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/* dht/dht.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
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* Copyright (C) 2009 Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* Author: G. Jungman
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*/
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#include <config.h>
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#include <stdlib.h>
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#include <gsl/gsl_errno.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_sf_bessel.h>
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#include <gsl/gsl_dht.h>
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gsl_dht *
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gsl_dht_alloc (size_t size)
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{
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gsl_dht * t;
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if(size == 0) {
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GSL_ERROR_VAL("size == 0", GSL_EDOM, 0);
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}
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t = (gsl_dht *)malloc(sizeof(gsl_dht));
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if(t == 0) {
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GSL_ERROR_VAL("out of memory", GSL_ENOMEM, 0);
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}
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t->size = size;
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t->xmax = -1.0; /* Make it clear that this needs to be calculated. */
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t->nu = -1.0;
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t->j = (double *)malloc((size+2)*sizeof(double));
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if(t->j == 0) {
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free(t);
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GSL_ERROR_VAL("could not allocate memory for j", GSL_ENOMEM, 0);
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}
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t->Jjj = (double *)malloc(size*(size+1)/2 * sizeof(double));
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if(t->Jjj == 0) {
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free(t->j);
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free(t);
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GSL_ERROR_VAL("could not allocate memory for Jjj", GSL_ENOMEM, 0);
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}
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t->J2 = (double *)malloc((size+1)*sizeof(double));
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if(t->J2 == 0) {
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free(t->Jjj);
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free(t->j);
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free(t);
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GSL_ERROR_VAL("could not allocate memory for J2", GSL_ENOMEM, 0);
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}
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return t;
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}
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/* Handle internal calculation of Bessel zeros. */
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static int
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dht_bessel_zeros(gsl_dht * t)
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{
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unsigned int s;
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gsl_sf_result z;
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int stat_z = 0;
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t->j[0] = 0.0;
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for(s=1; s < t->size + 2; s++) {
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stat_z += gsl_sf_bessel_zero_Jnu_e(t->nu, s, &z);
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t->j[s] = z.val;
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}
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if(stat_z != 0) {
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GSL_ERROR("could not compute bessel zeroes", GSL_EFAILED);
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}
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else {
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return GSL_SUCCESS;
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}
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}
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gsl_dht *
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gsl_dht_new (size_t size, double nu, double xmax)
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{
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int status;
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gsl_dht * dht = gsl_dht_alloc (size);
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if (dht == 0)
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return 0;
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status = gsl_dht_init(dht, nu, xmax);
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if (status)
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return 0;
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return dht;
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}
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int
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gsl_dht_init(gsl_dht * t, double nu, double xmax)
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{
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if(xmax <= 0.0) {
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GSL_ERROR ("xmax is not positive", GSL_EDOM);
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} else if(nu < 0.0) {
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GSL_ERROR ("nu is negative", GSL_EDOM);
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}
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else {
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size_t n, m;
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int stat_bz = GSL_SUCCESS;
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int stat_J = 0;
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double jN;
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if(nu != t->nu) {
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/* Recalculate Bessel zeros if necessary. */
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t->nu = nu;
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stat_bz = dht_bessel_zeros(t);
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}
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jN = t->j[t->size+1];
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t->xmax = xmax;
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t->kmax = jN / xmax;
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t->J2[0] = 0.0;
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for(m=1; m<t->size+1; m++) {
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gsl_sf_result J;
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stat_J += gsl_sf_bessel_Jnu_e(nu + 1.0, t->j[m], &J);
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t->J2[m] = J.val * J.val;
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}
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/* J_nu(j[n] j[m] / j[N]) = Jjj[n(n-1)/2 + m - 1], 1 <= n,m <= size
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*/
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for(n=1; n<t->size+1; n++) {
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for(m=1; m<=n; m++) {
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double arg = t->j[n] * t->j[m] / jN;
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gsl_sf_result J;
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stat_J += gsl_sf_bessel_Jnu_e(nu, arg, &J);
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t->Jjj[n*(n-1)/2 + m - 1] = J.val;
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}
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}
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if(stat_J != 0) {
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GSL_ERROR("error computing bessel function", GSL_EFAILED);
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}
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else {
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return stat_bz;
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}
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}
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}
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double gsl_dht_x_sample(const gsl_dht * t, int n)
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{
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return t->j[n+1]/t->j[t->size+1] * t->xmax;
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}
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double gsl_dht_k_sample(const gsl_dht * t, int n)
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{
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return t->j[n+1] / t->xmax;
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}
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void gsl_dht_free(gsl_dht * t)
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{
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RETURN_IF_NULL (t);
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free(t->J2);
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free(t->Jjj);
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free(t->j);
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free(t);
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}
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int
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gsl_dht_apply(const gsl_dht * t, double * f_in, double * f_out)
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{
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const double jN = t->j[t->size + 1];
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const double r = t->xmax / jN;
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size_t m;
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size_t i;
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for(m=0; m<t->size; m++) {
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double sum = 0.0;
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double Y;
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for(i=0; i<t->size; i++) {
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/* Need to find max and min so that we
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* address the symmetric Jjj matrix properly.
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* FIXME: we can presumably optimize this
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* by just running over the elements of Jjj
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* in a deterministic manner.
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*/
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size_t m_local;
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size_t n_local;
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if(i < m) {
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m_local = i;
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n_local = m;
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}
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else {
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m_local = m;
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n_local = i;
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}
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Y = t->Jjj[n_local*(n_local+1)/2 + m_local] / t->J2[i+1];
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sum += Y * f_in[i];
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}
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f_out[m] = sum * 2.0 * r*r;
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}
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return GSL_SUCCESS;
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}
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