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#define bard_N 15
#define bard_P 3
static double bard_x0[bard_P] = { 1.0, 1.0, 1.0 };
static double bard_epsrel = 1.0e-7;
static double bard_J[bard_N * bard_P];
static double bard_Y[bard_N] = {
0.14, 0.18, 0.22, 0.25, 0.29, 0.32, 0.35, 0.39, 0.37,
0.58, 0.73, 0.96, 1.34, 2.10, 4.39
};
static void
bard_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact1 = 8.214877306578963e-03;
const double bard_x1[bard_P] = { 8.241055975623580e-02,
1.133036092245175,
2.343695178435405 };
const double sumsq_exact2 = 17.42869333333333;
const double bard_x2[bard_P] = { 8.406666666666666e-01,
GSL_NAN, /* -inf */
GSL_NAN }; /* -inf */
const double *bard_x;
double sumsq_exact;
if (fabs(x[1]) < 10.0 && fabs(x[2]) < 10.0)
{
bard_x = bard_x1;
sumsq_exact = sumsq_exact1;
}
else
{
bard_x = bard_x2;
sumsq_exact = sumsq_exact2;
}
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < bard_P; ++i)
{
if (!gsl_finite(bard_x[i]))
continue;
gsl_test_rel(x[i], bard_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
bard_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 < bard_N; ++i)
{
double ui = i + 1.0;
double vi = 16.0 - i - 1.0;
double wi = GSL_MIN(ui, vi);
double yi = bard_Y[i];
double fi = yi - (x1 + (ui / (x2*vi + x3*wi)));
gsl_vector_set(f, i, fi);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
bard_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(bard_J, bard_N, bard_P);
double x2 = gsl_vector_get(x, 1);
double x3 = gsl_vector_get(x, 2);
size_t i;
for (i = 0; i < bard_N; ++i)
{
double ui = i + 1.0;
double vi = 16.0 - i - 1.0;
double wi = GSL_MIN(ui, vi);
double term = x2 * vi + x3 * wi;
gsl_matrix_set(&J.matrix, i, 0, -1.0);
gsl_matrix_set(&J.matrix, i, 1, ui * vi / (term * term));
gsl_matrix_set(&J.matrix, i, 2, ui * wi / (term * term));
}
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
bard_fvv (const gsl_vector * x, const gsl_vector * v,
void *params, gsl_vector * fvv)
{
double x2 = gsl_vector_get(x, 1);
double x3 = gsl_vector_get(x, 2);
double v2 = gsl_vector_get(v, 1);
double v3 = gsl_vector_get(v, 2);
size_t i;
for (i = 0; i < bard_N; ++i)
{
double ui = i + 1.0;
double vi = 16.0 - i - 1.0;
double wi = GSL_MIN(ui, vi);
double term1 = x2 * vi + x3 * wi;
double term2 = v2 * vi + v3 * wi;
double ratio = term2 / term1;
gsl_vector_set(fvv, i, -2.0 * ui * ratio * ratio / term1);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf bard_func =
{
bard_f,
bard_df,
bard_fvv,
bard_N,
bard_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem bard_problem =
{
"bard",
bard_x0,
NULL,
&bard_epsrel,
&bard_checksol,
&bard_func
};
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