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#define penalty2_N 8 /* 2*p */
#define penalty2_P 4
static double penalty2_x0[penalty2_P] = { 0.5, 0.5, 0.5, 0.5 };
static double penalty2_epsrel = 1.0e-12;
static double penalty2_J[penalty2_N * penalty2_P];
static void
penalty2_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
const double sumsq_exact = 9.37629300735544219e-06;
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
(void)x; /* avoid unused parameter warning */
}
static int
penalty2_f (const gsl_vector * x, void *params, gsl_vector * f)
{
const double alpha = 1.0e-5;
const double sqrt_alpha = sqrt(alpha);
double x1 = gsl_vector_get(x, 0);
size_t i;
double sum = penalty2_P * x1 * x1;
gsl_vector_set(f, 0, x1 - 0.2);
/* rows [2:p] */
for (i = 1; i < penalty2_P; ++i)
{
double xi = gsl_vector_get(x, i);
double xim1 = gsl_vector_get(x, i - 1);
double yi = exp(0.1*(i + 1.0)) + exp(0.1*i);
gsl_vector_set(f, i, sqrt_alpha*(exp(0.1*xi) + exp(0.1*xim1) - yi));
sum += (penalty2_P - i) * xi * xi;
}
/* rows [p+1:2p-1] */
for (i = penalty2_P; i < penalty2_N - 1; ++i)
{
double xi = gsl_vector_get(x, i - penalty2_P + 1);
gsl_vector_set(f, i, sqrt_alpha*(exp(0.1*xi) - exp(-0.1)));
}
/* row 2p */
gsl_vector_set(f, penalty2_N - 1, sum - 1.0);
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
penalty2_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(penalty2_J, penalty2_N, penalty2_P);
const double alpha = 1.0e-5;
const double sqrt_alpha = sqrt(alpha);
size_t i, j;
for (j = 0; j < penalty2_P; ++j)
{
double xj = gsl_vector_get(x, j);
double delta1j = (j == 0) ? 1.0 : 0.0;
/* first and last rows */
gsl_matrix_set(&J.matrix, 0, j, delta1j);
gsl_matrix_set(&J.matrix, penalty2_N - 1, j, 2.0 * (penalty2_P - j) * xj);
/* rows [2:p] */
for (i = 1; i < penalty2_P; ++i)
{
double xi = gsl_vector_get(x, i);
double xim1 = gsl_vector_get(x, i - 1);
double Jij;
if (i == j)
Jij = exp(0.1 * xi);
else if (i - 1 == j)
Jij = exp(0.1 * xim1);
else
Jij = 0.0;
Jij *= 0.1 * sqrt_alpha;
gsl_matrix_set(&J.matrix, i, j, Jij);
}
/* rows [p+1:2p-1] */
for (i = penalty2_P; i < penalty2_N - 1; ++i)
{
double xi = gsl_vector_get(x, i - penalty2_P + 1);
if (i - penalty2_P + 1 == j)
gsl_matrix_set(&J.matrix, i, j, 0.1 * sqrt_alpha * exp(0.1*xi));
else
gsl_matrix_set(&J.matrix, i, j, 0.0);
}
}
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
penalty2_fvv (const gsl_vector * x, const gsl_vector * v,
void *params, gsl_vector * fvv)
{
const double alpha = 1.0e-5;
const double sqrt_alpha = sqrt(alpha);
double v1 = gsl_vector_get(v, 0);
double sum = penalty2_P * v1 * v1;
size_t i;
/* first row */
gsl_vector_set(fvv, 0, 0.0);
/* rows [2:p] */
for (i = 1; i < penalty2_P; ++i)
{
double xi = gsl_vector_get(x, i);
double xim1 = gsl_vector_get(x, i - 1);
double vi = gsl_vector_get(v, i);
double vim1 = gsl_vector_get(v, i - 1);
double term1 = exp(xi / 10.0);
double term2 = exp(xim1 / 10.0);
gsl_vector_set(fvv, i,
sqrt_alpha / 100.0 * (term1 * vi * vi + term2 * vim1 * vim1));
sum += (penalty2_P - i) * vi * vi;
}
/* last row */
gsl_vector_set(fvv, penalty2_N - 1, 2.0 * sum);
/* rows [p+1:2p-1] */
for (i = penalty2_P; i < penalty2_N - 1; ++i)
{
double xi = gsl_vector_get(x, i - penalty2_P + 1);
double vi = gsl_vector_get(v, i - penalty2_P + 1);
gsl_vector_set(fvv, i, sqrt_alpha / 100.0 * exp(xi / 10.0) * vi * vi);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf penalty2_func =
{
penalty2_f,
penalty2_df,
penalty2_fvv,
penalty2_N,
penalty2_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem penalty2_problem =
{
"penalty2",
penalty2_x0,
NULL,
&penalty2_epsrel,
&penalty2_checksol,
&penalty2_func
};
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