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