diff options
Diffstat (limited to 'gsl-1.9/specfunc/bessel_Yn.c')
| -rw-r--r-- | gsl-1.9/specfunc/bessel_Yn.c | 217 |
1 files changed, 217 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/bessel_Yn.c b/gsl-1.9/specfunc/bessel_Yn.c new file mode 100644 index 0000000..c3140e5 --- /dev/null +++ b/gsl-1.9/specfunc/bessel_Yn.c @@ -0,0 +1,217 @@ +/* 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)); +} + |