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#define kowalik_N 11
#define kowalik_P 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_J[kowalik_N * kowalik_P];
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] = { GSL_NAN, /* inf */
-14.0758834005984603,
GSL_NAN, /* -inf */
GSL_NAN }; /* -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 (!gsl_finite(kowalik_x[i]))
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);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
kowalik_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(kowalik_J, kowalik_N, kowalik_P);
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.matrix, i, 0, -term1 / term2);
gsl_matrix_set(&J.matrix, i, 1, -ui*x1/term2);
gsl_matrix_set(&J.matrix, i, 2, ui*term1*x1 / (term2*term2));
gsl_matrix_set(&J.matrix, i, 3, term1*x1 / (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
kowalik_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 x4 = gsl_vector_get(x, 3);
double v1 = gsl_vector_get(v, 0);
double v2 = gsl_vector_get(v, 1);
double v3 = gsl_vector_get(v, 2);
double v4 = gsl_vector_get(v, 3);
size_t i;
for (i = 0; i < kowalik_N; ++i)
{
double ui = kowalik_U[i];
double term2 = ui*(ui + x3) + x4;
double term3 = ui*ui*v1 - ui*v3*x1 - v4*x1 +
ui*v1*x3 + v1*x4;
double term4 = ui*ui*(v3-v2) + v4*x2 +
ui*(v4 + v3*x2 - v2*x3) - v2*x4;
gsl_vector_set(fvv, i, 2.0*ui*term3*term4 / pow(term2, 3.0));
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf kowalik_func =
{
kowalik_f,
kowalik_df,
kowalik_fvv,
kowalik_N,
kowalik_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem kowalik_problem =
{
"kowalik",
kowalik_x0,
NULL,
&kowalik_epsrel,
&kowalik_checksol,
&kowalik_func
};
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