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#define lin3_N 50 /* can be anything >= p */
#define lin3_P 10 /* >= 3 */
static double lin3_x0[lin3_P] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
static double lin3_epsrel = 1.0e-8;
static double lin3_J[lin3_N * lin3_P];
static void
lin3_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double n = (double) lin3_N;
const double sumsq_exact = 0.5 * (n*n + 3*n - 6.0) / (2*n - 3.0);
const double sum_exact = 3.0 / (2.0*n - 3.0);
double sum = 0.0;
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 1; i < lin3_P - 1; ++i)
sum += (i + 1.0) * x[i];
gsl_test_rel(sum, sum_exact, epsrel, "%s/%s coeff sum",
sname, pname);
(void)x; /* avoid unused parameter warning */
}
static int
lin3_f (const gsl_vector * x, void *params, gsl_vector * f)
{
size_t i, j;
gsl_vector_set(f, 0, -1.0);
gsl_vector_set(f, lin3_N - 1, -1.0);
for (i = 1; i < lin3_N - 1; ++i)
{
double fi = 0.0;
for (j = 1; j < lin3_P - 1; ++j)
{
double xj = gsl_vector_get(x, j);
fi += (j + 1) * xj;
}
fi = i * fi - 1.0;
gsl_vector_set(f, i, fi);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
lin3_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(lin3_J, lin3_N, lin3_P);
size_t i, j;
gsl_matrix_set_zero(&J.matrix);
for (i = 1; i < lin3_N - 1; ++i)
{
for (j = 1; j < lin3_P - 1; ++j)
{
gsl_matrix_set(&J.matrix, i, j, i * (j + 1.0));
}
}
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
lin3_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 lin3_func =
{
lin3_f,
lin3_df,
lin3_fvv,
lin3_N,
lin3_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem lin3_problem =
{
"linear_rank1zeros",
lin3_x0,
NULL,
&lin3_epsrel,
&lin3_checksol,
&lin3_func
};
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