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#define box_N 10 /* can be >= p */
#define box_P 3
/* dogleg method fails with recommended starting point, so use
* a slightly easier x0 */
/*static double box_x0[box_P] = { 0.0, 10.0, 20.0 };*/
static double box_x0[box_P] = { 5.0, 10.0, 2.0 };
static double box_epsrel = 1.0e-12;
static double box_J[box_N * box_P];
static void
box_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
const double sumsq_exact = 0.0;
const double eps = 1.0e-6;
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
/* there are 3 possible solution vectors */
if (fabs(x[2] - 1.0) < eps)
{
/* case 1: x* = [ 1; 10; 1 ] */
gsl_test_rel(x[0], 1.0, epsrel, "%s/%s i=0",
sname, pname);
gsl_test_rel(x[1], 10.0, epsrel, "%s/%s i=1",
sname, pname);
gsl_test_rel(x[2], 1.0, epsrel, "%s/%s i=2",
sname, pname);
}
else if (fabs(x[2] + 1.0) < eps)
{
/* case 2: x* = [ 10; 1; -1 ] */
gsl_test_rel(x[0], 10.0, epsrel, "%s/%s i=0",
sname, pname);
gsl_test_rel(x[1], 1.0, epsrel, "%s/%s i=1",
sname, pname);
gsl_test_rel(x[2], -1.0, epsrel, "%s/%s i=2",
sname, pname);
}
else
{
/* case 3: x* = [ a; a; 0 ] for any a */
gsl_test_rel(x[0], x[1], epsrel, "%s/%s i=0,1",
sname, pname);
gsl_test_rel(x[2], 0.0, epsrel, "%s/%s i=2",
sname, pname);
}
}
static int
box_f (const gsl_vector * x, void *params, gsl_vector * f)
{
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
double x3 = gsl_vector_get(x, 2);
size_t i;
for (i = 0; i < box_N; ++i)
{
double ti = (i + 1.0) / 10.0;
double fi = exp(-x1*ti) - exp(-x2*ti) - x3*(exp(-ti) - exp(-10.0*ti));
gsl_vector_set(f, i, fi);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
box_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(box_J, box_N, box_P);
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
size_t i;
for (i = 0; i < box_N; ++i)
{
double ti = (i + 1.0) / 10.0;
double term1 = exp(-x1*ti);
double term2 = exp(-x2*ti);
double term3 = exp(-10.0*ti) - exp(-ti);
gsl_matrix_set(&J.matrix, i, 0, -ti*term1);
gsl_matrix_set(&J.matrix, i, 1, ti*term2);
gsl_matrix_set(&J.matrix, i, 2, term3);
}
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
box_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 < box_N; ++i)
{
double ti = (i + 1.0) / 10.0;
double term1 = exp(-x1*ti);
double term2 = exp(-x2*ti);
gsl_vector_set(fvv, i, ti * ti * (v1*v1*term1 - v2*v2*term2));
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf box_func =
{
box_f,
box_df,
box_fvv,
box_N,
box_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem box_problem =
{
"box3d",
box_x0,
NULL,
&box_epsrel,
&box_checksol,
&box_func
};
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