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#define gaussian_N 15
#define gaussian_P 3
static double gaussian_x0[gaussian_P] = { 0.4, 1.0, 0.0 };
static double gaussian_epsrel = 1.0e-10;
static double gaussian_J[gaussian_N * gaussian_P];
static double gaussian_Y[gaussian_N] = {
0.0009, 0.0044, 0.0175, 0.0540, 0.1295, 0.2420, 0.3521, 0.3989,
0.3521, 0.2420, 0.1295, 0.0540, 0.0175, 0.0044, 0.0009
};
static void
gaussian_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact = 1.12793276961871985e-08;
const double gaussian_x[gaussian_P] = { 0.398956137838762825,
1.00001908448786647,
0.0 };
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < gaussian_P; ++i)
{
gsl_test_rel(x[i], gaussian_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
gaussian_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 < gaussian_N; ++i)
{
double ti = (7.0 - i) / 2.0;
double yi = gaussian_Y[i];
double term = ti - x3;
double fi = x1 * exp(-x2*term*term/2.0) - yi;
gsl_vector_set(f, i, fi);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
gaussian_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(gaussian_J, gaussian_N, gaussian_P);
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 < gaussian_N; ++i)
{
double ti = (7.0 - i) / 2.0;
double term1 = ti - x3;
double term2 = exp(-x2*term1*term1/2.0);
gsl_matrix_set(&J.matrix, i, 0, term2);
gsl_matrix_set(&J.matrix, i, 1, -0.5*x1*term2*term1*term1);
gsl_matrix_set(&J.matrix, i, 2, x1*x2*term1*term2);
}
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
gaussian_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 v1 = gsl_vector_get(v, 0);
double v2 = gsl_vector_get(v, 1);
double v3 = gsl_vector_get(v, 2);
size_t i;
for (i = 0; i < gaussian_N; ++i)
{
double ti = (7.0 - i) / 2.0;
double term1 = ti - x3;
double term2 = exp(-x2*term1*term1/2.0);
gsl_vector_set(fvv, i, 0.25 * term2 *
(ti*ti*ti*ti*v2*v2*x1 -
4*ti*ti*ti*v2*x1*(v3*x2 + v2*x3) +
v2*x3*x3*(v2*x1*x3*x3 - 4*v1) +
4*v3*v3*x1*x2*(x2*x3*x3 - 1.0) +
4*v3*x3*(-2*v1*x2 + v2*x1*(x2*x3*x3 - 2.0)) +
ti*ti*(4*v3*v3*x1*x2*x2 + 2*v2*(-2*v1 + 3*x1*x3*(2*v3*x2 + v2*x3))) -
4*ti*(v2*v2*x1*x3*x3*x3 + 2*v3*x2*(-v1 + v3*x1*x2*x3) +
v2*(-2*v1*x3 + v3*x1*(-2.0 + 3*x2*x3*x3)))));
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf gaussian_func =
{
gaussian_f,
gaussian_df,
gaussian_fvv,
gaussian_N,
gaussian_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem gaussian_problem =
{
"gaussian",
gaussian_x0,
NULL,
&gaussian_epsrel,
&gaussian_checksol,
&gaussian_func
};
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