| /* specfunc/bessel_Inu.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_exp.h> |
| #include <gsl/gsl_sf_gamma.h> |
| #include <gsl/gsl_sf_bessel.h> |
| |
| #include "error.h" |
| |
| #include "bessel.h" |
| #include "bessel_temme.h" |
| |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| int |
| gsl_sf_bessel_Inu_scaled_e(double nu, double x, gsl_sf_result * result) |
| { |
| /* CHECK_POINTER(result) */ |
| |
| if(x < 0.0 || nu < 0.0) { |
| DOMAIN_ERROR(result); |
| } |
| else if(x*x < 10.0*(nu+1.0)) { |
| gsl_sf_result b; |
| double ex = exp(-x); |
| int stat = gsl_sf_bessel_IJ_taylor_e(nu, x, 1, 100, GSL_DBL_EPSILON, &b); |
| result->val = b.val * ex; |
| result->err = b.err * ex; |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); |
| return stat; |
| } |
| else if(0.5/(nu*nu + x*x) < GSL_ROOT3_DBL_EPSILON) { |
| return gsl_sf_bessel_Inu_scaled_asymp_unif_e(nu, x, result); |
| } |
| else { |
| int N = (int)(nu + 0.5); |
| double mu = nu - N; /* -1/2 <= mu <= 1/2 */ |
| double K_mu, K_mup1, Kp_mu; |
| double K_nu, K_nup1, K_num1; |
| double I_nu_ratio; |
| int stat_Irat; |
| int stat_Kmu; |
| int n; |
| |
| /* obtain K_mu, K_mup1 */ |
| if(x < 2.0) { |
| stat_Kmu = gsl_sf_bessel_K_scaled_temme(mu, x, &K_mu, &K_mup1, &Kp_mu); |
| } |
| else { |
| stat_Kmu = gsl_sf_bessel_K_scaled_steed_temme_CF2(mu, x, &K_mu, &K_mup1, &Kp_mu); |
| } |
| |
| /* recurse forward to obtain K_num1, K_nu */ |
| K_nu = K_mu; |
| K_nup1 = K_mup1; |
| |
| for(n=0; n<N; n++) { |
| K_num1 = K_nu; |
| K_nu = K_nup1; |
| K_nup1 = 2.0*(mu+n+1)/x * K_nu + K_num1; |
| } |
| |
| /* calculate I_{nu+1}/I_nu */ |
| stat_Irat = gsl_sf_bessel_I_CF1_ser(nu, x, &I_nu_ratio); |
| |
| /* solve for I_nu */ |
| result->val = 1.0/(x * (K_nup1 + I_nu_ratio * K_nu)); |
| result->err = GSL_DBL_EPSILON * (0.5*N + 2.0) * fabs(result->val); |
| |
| return GSL_ERROR_SELECT_2(stat_Kmu, stat_Irat); |
| } |
| } |
| |
| |
| int |
| gsl_sf_bessel_Inu_e(double nu, double x, gsl_sf_result * result) |
| { |
| gsl_sf_result b; |
| int stat_I = gsl_sf_bessel_Inu_scaled_e(nu, x, &b); |
| int stat_e = gsl_sf_exp_mult_err_e(x, fabs(x*GSL_DBL_EPSILON), |
| b.val, b.err, |
| result); |
| return GSL_ERROR_SELECT_2(stat_e, stat_I); |
| } |
| |
| |
| /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| #include "eval.h" |
| |
| double gsl_sf_bessel_Inu_scaled(double nu, double x) |
| { |
| EVAL_RESULT(gsl_sf_bessel_Inu_scaled_e(nu, x, &result)); |
| } |
| |
| |
| double gsl_sf_bessel_Inu(double nu, double x) |
| { |
| EVAL_RESULT(gsl_sf_bessel_Inu_e(nu, x, &result)); |
| } |