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Diffstat (limited to 'gsl-1.9/specfunc/hyperg_0F1.c')
| -rw-r--r-- | gsl-1.9/specfunc/hyperg_0F1.c | 178 |
1 files changed, 178 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/hyperg_0F1.c b/gsl-1.9/specfunc/hyperg_0F1.c new file mode 100644 index 0000000..004466e --- /dev/null +++ b/gsl-1.9/specfunc/hyperg_0F1.c @@ -0,0 +1,178 @@ +/* specfunc/hyperg_0F1.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 <gsl/gsl_sf_hyperg.h> + +#include "error.h" + +#define locEPS (1000.0*GSL_DBL_EPSILON) + + +/* Evaluate bessel_I(nu, x), allowing nu < 0. + * This is fine here because we do not not allow + * nu to be a negative integer. + * x > 0. + */ +static +int +hyperg_0F1_bessel_I(const double nu, const double x, gsl_sf_result * result) +{ + if(x > GSL_LOG_DBL_MAX) { + OVERFLOW_ERROR(result); + } + + if(nu < 0.0) { + const double anu = -nu; + const double s = 2.0/M_PI * sin(anu*M_PI); + const double ex = exp(x); + gsl_sf_result I; + gsl_sf_result K; + int stat_I = gsl_sf_bessel_Inu_scaled_e(anu, x, &I); + int stat_K = gsl_sf_bessel_Knu_scaled_e(anu, x, &K); + result->val = ex * I.val + s * (K.val / ex); + result->err = ex * I.err + fabs(s * K.err/ex); + result->err += fabs(s * (K.val/ex)) * GSL_DBL_EPSILON * anu * M_PI; + return GSL_ERROR_SELECT_2(stat_K, stat_I); + } + else { + const double ex = exp(x); + gsl_sf_result I; + int stat_I = gsl_sf_bessel_Inu_scaled_e(nu, x, &I); + result->val = ex * I.val; + result->err = ex * I.err + GSL_DBL_EPSILON * fabs(result->val); + return stat_I; + } +} + + +/* Evaluate bessel_J(nu, x), allowing nu < 0. + * This is fine here because we do not not allow + * nu to be a negative integer. + * x > 0. + */ +static +int +hyperg_0F1_bessel_J(const double nu, const double x, gsl_sf_result * result) +{ + if(nu < 0.0) { + const double anu = -nu; + const double s = sin(anu*M_PI); + const double c = cos(anu*M_PI); + gsl_sf_result J; + gsl_sf_result Y; + int stat_J = gsl_sf_bessel_Jnu_e(anu, x, &J); + int stat_Y = gsl_sf_bessel_Ynu_e(anu, x, &Y); + result->val = c * J.val - s * Y.val; + result->err = fabs(c * J.err) + fabs(s * Y.err); + result->err += fabs(anu * M_PI) * GSL_DBL_EPSILON * fabs(J.val + Y.val); + return GSL_ERROR_SELECT_2(stat_Y, stat_J); + } + else { + return gsl_sf_bessel_Jnu_e(nu, x, result); + } +} + + +/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ + +int +gsl_sf_hyperg_0F1_e(double c, double x, gsl_sf_result * result) +{ + const double rintc = floor(c + 0.5); + const int c_neg_integer = (c < 0.0 && fabs(c - rintc) < locEPS); + + /* CHECK_POINTER(result) */ + + if(c == 0.0 || c_neg_integer) { + DOMAIN_ERROR(result); + } + else if(x < 0.0) { + gsl_sf_result Jcm1; + gsl_sf_result lg_c; + double sgn; + int stat_g = gsl_sf_lngamma_sgn_e(c, &lg_c, &sgn); + int stat_J = hyperg_0F1_bessel_J(c-1.0, 2.0*sqrt(-x), &Jcm1); + if(stat_g != GSL_SUCCESS) { + result->val = 0.0; + result->err = 0.0; + return stat_g; + } + else if(Jcm1.val == 0.0) { + result->val = 0.0; + result->err = 0.0; + return stat_J; + } + else { + const double tl = log(-x)*0.5*(1.0-c); + double ln_pre_val = lg_c.val + tl; + double ln_pre_err = lg_c.err + 2.0 * GSL_DBL_EPSILON * fabs(tl); + return gsl_sf_exp_mult_err_e(ln_pre_val, ln_pre_err, + sgn*Jcm1.val, Jcm1.err, + result); + } + } + else if(x == 0.0) { + result->val = 1.0; + result->err = 1.0; + return GSL_SUCCESS; + } + else { + gsl_sf_result Icm1; + gsl_sf_result lg_c; + double sgn; + int stat_g = gsl_sf_lngamma_sgn_e(c, &lg_c, &sgn); + int stat_I = hyperg_0F1_bessel_I(c-1.0, 2.0*sqrt(x), &Icm1); + if(stat_g != GSL_SUCCESS) { + result->val = 0.0; + result->err = 0.0; + return stat_g; + } + else if(Icm1.val == 0.0) { + result->val = 0.0; + result->err = 0.0; + return stat_I; + } + else { + const double tl = log(x)*0.5*(1.0-c); + const double ln_pre_val = lg_c.val + tl; + const double ln_pre_err = lg_c.err + 2.0 * GSL_DBL_EPSILON * fabs(tl); + return gsl_sf_exp_mult_err_e(ln_pre_val, ln_pre_err, + sgn*Icm1.val, Icm1.err, + result); + } + } +} + + +/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ + +#include "eval.h" + +double gsl_sf_hyperg_0F1(const double c, const double x) +{ + EVAL_RESULT(gsl_sf_hyperg_0F1_e(c, x, &result)); +} |