| /* specfunc/bessel_Yn.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_gamma.h> |
| #include <gsl/gsl_sf_psi.h> |
| #include <gsl/gsl_sf_bessel.h> |
| |
| #include "error.h" |
| |
| #include "bessel.h" |
| #include "bessel_amp_phase.h" |
| #include "bessel_olver.h" |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| /* assumes n >= 1 */ |
| static int bessel_Yn_small_x(const int n, const double x, gsl_sf_result * result) |
| { |
| int k; |
| double y = 0.25 * x * x; |
| double ln_x_2 = log(0.5*x); |
| gsl_sf_result ln_nm1_fact; |
| double k_term; |
| double term1, sum1, ln_pre1; |
| double term2, sum2, pre2; |
| |
| gsl_sf_lnfact_e((unsigned int)(n-1), &ln_nm1_fact); |
| |
| ln_pre1 = -n*ln_x_2 + ln_nm1_fact.val; |
| if(ln_pre1 > GSL_LOG_DBL_MAX - 3.0) GSL_ERROR ("error", GSL_EOVRFLW); |
| |
| sum1 = 1.0; |
| k_term = 1.0; |
| for(k=1; k<=n-1; k++) { |
| k_term *= y/(k * (n-k)); |
| sum1 += k_term; |
| } |
| term1 = -exp(ln_pre1) * sum1 / M_PI; |
| |
| pre2 = -exp(n*ln_x_2) / M_PI; |
| if(fabs(pre2) > 0.0) { |
| const int KMAX = 20; |
| gsl_sf_result psi_n; |
| gsl_sf_result npk_fact; |
| double yk = 1.0; |
| double k_fact = 1.0; |
| double psi_kp1 = -M_EULER; |
| double psi_npkp1; |
| gsl_sf_psi_int_e(n, &psi_n); |
| gsl_sf_fact_e((unsigned int)n, &npk_fact); |
| psi_npkp1 = psi_n.val + 1.0/n; |
| sum2 = (psi_kp1 + psi_npkp1 - 2.0*ln_x_2)/npk_fact.val; |
| for(k=1; k<KMAX; k++) { |
| psi_kp1 += 1./k; |
| psi_npkp1 += 1./(n+k); |
| k_fact *= k; |
| npk_fact.val *= n+k; |
| yk *= -y; |
| k_term = yk*(psi_kp1 + psi_npkp1 - 2.0*ln_x_2)/(k_fact*npk_fact.val); |
| sum2 += k_term; |
| } |
| term2 = pre2 * sum2; |
| } |
| else { |
| term2 = 0.0; |
| } |
| |
| result->val = term1 + term2; |
| result->err = GSL_DBL_EPSILON * (fabs(ln_pre1)*fabs(term1) + fabs(term2)); |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); |
| |
| return GSL_SUCCESS; |
| } |
| |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| |
| int |
| gsl_sf_bessel_Yn_e(int n, const 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 = -1; |
| } |
| |
| /* CHECK_POINTER(result) */ |
| |
| if(n == 0) { |
| int status = gsl_sf_bessel_Y0_e(x, result); |
| result->val *= sign; |
| return status; |
| } |
| else if(n == 1) { |
| int status = gsl_sf_bessel_Y1_e(x, result); |
| result->val *= sign; |
| return status; |
| } |
| else { |
| if(x <= 0.0) { |
| DOMAIN_ERROR(result); |
| } |
| if(x < 5.0) { |
| int status = bessel_Yn_small_x(n, x, result); |
| result->val *= sign; |
| return status; |
| } |
| else if(GSL_ROOT3_DBL_EPSILON * x > (n*n + 1.0)) { |
| int status = gsl_sf_bessel_Ynu_asympx_e((double)n, x, result); |
| result->val *= sign; |
| return status; |
| } |
| else if(n > 50) { |
| int status = gsl_sf_bessel_Ynu_asymp_Olver_e((double)n, x, result); |
| result->val *= sign; |
| return status; |
| } |
| else { |
| double two_over_x = 2.0/x; |
| gsl_sf_result r_by; |
| gsl_sf_result r_bym; |
| int stat_1 = gsl_sf_bessel_Y1_e(x, &r_by); |
| int stat_0 = gsl_sf_bessel_Y0_e(x, &r_bym); |
| double bym = r_bym.val; |
| double by = r_by.val; |
| double byp; |
| int j; |
| |
| for(j=1; j<n; j++) { |
| byp = j*two_over_x*by - bym; |
| bym = by; |
| by = byp; |
| } |
| result->val = sign * by; |
| result->err = fabs(result->val) * (fabs(r_by.err/r_by.val) + fabs(r_bym.err/r_bym.val)); |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); |
| |
| return GSL_ERROR_SELECT_2(stat_1, stat_0); |
| } |
| } |
| } |
| |
| |
| int |
| gsl_sf_bessel_Yn_array(const int nmin, const int nmax, const double x, double * result_array) |
| { |
| /* CHECK_POINTER(result_array) */ |
| |
| if(nmin < 0 || nmax < nmin || x <= 0.0) { |
| int j; |
| for(j=0; j<=nmax-nmin; j++) result_array[j] = 0.0; |
| GSL_ERROR ("error", GSL_EDOM); |
| } |
| else { |
| gsl_sf_result r_Ynm1; |
| gsl_sf_result r_Yn; |
| int stat_nm1 = gsl_sf_bessel_Yn_e(nmin, x, &r_Ynm1); |
| int stat_n = gsl_sf_bessel_Yn_e(nmin+1, x, &r_Yn); |
| double Ynp1; |
| double Yn = r_Yn.val; |
| double Ynm1 = r_Ynm1.val; |
| int n; |
| |
| int stat = GSL_ERROR_SELECT_2(stat_nm1, stat_n); |
| |
| if(stat == GSL_SUCCESS) { |
| for(n=nmin+1; n<=nmax+1; n++) { |
| result_array[n-nmin-1] = Ynm1; |
| Ynp1 = -Ynm1 + 2.0*n/x * Yn; |
| Ynm1 = Yn; |
| Yn = Ynp1; |
| } |
| } |
| else { |
| for(n=nmin; n<=nmax; n++) { |
| result_array[n-nmin] = 0.0; |
| } |
| } |
| |
| return stat; |
| } |
| } |
| |
| |
| /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| #include "eval.h" |
| |
| double gsl_sf_bessel_Yn(const int n, const double x) |
| { |
| EVAL_RESULT(gsl_sf_bessel_Yn_e(n, x, &result)); |
| } |
| |