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#define rat42_N 9
#define rat42_P 3
static double rat42_x0a[rat42_P] = { 100.0, 1.0, 0.1 };
static double rat42_x0b[rat42_P] = { 75.0, 2.5, 0.07 };
static double rat42_epsrel = 1.0e-7;
static double rat42_J[rat42_N * rat42_P];
static double rat42_sigma[rat42_P] = {
1.7340283401E+00, 8.8295217536E-02, 3.4465663377E-03
};
static double rat42_X[rat42_N] = { 9.0, 14.0, 21.0, 28.0, 42.0,
57.0, 63.0, 70.0, 79.0 };
static double rat42_F[rat42_N] = { 8.930, 10.800, 18.590, 22.330,
39.350, 56.110, 61.730, 64.620,
67.080 };
static void
rat42_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact = 8.0565229338E+00;
const double rat42_x[rat42_P] = { 7.2462237576E+01,
2.6180768402E+00,
6.7359200066E-02 };
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < rat42_P; ++i)
{
gsl_test_rel(x[i], rat42_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
rat42_f (const gsl_vector * x, void *params, gsl_vector * f)
{
double b[rat42_P];
size_t i;
for (i = 0; i < rat42_P; i++)
{
b[i] = gsl_vector_get(x, i);
}
for (i = 0; i < rat42_N; i++)
{
double xi = rat42_X[i];
double yi = b[0] / (1.0 + exp(b[1] - b[2]*xi));
gsl_vector_set (f, i, yi - rat42_F[i]);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
rat42_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(rat42_J, rat42_N, rat42_P);
double b[rat42_P];
size_t i;
for (i = 0; i < rat42_P; i++)
{
b[i] = gsl_vector_get(x, i);
}
for (i = 0; i < rat42_N; i++)
{
double xi = rat42_X[i];
double term1 = exp(b[1] - b[2]*xi);
double term2 = 1.0 + term1;
gsl_matrix_set (&J.matrix, i, 0, 1.0 / term2);
gsl_matrix_set (&J.matrix, i, 1, -b[0] * term1 / (term2 * term2));
gsl_matrix_set (&J.matrix, i, 2, b[0] * term1 * xi / (term2 * 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 int
rat42_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 < rat42_N; i++)
{
double ti = rat42_X[i];
double term1 = exp(x2);
double term2 = exp(ti * x3);
gsl_vector_set(fvv, i,
-pow(term1 + term2, -3.0) * term1 * term2 *
(v2 - ti*v3) * (term1*(2*v1 - v2*x1 + ti*v3*x1) +
term2*(2*v1 + x1*(v2 - ti*v3))));
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf rat42_func =
{
rat42_f,
rat42_df,
rat42_fvv,
rat42_N,
rat42_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem rat42a_problem =
{
"nist-rat42a",
rat42_x0a,
rat42_sigma,
&rat42_epsrel,
&rat42_checksol,
&rat42_func
};
static test_fdf_problem rat42b_problem =
{
"nist-rat42b",
rat42_x0b,
rat42_sigma,
&rat42_epsrel,
&rat42_checksol,
&rat42_func
};
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