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/* dht/dht.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/* Author: G. Jungman
*/
#include <config.h>
#include <stdlib.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_sf_bessel.h>
#include <gsl/gsl_dht.h>
gsl_dht *
gsl_dht_alloc (size_t size)
{
gsl_dht * t;
if(size == 0) {
GSL_ERROR_VAL("size == 0", GSL_EDOM, 0);
}
t = (gsl_dht *)malloc(sizeof(gsl_dht));
if(t == 0) {
GSL_ERROR_VAL("out of memory", GSL_ENOMEM, 0);
}
t->size = size;
t->xmax = -1.0; /* Make it clear that this needs to be calculated. */
t->nu = -1.0;
t->j = (double *)malloc((size+2)*sizeof(double));
if(t->j == 0) {
free(t);
GSL_ERROR_VAL("could not allocate memory for j", GSL_ENOMEM, 0);
}
t->Jjj = (double *)malloc(size*(size+1)/2 * sizeof(double));
if(t->Jjj == 0) {
free(t->j);
free(t);
GSL_ERROR_VAL("could not allocate memory for Jjj", GSL_ENOMEM, 0);
}
t->J2 = (double *)malloc((size+1)*sizeof(double));
if(t->J2 == 0) {
free(t->Jjj);
free(t->j);
free(t);
GSL_ERROR_VAL("could not allocate memory for J2", GSL_ENOMEM, 0);
}
return t;
}
/* Handle internal calculation of Bessel zeros. */
static int
dht_bessel_zeros(gsl_dht * t)
{
unsigned int s;
gsl_sf_result z;
int stat_z = 0;
t->j[0] = 0.0;
for(s=1; s < t->size + 2; s++) {
stat_z += gsl_sf_bessel_zero_Jnu_e(t->nu, s, &z);
t->j[s] = z.val;
}
if(stat_z != 0) {
GSL_ERROR("could not compute bessel zeroes", GSL_EFAILED);
}
else {
return GSL_SUCCESS;
}
}
gsl_dht *
gsl_dht_new (size_t size, double nu, double xmax)
{
int status;
gsl_dht * dht = gsl_dht_alloc (size);
if (dht == 0)
return 0;
status = gsl_dht_init(dht, nu, xmax);
if (status)
return 0;
return dht;
}
int
gsl_dht_init(gsl_dht * t, double nu, double xmax)
{
if(xmax <= 0.0) {
GSL_ERROR ("xmax is not positive", GSL_EDOM);
} else if(nu < 0.0) {
GSL_ERROR ("nu is negative", GSL_EDOM);
}
else {
size_t n, m;
int stat_bz = GSL_SUCCESS;
int stat_J = 0;
double jN;
if(nu != t->nu) {
/* Recalculate Bessel zeros if necessary. */
t->nu = nu;
stat_bz = dht_bessel_zeros(t);
}
jN = t->j[t->size+1];
t->xmax = xmax;
t->kmax = jN / xmax;
t->J2[0] = 0.0;
for(m=1; m<t->size+1; m++) {
gsl_sf_result J;
stat_J += gsl_sf_bessel_Jnu_e(nu + 1.0, t->j[m], &J);
t->J2[m] = J.val * J.val;
}
/* J_nu(j[n] j[m] / j[N]) = Jjj[n(n-1)/2 + m - 1], 1 <= n,m <= size
*/
for(n=1; n<t->size+1; n++) {
for(m=1; m<=n; m++) {
double arg = t->j[n] * t->j[m] / jN;
gsl_sf_result J;
stat_J += gsl_sf_bessel_Jnu_e(nu, arg, &J);
t->Jjj[n*(n-1)/2 + m - 1] = J.val;
}
}
if(stat_J != 0) {
GSL_ERROR("error computing bessel function", GSL_EFAILED);
}
else {
return stat_bz;
}
}
}
double gsl_dht_x_sample(const gsl_dht * t, int n)
{
return t->j[n+1]/t->j[t->size+1] * t->xmax;
}
double gsl_dht_k_sample(const gsl_dht * t, int n)
{
return t->j[n+1] / t->xmax;
}
void gsl_dht_free(gsl_dht * t)
{
free(t->J2);
free(t->Jjj);
free(t->j);
free(t);
}
int
gsl_dht_apply(const gsl_dht * t, double * f_in, double * f_out)
{
const double jN = t->j[t->size + 1];
const double r = t->xmax / jN;
size_t m;
size_t i;
for(m=0; m<t->size; m++) {
double sum = 0.0;
double Y;
for(i=0; i<t->size; i++) {
/* Need to find max and min so that we
* address the symmetric Jjj matrix properly.
* FIXME: we can presumably optimize this
* by just running over the elements of Jjj
* in a deterministic manner.
*/
size_t m_local;
size_t n_local;
if(i < m) {
m_local = i;
n_local = m;
}
else {
m_local = m;
n_local = i;
}
Y = t->Jjj[n_local*(n_local+1)/2 + m_local] / t->J2[i+1];
sum += Y * f_in[i];
}
f_out[m] = sum * 2.0 * r*r;
}
return GSL_SUCCESS;
}
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