| /* randist/gausstail.c |
| * |
| * Copyright (C) 1996, 1997, 1998, 1999, 2000 James Theiler, Brian Gough |
| * |
| * 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. |
| */ |
| |
| #include <config.h> |
| #include <math.h> |
| #include <gsl/gsl_math.h> |
| #include <gsl/gsl_rng.h> |
| #include <gsl/gsl_randist.h> |
| #include <gsl/gsl_sf_erf.h> |
| |
| double |
| gsl_ran_gaussian_tail (const gsl_rng * r, const double a, const double sigma) |
| { |
| /* Returns a gaussian random variable larger than a |
| * This implementation does one-sided upper-tailed deviates. |
| */ |
| |
| double s = a / sigma; |
| |
| if (s < 1) |
| { |
| /* For small s, use a direct rejection method. The limit s < 1 |
| can be adjusted to optimise the overall efficiency */ |
| |
| double x; |
| |
| do |
| { |
| x = gsl_ran_gaussian (r, 1.0); |
| } |
| while (x < s); |
| return x * sigma; |
| } |
| else |
| { |
| /* Use the "supertail" deviates from the last two steps |
| * of Marsaglia's rectangle-wedge-tail method, as described |
| * in Knuth, v2, 3rd ed, pp 123-128. (See also exercise 11, p139, |
| * and the solution, p586.) |
| */ |
| |
| double u, v, x; |
| |
| do |
| { |
| u = gsl_rng_uniform (r); |
| do |
| { |
| v = gsl_rng_uniform (r); |
| } |
| while (v == 0.0); |
| x = sqrt (s * s - 2 * log (v)); |
| } |
| while (x * u > s); |
| return x * sigma; |
| } |
| } |
| |
| double |
| gsl_ran_gaussian_tail_pdf (const double x, const double a, const double sigma) |
| { |
| if (x < a) |
| { |
| return 0; |
| } |
| else |
| { |
| double N, p; |
| double u = x / sigma ; |
| |
| double f = gsl_sf_erfc (a / (sqrt (2.0) * sigma)); |
| |
| N = 0.5 * f; |
| |
| p = (1 / (N * sqrt (2 * M_PI) * sigma)) * exp (-u * u / 2); |
| |
| return p; |
| } |
| } |
| |
| double |
| gsl_ran_ugaussian_tail (const gsl_rng * r, const double a) |
| { |
| return gsl_ran_gaussian_tail (r, a, 1.0) ; |
| } |
| |
| double |
| gsl_ran_ugaussian_tail_pdf (const double x, const double a) |
| { |
| return gsl_ran_gaussian_tail_pdf (x, a, 1.0) ; |
| } |