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#define brown2_N 5
#define brown2_P 5
static double brown2_x0[brown2_P] = { 0.5, 0.5, 0.5, 0.5, 0.5 };
static double brown2_epsrel = 1.0e-12;
static double brown2_J[brown2_N * brown2_P];
static void
brown2_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
double sumsq_exact;
double alpha;
const double p = (double) brown2_P;
double alpha1mp, lhs, lastel;
if (sumsq < 0.5)
{
/* sumsq = 0 case */
sumsq_exact = 0.0;
alpha = x[0];
alpha1mp = pow(alpha, 1.0 - p);
lhs = p*pow(alpha, p) - (p + 1)/alpha1mp;
lastel = alpha1mp;
gsl_test_rel(lhs, -1.0, epsrel, "%s/%s alpha lhs",
sname, pname);
}
else
{
/* sumsq = 1 case */
sumsq_exact = 1.0;
alpha = 0.0;
lastel = p + 1.0;
}
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 1; i < brown2_P - 1; ++i)
{
gsl_test_rel(x[i], alpha, epsrel, "%s/%s i=%zu",
sname, pname, i);
}
gsl_test_rel(x[brown2_P - 1], lastel, epsrel, "%s/%s last element",
sname, pname);
}
static int
brown2_f (const gsl_vector * x, void *params, gsl_vector * f)
{
size_t i;
double sum = -(brown2_N + 1.0);
double prod = 1.0;
for (i = 0; i < brown2_N; ++i)
{
double xi = gsl_vector_get(x, i);
sum += xi;
prod *= xi;
}
for (i = 0; i < brown2_N - 1; ++i)
{
double xi = gsl_vector_get(x, i);
gsl_vector_set(f, i, xi + sum);
}
gsl_vector_set(f, brown2_N - 1, prod - 1.0);
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
brown2_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(brown2_J, brown2_N, brown2_P);
size_t i, j;
for (j = 0; j < brown2_P; ++j)
{
double prod = 1.0;
for (i = 0; i < brown2_N - 1; i++)
{
double Jij = (i == j) ? 2.0 : 1.0;
gsl_matrix_set(&J.matrix, i, j, Jij);
}
for (i = 0; i < brown2_N; i++)
{
if (i != j)
prod *= gsl_vector_get(x, i);
}
gsl_matrix_set(&J.matrix, brown2_N - 1, j, prod);
}
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
brown2_fvv (const gsl_vector * x, const gsl_vector * v,
void *params, gsl_vector * fvv)
{
size_t i, j, k;
double sum = 0.0;
gsl_vector_set_zero(fvv);
for (k = 0; k < brown2_P; ++k)
{
double vk = gsl_vector_get(v, k);
for (i = 0; i < brown2_P; ++i)
{
double vi = gsl_vector_get(v, i);
double delta = (i == k) ? 1.0 : 0.0;
double prod = 1.0;
for (j = 0; j < brown2_N; ++j)
{
if (j != i && j != k)
{
double xj = gsl_vector_get(x, j);
prod *= xj;
}
}
sum += vk * vi * (1.0 - delta) * prod;
}
}
gsl_vector_set(fvv, brown2_N - 1, sum);
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf brown2_func =
{
brown2_f,
brown2_df,
brown2_fvv,
brown2_N,
brown2_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem brown2_problem =
{
"brown_almost_linear",
brown2_x0,
NULL,
&brown2_epsrel,
&brown2_checksol,
&brown2_func
};
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