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#define lin2_N 20 /* can be anything >= p */
#define lin2_P 5
#define lin2_NTRIES 3
static double lin2_x0[lin2_P] = { 1.0, 1.0, 1.0, 1.0, 1.0 };
static double lin2_epsrel = 1.0e-11;
static void
lin2_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double n = (double) lin2_N;
const double sumsq_exact = 0.5 * (n*(n - 1.0)) / (2.0*n + 1.0);
const double sum_exact = 3.0 / (2.0*n + 1.0);
double sum = 0.0;
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < lin2_P; ++i)
sum += (i + 1.0) * x[i];
gsl_test_rel(sum, sum_exact, epsrel, "%s/%s coeff sum",
sname, pname);
}
static int
lin2_f (const gsl_vector * x, void *params, gsl_vector * f)
{
size_t i, j;
for (i = 0; i < lin2_N; ++i)
{
double fi = 0.0;
for (j = 0; j < lin2_P; ++j)
{
double xj = gsl_vector_get(x, j);
fi += (j + 1) * xj;
}
fi = (i + 1) * fi - 1.0;
gsl_vector_set(f, i, fi);
}
return GSL_SUCCESS;
}
static int
lin2_df (const gsl_vector * x, void *params, gsl_matrix * J)
{
size_t i, j;
for (i = 0; i < lin2_N; ++i)
{
for (j = 0; j < lin2_P; ++j)
{
gsl_matrix_set(J, i, j, (i + 1.0) * (j + 1.0));
}
}
return GSL_SUCCESS;
}
static gsl_multifit_function_fdf lin2_func =
{
&lin2_f,
&lin2_df,
NULL,
lin2_N,
lin2_P,
NULL,
0,
0
};
static test_fdf_problem lin2_problem =
{
"linear_rank1",
lin2_x0,
NULL,
&lin2_epsrel,
lin2_NTRIES,
&lin2_checksol,
&lin2_func
};
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