| /* 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)); |
| } |