|
Packit |
67cb25 |
#define watson_N 31
|
|
Packit |
67cb25 |
#define watson_P 6
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static double watson_x0[watson_P] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };
|
|
Packit |
67cb25 |
static double watson_epsrel = 1.0e-6;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
watson_checksol(const double x[], const double sumsq,
|
|
Packit |
67cb25 |
const double epsrel, const char *sname,
|
|
Packit |
67cb25 |
const char *pname)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t i;
|
|
Packit |
67cb25 |
const double sumsq_exact = 2.287670053552372e-03;
|
|
Packit |
67cb25 |
const double watson_x[watson_P] = {
|
|
Packit |
67cb25 |
-1.572508640629858e-02, 1.012434869366059e+00, -2.329916259263380e-01,
|
|
Packit |
67cb25 |
1.260430087686035e+00, -1.513728922580576e+00, 9.929964323646112e-01 };
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
|
|
Packit |
67cb25 |
sname, pname);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < watson_P; ++i)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
gsl_test_rel(x[i], watson_x[i], epsrel, "%s/%s i=%zu",
|
|
Packit |
67cb25 |
sname, pname, i);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static int
|
|
Packit |
67cb25 |
watson_f (const gsl_vector * x, void *params, gsl_vector * f)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
const double x1 = gsl_vector_get(x, 0);
|
|
Packit |
67cb25 |
const double x2 = gsl_vector_get(x, 1);
|
|
Packit |
67cb25 |
size_t i, j;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < watson_N - 2; ++i)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double ti = (i + 1) / 29.0;
|
|
Packit |
67cb25 |
double tjm1 = 1.0, tjm2 = 1.0;
|
|
Packit |
67cb25 |
double sum1 = 0.0, sum2 = 0.0;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < watson_P; ++j)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double xj = gsl_vector_get(x, j);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
sum1 += xj * tjm1;
|
|
Packit |
67cb25 |
tjm1 *= ti;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (j > 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
sum2 += j * xj * tjm2;
|
|
Packit |
67cb25 |
tjm2 *= ti;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_vector_set (f, i, sum2 - sum1*sum1 - 1.0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_vector_set(f, watson_N - 2, x1);
|
|
Packit |
67cb25 |
gsl_vector_set(f, watson_N - 1, x2 - x1*x1 - 1.0);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
(void)params; /* avoid unused parameter warning */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static int
|
|
Packit |
67cb25 |
watson_df (const gsl_vector * x, void *params, gsl_matrix * J)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double x1 = gsl_vector_get (x, 0);
|
|
Packit |
67cb25 |
size_t i, j;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_matrix_set_zero(J);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < watson_N - 2; ++i)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double ti = (i + 1) / 29.0;
|
|
Packit |
67cb25 |
double tjm1 = 1.0, tjm2 = 1.0;
|
|
Packit |
67cb25 |
double sum1 = 0.0;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < watson_P; ++j)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double xj = gsl_vector_get(x, j);
|
|
Packit |
67cb25 |
sum1 += xj * tjm1;
|
|
Packit |
67cb25 |
tjm1 *= ti;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
tjm1 = 1.0;
|
|
Packit |
67cb25 |
tjm2 = 1.0;
|
|
Packit |
67cb25 |
for (j = 0; j < watson_P; ++j)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
gsl_matrix_set(J, i, j, j * tjm2 - 2.0*sum1*tjm1);
|
|
Packit |
67cb25 |
tjm1 *= ti;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (j > 0)
|
|
Packit |
67cb25 |
tjm2 *= ti;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_matrix_set(J, watson_N - 2, 0, 1.0);
|
|
Packit |
67cb25 |
gsl_matrix_set(J, watson_N - 1, 0, -2.0*x1);
|
|
Packit |
67cb25 |
gsl_matrix_set(J, watson_N - 1, 1, 1.0);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
(void)params; /* avoid unused parameter warning */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static int
|
|
Packit |
67cb25 |
watson_fvv (const gsl_vector * x, const gsl_vector * v,
|
|
Packit |
67cb25 |
void *params, gsl_vector * fvv)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double v1 = gsl_vector_get (v, 0);
|
|
Packit |
67cb25 |
size_t i, j;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < watson_N - 2; ++i)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double ti = (i + 1) / 29.0;
|
|
Packit |
67cb25 |
double sum = 0.0;
|
|
Packit |
67cb25 |
double tjm1 = 1.0;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < watson_P; ++j)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double vj = gsl_vector_get(v, j);
|
|
Packit |
67cb25 |
sum += vj * tjm1;
|
|
Packit |
67cb25 |
tjm1 *= ti;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_vector_set(fvv, i, -2.0*sum*sum);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_vector_set(fvv, watson_N - 2, 0.0);
|
|
Packit |
67cb25 |
gsl_vector_set(fvv, watson_N - 1, -2.0*v1*v1);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
(void)x; /* avoid unused parameter warning */
|
|
Packit |
67cb25 |
(void)params; /* avoid unused parameter warning */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static gsl_multifit_nlinear_fdf watson_func =
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
watson_f,
|
|
Packit |
67cb25 |
watson_df,
|
|
Packit |
67cb25 |
watson_fvv,
|
|
Packit |
67cb25 |
watson_N,
|
|
Packit |
67cb25 |
watson_P,
|
|
Packit |
67cb25 |
NULL,
|
|
Packit |
67cb25 |
0,
|
|
Packit |
67cb25 |
0,
|
|
Packit |
67cb25 |
0
|
|
Packit |
67cb25 |
};
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static test_fdf_problem watson_problem =
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
"watson",
|
|
Packit |
67cb25 |
watson_x0,
|
|
Packit |
67cb25 |
NULL,
|
|
Packit |
67cb25 |
NULL,
|
|
Packit |
67cb25 |
&watson_epsrel,
|
|
Packit |
67cb25 |
&watson_checksol,
|
|
Packit |
67cb25 |
&watson_func
|
|
Packit |
67cb25 |
};
|