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