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#define rat43_N 15
#define rat43_P 4
static double rat43_x0a[rat43_P] = { 100.0, 10.0, 1.0, 1.0 };
static double rat43_x0b[rat43_P] = { 700.0, 5.0, 0.75, 1.3 };
static double rat43_epsrel = 1.0e-6;
static double rat43_J[rat43_N * rat43_P];
static double rat43_sigma[rat43_P] = {
1.6302297817E+01, 2.0828735829E+00,
1.9566123451E-01, 6.8761936385E-01
};
static double rat43_F[rat43_N] = { 16.08, 33.83, 65.80, 97.20, 191.55,
326.20, 386.87, 520.53, 590.03,
651.92, 724.93, 699.56, 689.96,
637.56, 717.41 };
static void
rat43_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact = 8.7864049080E+03;
const double rat43_x[rat43_P] = { 6.9964151270E+02,
5.2771253025E+00,
7.5962938329E-01,
1.2792483859E+00 };
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < rat43_P; ++i)
{
gsl_test_rel(x[i], rat43_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
rat43_f (const gsl_vector * x, void *params, gsl_vector * f)
{
double b[rat43_P];
size_t i;
for (i = 0; i < rat43_P; i++)
{
b[i] = gsl_vector_get(x, i);
}
for (i = 0; i < rat43_N; i++)
{
double xi = i + 1.0;
double e = exp(b[1] - b[2]*xi);
double yi = b[0] / pow(1.0 + e, 1.0 / b[3]);
gsl_vector_set (f, i, yi - rat43_F[i]);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
rat43_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(rat43_J, rat43_N, rat43_P);
double b[rat43_P];
size_t i;
for (i = 0; i < rat43_P; i++)
{
b[i] = gsl_vector_get(x, i);
}
for (i = 0; i < rat43_N; i++)
{
double xi = i + 1.0;
double e = exp(b[1] - b[2]*xi);
double term1 = 1.0 + e;
double term2 = pow(term1, -1.0 / b[3]);
gsl_matrix_set (&J.matrix, i, 0, term2);
gsl_matrix_set (&J.matrix, i, 1, -b[0] / b[3] * e * term2 / term1);
gsl_matrix_set (&J.matrix, i, 2, b[0] / b[3] * xi * e * term2 / term1);
gsl_matrix_set (&J.matrix, i, 3, b[0] / b[3] / b[3] * log(term1) * term2);
}
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 gsl_multilarge_nlinear_fdf rat43_func =
{
rat43_f,
rat43_df,
NULL, /* analytic expression too complex */
rat43_N,
rat43_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem rat43a_problem =
{
"nist-rat43a",
rat43_x0a,
rat43_sigma,
&rat43_epsrel,
&rat43_checksol,
&rat43_func
};
static test_fdf_problem rat43b_problem =
{
"nist-rat43b",
rat43_x0b,
rat43_sigma,
&rat43_epsrel,
&rat43_checksol,
&rat43_func
};
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