define biggs_NTRIES 2
static double biggs_x0[biggs_P] = { 1.0, 2.0, 1.0, 1.0, 1.0, 1.0 };
static double biggs_epsrel = 1.0e-9;
static void
biggs_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
const double sumsq_exact = 0.0;
const double biggs_x[biggs_P] = { 1.0, 10.0, 1.0, 5.0, 4.0, 3.0 };
const double norm_exact = 12.3288280059380;
gsl_vector_const_view v = gsl_vector_const_view_array(biggs_x, biggs_P);
double norm = gsl_blas_dnrm2(&v.vector);
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
/*
* the solution vector is not unique due to permutations, so test
* the norm instead of individual elements
*/
gsl_test_rel(norm, norm_exact, epsrel, "%s/%s norm",
sname, pname);
}
static int
biggs_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);
double x4 = gsl_vector_get(x, 3);
double x5 = gsl_vector_get(x, 4);
double x6 = gsl_vector_get(x, 5);
size_t i;
for (i = 0; i < biggs_N; ++i)
{
double ti = 0.1 * (i + 1.0);
double yi = exp(-ti) - 5*exp(-10*ti) + 3*exp(-4*ti);
double fi = x3*exp(-ti*x1) - x4*exp(-ti*x2) + x6*exp(-ti*x5) - yi;
gsl_vector_set(f, i, fi);
}
return GSL_SUCCESS;
}
static int
biggs_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);
double x4 = gsl_vector_get(x, 3);
double x5 = gsl_vector_get(x, 4);
double x6 = gsl_vector_get(x, 5);
size_t i;
for (i = 0; i < biggs_N; ++i)
{
double ti = 0.1 * (i + 1.0);
gsl_matrix_set(J, i, 0, -ti*x3*exp(-ti*x1));
gsl_matrix_set(J, i, 1, ti*x4*exp(-ti*x2));
gsl_matrix_set(J, i, 2, exp(-ti*x1));
gsl_matrix_set(J, i, 3, -exp(-ti*x2));
gsl_matrix_set(J, i, 4, -ti*x6*exp(-ti*x5));
gsl_matrix_set(J, i, 5, exp(-ti*x5));
}
return GSL_SUCCESS;
}
static gsl_multifit_function_fdf biggs_func =
{
&biggs_f,
&biggs_df,
NULL,
biggs_N,
biggs_P,
NULL,
0,
0
};
static test_fdf_problem biggs_problem =
{
"biggs",
biggs_x0,
NULL,
&biggs_epsrel,
biggs_NTRIES,
&biggs_checksol,
&biggs_func
};