#define biggs_N 6 /* >= p */
#define biggs_P 6
/* dogleg method has trouble converging from recommended starting point,
* so we use an x0 which is a little closer to the true solution */
/*static double biggs_x0[biggs_P] = { 1.0, 2.0, 1.0, 1.0, 1.0, 1.0 };*/
static double biggs_x0[biggs_P] = { 1.0, 8.0, 1.0, 2.0, 3.0, 2.0 };
static double biggs_epsrel = 1.0e-9;
static double biggs_J[biggs_N * biggs_P];
static void
biggs_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
#if 0
const double sumsq_exact = 0.0;
#endif
const double biggs_x[biggs_P] = { 1.0, 10.0, 1.0, 5.0, 4.0, 3.0 };
const double norm_exact = 12.3288280059380;
gsl_vector_const_view v = gsl_vector_const_view_array(biggs_x, biggs_P);
double norm = gsl_blas_dnrm2(&v.vector);
#if 0
/* some solvers have difficulty reaching sumsq = 0 to sufficient
* decimal places */
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
#endif
/*
* the solution vector is not unique due to permutations, so test
* the norm instead of individual elements
*/
gsl_test_rel(norm, norm_exact, epsrel, "%s/%s norm",
sname, pname);
(void)x; /* avoid unused parameter warning */
(void)sumsq; /* avoid unused parameter warning */
}
static int
biggs_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);
double x4 = gsl_vector_get(x, 3);
double x5 = gsl_vector_get(x, 4);
double x6 = gsl_vector_get(x, 5);
size_t i;
for (i = 0; i < biggs_N; ++i)
{
double ti = 0.1 * (i + 1.0);
double yi = exp(-ti) - 5*exp(-10*ti) + 3*exp(-4*ti);
double fi = x3*exp(-ti*x1) - x4*exp(-ti*x2) + x6*exp(-ti*x5) - yi;
gsl_vector_set(f, i, fi);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
biggs_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(biggs_J, biggs_N, biggs_P);
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
double x3 = gsl_vector_get(x, 2);
double x4 = gsl_vector_get(x, 3);
double x5 = gsl_vector_get(x, 4);
double x6 = gsl_vector_get(x, 5);
size_t i;
for (i = 0; i < biggs_N; ++i)
{
double ti = 0.1 * (i + 1.0);
gsl_matrix_set(&J.matrix, i, 0, -ti*x3*exp(-ti*x1));
gsl_matrix_set(&J.matrix, i, 1, ti*x4*exp(-ti*x2));
gsl_matrix_set(&J.matrix, i, 2, exp(-ti*x1));
gsl_matrix_set(&J.matrix, i, 3, -exp(-ti*x2));
gsl_matrix_set(&J.matrix, i, 4, -ti*x6*exp(-ti*x5));
gsl_matrix_set(&J.matrix, i, 5, exp(-ti*x5));
}
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
biggs_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 x3 = gsl_vector_get(x, 2);
double x4 = gsl_vector_get(x, 3);
double x5 = gsl_vector_get(x, 4);
double x6 = gsl_vector_get(x, 5);
double v1 = gsl_vector_get(v, 0);
double v2 = gsl_vector_get(v, 1);
double v3 = gsl_vector_get(v, 2);
double v4 = gsl_vector_get(v, 3);
double v5 = gsl_vector_get(v, 4);
double v6 = gsl_vector_get(v, 5);
size_t i;
for (i = 0; i < biggs_N; ++i)
{
double ti = 0.1 * (i + 1.0);
double term1 = exp(-ti * x1);
double term2 = exp(-ti * x2);
double term3 = exp(-ti * x5);
gsl_vector_set(fvv, i, ti * term1 * term2 * term3 *
(v1/(term2*term3)*(-2*v3 + ti*v1*x3) -
v2/(term1*term3)*(-2*v4 + ti*v2*x4) +
v5/(term1*term2)*(-2*v6 + ti*v5*x6)));
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf biggs_func =
{
biggs_f,
biggs_df,
biggs_fvv,
biggs_N,
biggs_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem biggs_problem =
{
"biggs",
biggs_x0,
NULL,
&biggs_epsrel,
&biggs_checksol,
&biggs_func
};