#define biggs_N 20 /* >= 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, 5.0, 1.0, 2.0, 3.0, 2.0 };
static double biggs_epsrel = 1.0e-9;
static void
biggs_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
const double sumsq_exact = 0.0;
const double biggs_x[biggs_P] = { 1.0, 10.0, 1.0, 5.0, 4.0, 3.0 };
size_t i;
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < biggs_P; ++i)
{
gsl_test_rel(x[i], biggs_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
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 (const gsl_vector * x, void *params, gsl_matrix * J)
{
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, i, 0, -ti*x3*exp(-ti*x1));
gsl_matrix_set(J, i, 1, ti*x4*exp(-ti*x2));
gsl_matrix_set(J, i, 2, exp(-ti*x1));
gsl_matrix_set(J, i, 3, -exp(-ti*x2));
gsl_matrix_set(J, i, 4, -ti*x6*exp(-ti*x5));
gsl_matrix_set(J, i, 5, exp(-ti*x5));
}
(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_multifit_nlinear_fdf biggs_func =
{
biggs_f,
biggs_df,
biggs_fvv,
biggs_N,
biggs_P,
NULL,
0,
0,
0
};
static test_fdf_problem biggs_problem =
{
"biggs",
biggs_x0,
NULL,
NULL,
&biggs_epsrel,
&biggs_checksol,
&biggs_func
};