#define kowalik_N 11
#define kowalik_P 4
#define kowalik_NTRIES 4
static double kowalik_x0[kowalik_P] = { 0.25, 0.39, 0.415, 0.39 };
static double kowalik_epsrel = 1.0e-7;
static double kowalik_Y[kowalik_N] = {
0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
0.0456, 0.0342, 0.0323, 0.0235, 0.0246
};
static double kowalik_U[kowalik_N] = {
4.0000, 2.0000, 1.0000, 0.5000, 0.2500, 0.1670,
0.1250, 0.1000, 0.0833, 0.0714, 0.0625
};
static void
kowalik_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
gsl_vector_const_view v = gsl_vector_const_view_array(x, kowalik_P);
const double norm = gsl_blas_dnrm2(&v.vector);
const double sumsq_exact1 = 3.075056038492370e-04;
const double kowalik_x1[kowalik_P] = { 1.928069345723978e-01,
1.912823290344599e-01,
1.230565070690708e-01,
1.360623308065148e-01 };
const double sumsq_exact2 = 0.00102734304869549252;
const double kowalik_x2[kowalik_P] = { -99999.9, /* inf */
-14.0758834005984603,
-99999.9, /* -inf */
-99999.9 }; /* -inf */
const double *kowalik_x;
double sumsq_exact;
if (norm < 10.0)
{
kowalik_x = kowalik_x1;
sumsq_exact = sumsq_exact1;
}
else
{
kowalik_x = kowalik_x2;
sumsq_exact = sumsq_exact2;
}
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < kowalik_P; ++i)
{
if (kowalik_x[i] < -90000.0)
continue;
gsl_test_rel(x[i], kowalik_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
kowalik_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 x4 = gsl_vector_get(x, 3);
size_t i;
for (i = 0; i < kowalik_N; ++i)
{
double yi = kowalik_Y[i];
double ui = kowalik_U[i];
double fi = yi - (x1*ui*(ui+x2)) / (x4 + ui*(ui + x3));
gsl_vector_set(f, i, fi);
}
return GSL_SUCCESS;
}
static int
kowalik_df (const gsl_vector * x, void *params, gsl_matrix * J)
{
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
double x3 = gsl_vector_get(x, 2);
double x4 = gsl_vector_get(x, 3);
size_t i;
for (i = 0; i < kowalik_N; ++i)
{
double ui = kowalik_U[i];
double term1 = ui*(ui + x2);
double term2 = ui*(ui + x3) + x4;
gsl_matrix_set(J, i, 0, -term1 / term2);
gsl_matrix_set(J, i, 1, -ui*x1/term2);
gsl_matrix_set(J, i, 2, ui*term1*x1 / (term2*term2));
gsl_matrix_set(J, i, 3, term1*x1 / (term2*term2));
}
return GSL_SUCCESS;
}
static gsl_multifit_function_fdf kowalik_func =
{
&kowalik_f,
&kowalik_df,
NULL,
kowalik_N,
kowalik_P,
NULL,
0,
0
};
static test_fdf_problem kowalik_problem =
{
"kowalik",
kowalik_x0,
NULL,
&kowalik_epsrel,
kowalik_NTRIES,
&kowalik_checksol,
&kowalik_func
};