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/* specfunc/bessel_Jn.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 <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_pow_int.h>
#include "bessel.h"
#include "bessel_amp_phase.h"
#include "bessel_olver.h"
#include <gsl/gsl_sf_bessel.h>
/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
int gsl_sf_bessel_Jn_e(int n, double x, gsl_sf_result * result)
{
int sign = 1;
if(n < 0) {
/* reduce to case n >= 0 */
n = -n;
if(GSL_IS_ODD(n)) sign = -sign;
}
if(x < 0.0) {
/* reduce to case x >= 0. */
x = -x;
if(GSL_IS_ODD(n)) sign = -sign;
}
/* CHECK_POINTER(result) */
if(n == 0) {
gsl_sf_result b0;
int stat_J0 = gsl_sf_bessel_J0_e(x, &b0);
result->val = sign * b0.val;
result->err = b0.err;
return stat_J0;
}
else if(n == 1) {
gsl_sf_result b1;
int stat_J1 = gsl_sf_bessel_J1_e(x, &b1);
result->val = sign * b1.val;
result->err = b1.err;
return stat_J1;
}
else {
if(x == 0.0) {
result->val = 0.0;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(x*x < 10.0*(n+1.0)*GSL_ROOT5_DBL_EPSILON) {
gsl_sf_result b;
int status = gsl_sf_bessel_IJ_taylor_e((double)n, x, -1, 50, GSL_DBL_EPSILON, &b);
result->val = sign * b.val;
result->err = b.err;
result->err += GSL_DBL_EPSILON * fabs(result->val);
return status;
}
else if(GSL_ROOT4_DBL_EPSILON * x > (n*n+1.0)) {
int status = gsl_sf_bessel_Jnu_asympx_e((double)n, x, result);
result->val *= sign;
return status;
}
else if(n > 50) {
int status = gsl_sf_bessel_Jnu_asymp_Olver_e((double)n, x, result);
result->val *= sign;
return status;
}
else if(x > 1000.0)
{
/* We need this to avoid feeding large x to CF1; note that
* due to the above check, we know that n <= 50.
*/
int status = gsl_sf_bessel_Jnu_asympx_e((double)n, x, result);
result->val *= sign;
return status;
}
else {
double ans;
double err;
double ratio;
double sgn;
int stat_b;
int stat_CF1 = gsl_sf_bessel_J_CF1((double)n, x, &ratio, &sgn);
/* backward recurrence */
double Jkp1 = GSL_SQRT_DBL_MIN * ratio;
double Jk = GSL_SQRT_DBL_MIN;
double Jkm1;
int k;
for(k=n; k>0; k--) {
Jkm1 = 2.0*k/x * Jk - Jkp1;
Jkp1 = Jk;
Jk = Jkm1;
}
if(fabs(Jkp1) > fabs(Jk)) {
gsl_sf_result b1;
stat_b = gsl_sf_bessel_J1_e(x, &b1);
ans = b1.val/Jkp1 * GSL_SQRT_DBL_MIN;
err = b1.err/Jkp1 * GSL_SQRT_DBL_MIN;
}
else {
gsl_sf_result b0;
stat_b = gsl_sf_bessel_J0_e(x, &b0);
ans = b0.val/Jk * GSL_SQRT_DBL_MIN;
err = b0.err/Jk * GSL_SQRT_DBL_MIN;
}
result->val = sign * ans;
result->err = fabs(err);
return GSL_ERROR_SELECT_2(stat_CF1, stat_b);
}
}
}
int
gsl_sf_bessel_Jn_array(int nmin, int nmax, double x, double * result_array)
{
/* CHECK_POINTER(result_array) */
if(nmin < 0 || nmax < nmin) {
int n;
for(n=nmax; n>=nmin; n--) {
result_array[n-nmin] = 0.0;
}
GSL_ERROR ("domain error", GSL_EDOM);
}
else if(x == 0.0) {
int n;
for(n=nmax; n>=nmin; n--) {
result_array[n-nmin] = 0.0;
}
if(nmin == 0) result_array[0] = 1.0;
return GSL_SUCCESS;
}
else {
gsl_sf_result r_Jnp1;
gsl_sf_result r_Jn;
int stat_np1 = gsl_sf_bessel_Jn_e(nmax+1, x, &r_Jnp1);
int stat_n = gsl_sf_bessel_Jn_e(nmax, x, &r_Jn);
int stat = GSL_ERROR_SELECT_2(stat_np1, stat_n);
double Jnp1 = r_Jnp1.val;
double Jn = r_Jn.val;
double Jnm1;
int n;
if(stat == GSL_SUCCESS) {
for(n=nmax; n>=nmin; n--) {
result_array[n-nmin] = Jn;
Jnm1 = -Jnp1 + 2.0*n/x * Jn;
Jnp1 = Jn;
Jn = Jnm1;
}
}
else {
for(n=nmax; n>=nmin; n--) {
result_array[n-nmin] = 0.0;
}
}
return stat;
}
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_bessel_Jn(const int n, const double x)
{
EVAL_RESULT(gsl_sf_bessel_Jn_e(n, x, &result));
}
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