#define lin1_N 11 /* can be anything >= p */
#define lin1_P 5
static double lin1_x0[lin1_P] = { 1.0, 1.0, 1.0, 1.0, 1.0 };
static double lin1_epsrel = 1.0e-10;
static double lin1_J[lin1_N * lin1_P];
static void
lin1_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact = (double) (lin1_N - lin1_P);
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < lin1_P; ++i)
{
gsl_test_rel(x[i], -1.0, epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
lin1_f (const gsl_vector * x, void *params, gsl_vector * f)
{
size_t i, j;
for (i = 0; i < lin1_N; ++i)
{
double fi = 0.0;
for (j = 0; j < lin1_P; ++j)
{
double xj = gsl_vector_get(x, j);
double Aij = (i == j) ? 1.0 : 0.0;
Aij -= 2.0 / lin1_N;
fi += Aij * xj;
}
fi -= 1.0;
gsl_vector_set(f, i, fi);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
lin1_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
const gsl_vector * u, void * params, gsl_vector * v,
gsl_matrix * JTJ)
{
gsl_matrix_view J = gsl_matrix_view_array(lin1_J, lin1_N, lin1_P);
size_t i, j;
for (i = 0; i < lin1_N; ++i)
{
for (j = 0; j < lin1_P; ++j)
{
double Jij = (i == j) ? 1.0 : 0.0;
Jij -= 2.0 / lin1_N;
gsl_matrix_set(&J.matrix, i, j, Jij);
}
}
if (v)
gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
if (JTJ)
gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
(void)x; /* avoid unused parameter warning */
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
lin1_fvv (const gsl_vector * x, const gsl_vector * v,
void *params, gsl_vector * fvv)
{
(void)x; /* avoid unused parameter warnings */
(void)v;
(void)params;
gsl_vector_set_zero(fvv);
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf lin1_func =
{
lin1_f,
lin1_df,
lin1_fvv,
lin1_N,
lin1_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem lin1_problem =
{
"linear_full",
lin1_x0,
NULL,
&lin1_epsrel,
&lin1_checksol,
&lin1_func
};