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#define vardim_N 7 /* p + 2 */
#define vardim_P 5
static double vardim_x0[vardim_P] = { 0.8, 0.6, 0.4, 0.2, 0.0 };
static double vardim_epsrel = 1.0e-12;
static double vardim_J[vardim_N * vardim_P];
static void
vardim_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact = 0.0;
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < vardim_P; ++i)
{
gsl_test_rel(x[i], 1.0, epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
vardim_f (const gsl_vector * x, void *params, gsl_vector * f)
{
size_t i;
double sum = 0.0;
for (i = 0; i < vardim_P; ++i)
{
double xi = gsl_vector_get(x, i);
gsl_vector_set(f, i, xi - 1.0);
sum += (i + 1.0) * (xi - 1.0);
}
gsl_vector_set(f, vardim_P, sum);
gsl_vector_set(f, vardim_P + 1, sum*sum);
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
vardim_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(vardim_J, vardim_N, vardim_P);
size_t i;
double sum = 0.0;
gsl_matrix_view m = gsl_matrix_submatrix(&J.matrix, 0, 0, vardim_P, vardim_P);
gsl_matrix_set_identity(&m.matrix);
for (i = 0; i < vardim_P; ++i)
{
double xi = gsl_vector_get(x, i);
sum += (i + 1.0) * (xi - 1.0);
}
for (i = 0; i < vardim_P; ++i)
{
gsl_matrix_set(&J.matrix, vardim_P, i, i + 1.0);
gsl_matrix_set(&J.matrix, vardim_P + 1, i, 2*(i + 1.0)*sum);
}
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)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
vardim_fvv (const gsl_vector * x, const gsl_vector * v,
void *params, gsl_vector * fvv)
{
size_t i;
double sum = 0.0;
gsl_vector_set_zero(fvv);
for (i = 0; i < vardim_P; ++i)
{
double vi = gsl_vector_get(v, i);
sum += (i + 1.0) * vi;
}
gsl_vector_set(fvv, vardim_N - 1, 2.0 * sum * sum);
(void)x; /* avoid unused parameter warning */
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf vardim_func =
{
vardim_f,
vardim_df,
vardim_fvv,
vardim_N,
vardim_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem vardim_problem =
{
"vardim",
vardim_x0,
NULL,
&vardim_epsrel,
&vardim_checksol,
&vardim_func
};
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