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#define beale_N 3
#define beale_P 2
static double beale_x0[beale_P] = { 1.0, 1.0 };
static double beale_epsrel = 1.0e-12;
static double beale_J[beale_N * beale_P];
static double beale_Y[beale_N] = { 1.5, 2.25, 2.625 };
static void
beale_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact = 0.0;
const double beale_x[beale_P] = { 3.0, 0.5 };
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < beale_P; ++i)
{
gsl_test_rel(x[i], beale_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
beale_f (const gsl_vector * x, void *params, gsl_vector * f)
{
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
size_t i;
for (i = 0; i < beale_N; ++i)
{
double yi = beale_Y[i];
double term = pow(x2, i + 1.0);
double fi = yi - x1*(1.0 - term);
gsl_vector_set(f, i, fi);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
beale_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(beale_J, beale_N, beale_P);
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
size_t i;
for (i = 0; i < beale_N; ++i)
{
double term = pow(x2, (double) i);
gsl_matrix_set(&J.matrix, i, 0, term*x2 - 1.0);
gsl_matrix_set(&J.matrix, i, 1, (i + 1.0) * x1 * term);
}
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
beale_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 v1 = gsl_vector_get(v, 0);
double v2 = gsl_vector_get(v, 1);
size_t i;
for (i = 0; i < beale_N; ++i)
{
double term = pow(x2, (double)i - 1.0);
gsl_vector_set(fvv, i, (i + 1.0) * v2 * term *
(i * v2 * x1 + 2.0 * v1 * x2));
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf beale_func =
{
beale_f,
beale_df,
beale_fvv,
beale_N,
beale_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem beale_problem =
{
"beale",
beale_x0,
NULL,
&beale_epsrel,
&beale_checksol,
&beale_func
};
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