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test_helical.c
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test_helical.c
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#define helical_N 3
#define helical_P 3
static double helical_x0[helical_P] = { -1.0, 0.0, 0.0 };
static double helical_x[helical_P] = { 1.0, 0.0, 0.0 };
static double helical_epsrel = 1.0e-12;
static double helical_J[helical_N * helical_P];
static void
helical_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 < helical_P; ++i)
{
gsl_test_rel(x[i], helical_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
helical_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 theta = (x1 >= 0.0) ? 0.0 : 5.0;
double nx = gsl_hypot(x1, x2);
gsl_vector_set(f, 0, 10.0 * (x3 - 5.0/M_PI*atan(x2 / x1) - theta));
gsl_vector_set(f, 1, 10.0*(nx - 1.0));
gsl_vector_set(f, 2, x3);
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
helical_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(helical_J, helical_N, helical_P);
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
double nx = gsl_hypot(x1, x2);
double nx_sq = nx * nx;
double term1 = 50.0 / (M_PI * nx_sq);
double term2 = 10.0 / nx;
gsl_matrix_set(&J.matrix, 0, 0, term1*x2);
gsl_matrix_set(&J.matrix, 0, 1, -term1*x1);
gsl_matrix_set(&J.matrix, 0, 2, 10.0);
gsl_matrix_set(&J.matrix, 1, 0, term2*x1);
gsl_matrix_set(&J.matrix, 1, 1, term2*x2);
gsl_matrix_set(&J.matrix, 1, 2, 0.0);
gsl_matrix_set(&J.matrix, 2, 0, 0.0);
gsl_matrix_set(&J.matrix, 2, 1, 0.0);
gsl_matrix_set(&J.matrix, 2, 2, 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)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
helical_fvv (const gsl_vector * x, const gsl_vector * v,
void *params, gsl_vector * fvv)
{
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
double v1 = gsl_vector_get(v, 0);
double v2 = gsl_vector_get(v, 1);
double term1 = v2*x1 - v1*x2;
double term2 = v1*x1 + v2*x2;
double term3 = x1*x1 + x2*x2;
gsl_vector_set(fvv, 0, 100.0 / M_PI * (term1 / term3) * (term2 / term3));
gsl_vector_set(fvv, 1, 10.0 * (term1 * term1) / pow(term3, 1.5));
gsl_vector_set(fvv, 2, 0.0);
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf helical_func =
{
helical_f,
helical_df,
helical_fvv,
helical_N,
helical_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem helical_problem =
{
"helical",
helical_x0,
NULL,
&helical_epsrel,
&helical_checksol,
&helical_func
};