|
Packit |
67cb25 |
#define meyer_N 16
|
|
Packit |
67cb25 |
#define meyer_P 3
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static double meyer_x0[meyer_P] = { 0.02, 4000.0, 250.0 };
|
|
Packit |
67cb25 |
static double meyer_epsrel = 1.0e-7;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static double meyer_J[meyer_N * meyer_P];
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static double meyer_Y[meyer_N] = {
|
|
Packit |
67cb25 |
34780., 28610., 23650., 19630., 16370., 13720., 11540.,
|
|
Packit |
67cb25 |
9744., 8261., 7030., 6005., 5147., 4427., 3820.,
|
|
Packit |
67cb25 |
3307., 2872.
|
|
Packit |
67cb25 |
};
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
meyer_checksol(const double x[], const double sumsq,
|
|
Packit |
67cb25 |
const double epsrel, const char *sname,
|
|
Packit |
67cb25 |
const char *pname)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t i;
|
|
Packit |
67cb25 |
const double sumsq_exact = 8.794585517053883e+01;
|
|
Packit |
67cb25 |
const double meyer_x[meyer_P] = { 5.609636471049458e-03,
|
|
Packit |
67cb25 |
6.181346346283188e+03,
|
|
Packit |
67cb25 |
3.452236346240292e+02 };
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
|
|
Packit |
67cb25 |
sname, pname);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < meyer_P; ++i)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
gsl_test_rel(x[i], meyer_x[i], epsrel, "%s/%s i=%zu",
|
|
Packit |
67cb25 |
sname, pname, i);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static int
|
|
Packit |
67cb25 |
meyer_f (const gsl_vector * x, void *params, gsl_vector * f)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double x1 = gsl_vector_get(x, 0);
|
|
Packit |
67cb25 |
double x2 = gsl_vector_get(x, 1);
|
|
Packit |
67cb25 |
double x3 = gsl_vector_get(x, 2);
|
|
Packit |
67cb25 |
size_t i;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < meyer_N; ++i)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double ti = 45.0 + 5.0*(i + 1.0);
|
|
Packit |
67cb25 |
double yi = meyer_Y[i];
|
|
Packit |
67cb25 |
double fi = x1 * exp(x2 / (ti + x3)) - yi;
|
|
Packit |
67cb25 |
gsl_vector_set(f, i, fi);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
(void)params; /* avoid unused parameter warning */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static int
|
|
Packit |
67cb25 |
meyer_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
|
|
Packit |
67cb25 |
const gsl_vector * u, void * params, gsl_vector * v,
|
|
Packit |
67cb25 |
gsl_matrix * JTJ)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
gsl_matrix_view J = gsl_matrix_view_array(meyer_J, meyer_N, meyer_P);
|
|
Packit |
67cb25 |
double x1 = gsl_vector_get(x, 0);
|
|
Packit |
67cb25 |
double x2 = gsl_vector_get(x, 1);
|
|
Packit |
67cb25 |
double x3 = gsl_vector_get(x, 2);
|
|
Packit |
67cb25 |
size_t i;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < meyer_N; ++i)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double ti = 45.0 + 5.0*(i + 1.0);
|
|
Packit |
67cb25 |
double term1 = ti + x3;
|
|
Packit |
67cb25 |
double term2 = exp(x2 / term1);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_matrix_set(&J.matrix, i, 0, term2);
|
|
Packit |
67cb25 |
gsl_matrix_set(&J.matrix, i, 1, x1*term2/term1);
|
|
Packit |
67cb25 |
gsl_matrix_set(&J.matrix, i, 2, -x1*x2*term2/(term1*term1));
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (v)
|
|
Packit |
67cb25 |
gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (JTJ)
|
|
Packit |
67cb25 |
gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
(void)params; /* avoid unused parameter warning */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static int
|
|
Packit |
67cb25 |
meyer_fvv (const gsl_vector * x, const gsl_vector * v,
|
|
Packit |
67cb25 |
void *params, gsl_vector * fvv)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double x1 = gsl_vector_get(x, 0);
|
|
Packit |
67cb25 |
double x2 = gsl_vector_get(x, 1);
|
|
Packit |
67cb25 |
double x3 = gsl_vector_get(x, 2);
|
|
Packit |
67cb25 |
double v1 = gsl_vector_get(v, 0);
|
|
Packit |
67cb25 |
double v2 = gsl_vector_get(v, 1);
|
|
Packit |
67cb25 |
double v3 = gsl_vector_get(v, 2);
|
|
Packit |
67cb25 |
size_t i;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < meyer_N; ++i)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double ti = 45.0 + 5.0*(i + 1.0);
|
|
Packit |
67cb25 |
double term1 = ti + x3;
|
|
Packit |
67cb25 |
double term2 = exp(x2 / term1);
|
|
Packit |
67cb25 |
double term3 = v2*term1 - v3*x2;
|
|
Packit |
67cb25 |
double term4 = 2*ti*ti*v1 - v3*x1*(x2 + 2*x3) +
|
|
Packit |
67cb25 |
x3*(v2*x1 + 2*v1*x3) +
|
|
Packit |
67cb25 |
ti*(v2*x1 - 2*v3*x1 + 4*v1*x3);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_vector_set(fvv, i, term2 * term3 * term4 / pow(term1, 4.0));
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
(void)params; /* avoid unused parameter warning */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static gsl_multilarge_nlinear_fdf meyer_func =
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
meyer_f,
|
|
Packit |
67cb25 |
meyer_df,
|
|
Packit |
67cb25 |
meyer_fvv,
|
|
Packit |
67cb25 |
meyer_N,
|
|
Packit |
67cb25 |
meyer_P,
|
|
Packit |
67cb25 |
NULL,
|
|
Packit |
67cb25 |
0,
|
|
Packit |
67cb25 |
0,
|
|
Packit |
67cb25 |
0,
|
|
Packit |
67cb25 |
0
|
|
Packit |
67cb25 |
};
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static test_fdf_problem meyer_problem =
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
"meyer",
|
|
Packit |
67cb25 |
meyer_x0,
|
|
Packit |
67cb25 |
NULL,
|
|
Packit |
67cb25 |
&meyer_epsrel,
|
|
Packit |
67cb25 |
&meyer_checksol,
|
|
Packit |
67cb25 |
&meyer_func
|
|
Packit |
67cb25 |
};
|