diff options
Diffstat (limited to 'gsl-1.9/specfunc/bessel_Knu.c')
| -rw-r--r-- | gsl-1.9/specfunc/bessel_Knu.c | 164 |
1 files changed, 164 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/bessel_Knu.c b/gsl-1.9/specfunc/bessel_Knu.c new file mode 100644 index 0000000..c9d5b85 --- /dev/null +++ b/gsl-1.9/specfunc/bessel_Knu.c @@ -0,0 +1,164 @@ +/* specfunc/bessel_Knu.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_Knu_scaled_e(const double nu, const double x, gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if(x <= 0.0 || nu < 0.0) { + DOMAIN_ERROR(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; + int n; + + if(x < 2.0) { + gsl_sf_bessel_K_scaled_temme(mu, x, &K_mu, &K_mup1, &Kp_mu); + } + else { + 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; + } + + result->val = K_nu; + result->err = 2.0 * GSL_DBL_EPSILON * (N + 4.0) * fabs(result->val); + return GSL_SUCCESS; + } +} + + +int +gsl_sf_bessel_Knu_e(const double nu, const double x, gsl_sf_result * result) +{ + gsl_sf_result b; + int stat_K = gsl_sf_bessel_Knu_scaled_e(nu, x, &b); + int stat_e = gsl_sf_exp_mult_err_e(-x, 0.0, b.val, b.err, result); + return GSL_ERROR_SELECT_2(stat_e, stat_K); +} + + +int +gsl_sf_bessel_lnKnu_e(const double nu, const double x, gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if(x <= 0.0 || nu < 0.0) { + DOMAIN_ERROR(result); + } + else if(nu == 0.0) { + gsl_sf_result K_scaled; + /* This cannot underflow, and + * it will not throw GSL_EDOM + * since that is already checked. + */ + gsl_sf_bessel_K0_scaled_e(x, &K_scaled); + result->val = -x + log(fabs(K_scaled.val)); + result->err = GSL_DBL_EPSILON * fabs(x) + fabs(K_scaled.err/K_scaled.val); + result->err += GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } + else if(x < 2.0 && nu > 1.0) { + /* Make use of the inequality + * Knu(x) <= 1/2 (2/x)^nu Gamma(nu), + * which follows from the integral representation + * [Abramowitz+Stegun, 9.6.23 (2)]. With this + * we decide whether or not there is an overflow + * problem because x is small. + */ + double ln_bound; + gsl_sf_result lg_nu; + gsl_sf_lngamma_e(nu, &lg_nu); + ln_bound = -M_LN2 - nu*log(0.5*x) + lg_nu.val; + if(ln_bound > GSL_LOG_DBL_MAX - 20.0) { + /* x must be very small or nu very large (or both). + */ + double xi = 0.25*x*x; + double sum = 1.0 - xi/(nu-1.0); + if(nu > 2.0) sum += (xi/(nu-1.0)) * (xi/(nu-2.0)); + result->val = ln_bound + log(sum); + result->err = lg_nu.err; + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } + /* can drop-through here */ + } + + + { + /* We passed the above tests, so no problem. + * Evaluate as usual. Note the possible drop-through + * in the above code! + */ + gsl_sf_result K_scaled; + gsl_sf_bessel_Knu_scaled_e(nu, x, &K_scaled); + result->val = -x + log(fabs(K_scaled.val)); + result->err = GSL_DBL_EPSILON * fabs(x) + fabs(K_scaled.err/K_scaled.val); + result->err += GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } +} + + +/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ + +#include "eval.h" + +double gsl_sf_bessel_Knu_scaled(const double nu, const double x) +{ + EVAL_RESULT(gsl_sf_bessel_Knu_scaled_e(nu, x, &result)); +} + +double gsl_sf_bessel_Knu(const double nu, const double x) +{ + EVAL_RESULT(gsl_sf_bessel_Knu_e(nu, x, &result)); +} + +double gsl_sf_bessel_lnKnu(const double nu, const double x) +{ + EVAL_RESULT(gsl_sf_bessel_lnKnu_e(nu, x, &result)); +} |