diff options
Diffstat (limited to 'gsl-1.9/specfunc/beta_inc.c')
| -rw-r--r-- | gsl-1.9/specfunc/beta_inc.c | 180 |
1 files changed, 180 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/beta_inc.c b/gsl-1.9/specfunc/beta_inc.c new file mode 100644 index 0000000..bd840b6 --- /dev/null +++ b/gsl-1.9/specfunc/beta_inc.c @@ -0,0 +1,180 @@ +/* specfunc/beta_inc.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_log.h> +#include <gsl/gsl_sf_exp.h> +#include <gsl/gsl_sf_gamma.h> + +#include "error.h" +#include "check.h" + +static +int +beta_cont_frac( + const double a, + const double b, + const double x, + gsl_sf_result * result + ) +{ + const unsigned int max_iter = 512; /* control iterations */ + const double cutoff = 2.0 * GSL_DBL_MIN; /* control the zero cutoff */ + unsigned int iter_count = 0; + double cf; + + /* standard initialization for continued fraction */ + double num_term = 1.0; + double den_term = 1.0 - (a+b)*x/(a+1.0); + if (fabs(den_term) < cutoff) den_term = cutoff; + den_term = 1.0/den_term; + cf = den_term; + + while(iter_count < max_iter) { + const int k = iter_count + 1; + double coeff = k*(b-k)*x/(((a-1.0)+2*k)*(a+2*k)); + double delta_frac; + + /* first step */ + den_term = 1.0 + coeff*den_term; + num_term = 1.0 + coeff/num_term; + if(fabs(den_term) < cutoff) den_term = cutoff; + if(fabs(num_term) < cutoff) num_term = cutoff; + den_term = 1.0/den_term; + + delta_frac = den_term * num_term; + cf *= delta_frac; + + coeff = -(a+k)*(a+b+k)*x/((a+2*k)*(a+2*k+1.0)); + + /* second step */ + den_term = 1.0 + coeff*den_term; + num_term = 1.0 + coeff/num_term; + if(fabs(den_term) < cutoff) den_term = cutoff; + if(fabs(num_term) < cutoff) num_term = cutoff; + den_term = 1.0/den_term; + + delta_frac = den_term*num_term; + cf *= delta_frac; + + if(fabs(delta_frac-1.0) < 2.0*GSL_DBL_EPSILON) break; + + ++iter_count; + } + + result->val = cf; + result->err = iter_count * 4.0 * GSL_DBL_EPSILON * fabs(cf); + + if(iter_count >= max_iter) + GSL_ERROR ("error", GSL_EMAXITER); + else + return GSL_SUCCESS; +} + + + +/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ + +int +gsl_sf_beta_inc_e( + const double a, + const double b, + const double x, + gsl_sf_result * result + ) +{ + if(a <= 0.0 || b <= 0.0 || x < 0.0 || x > 1.0) { + DOMAIN_ERROR(result); + } + else if(x == 0.0) { + result->val = 0.0; + result->err = 0.0; + return GSL_SUCCESS; + } + else if(x == 1.0) { + result->val = 1.0; + result->err = 0.0; + return GSL_SUCCESS; + } + else { + gsl_sf_result ln_beta; + gsl_sf_result ln_x; + gsl_sf_result ln_1mx; + gsl_sf_result prefactor; + const int stat_ln_beta = gsl_sf_lnbeta_e(a, b, &ln_beta); + const int stat_ln_1mx = gsl_sf_log_1plusx_e(-x, &ln_1mx); + const int stat_ln_x = gsl_sf_log_e(x, &ln_x); + const int stat_ln = GSL_ERROR_SELECT_3(stat_ln_beta, stat_ln_1mx, stat_ln_x); + + const double ln_pre_val = -ln_beta.val + a * ln_x.val + b * ln_1mx.val; + const double ln_pre_err = ln_beta.err + fabs(a*ln_x.err) + fabs(b*ln_1mx.err); + const int stat_exp = gsl_sf_exp_err_e(ln_pre_val, ln_pre_err, &prefactor); + + if(stat_ln != GSL_SUCCESS) { + result->val = 0.0; + result->err = 0.0; + GSL_ERROR ("error", GSL_ESANITY); + } + + if(x < (a + 1.0)/(a+b+2.0)) { + /* Apply continued fraction directly. */ + gsl_sf_result cf; + const int stat_cf = beta_cont_frac(a, b, x, &cf); + int stat; + result->val = prefactor.val * cf.val / a; + result->err = (fabs(prefactor.err * cf.val) + fabs(prefactor.val * cf.err))/a; + + stat = GSL_ERROR_SELECT_2(stat_exp, stat_cf); + if(stat == GSL_SUCCESS) { + CHECK_UNDERFLOW(result); + } + return stat; + } + else { + /* Apply continued fraction after hypergeometric transformation. */ + gsl_sf_result cf; + const int stat_cf = beta_cont_frac(b, a, 1.0-x, &cf); + int stat; + const double term = prefactor.val * cf.val / b; + result->val = 1.0 - term; + result->err = fabs(prefactor.err * cf.val)/b; + result->err += fabs(prefactor.val * cf.err)/b; + result->err += 2.0 * GSL_DBL_EPSILON * (1.0 + fabs(term)); + stat = GSL_ERROR_SELECT_2(stat_exp, stat_cf); + if(stat == GSL_SUCCESS) { + CHECK_UNDERFLOW(result); + } + return stat; + } + } +} + + +/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ + +#include "eval.h" + +double gsl_sf_beta_inc(const double a, const double b, const double x) +{ + EVAL_RESULT(gsl_sf_beta_inc_e(a, b, x, &result)); +} |