| /* randist/rayleigh.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_rng.h> |
| #include <gsl/gsl_randist.h> |
| |
| /* The Rayleigh distribution has the form |
| |
| p(x) dx = (x / sigma^2) exp(-x^2/(2 sigma^2)) dx |
| |
| for x = 0 ... +infty */ |
| |
| double |
| gsl_ran_rayleigh (const gsl_rng * r, const double sigma) |
| { |
| double u = gsl_rng_uniform_pos (r); |
| |
| return sigma * sqrt(-2.0 * log (u)); |
| } |
| |
| double |
| gsl_ran_rayleigh_pdf (const double x, const double sigma) |
| { |
| if (x < 0) |
| { |
| return 0 ; |
| } |
| else |
| { |
| double u = x / sigma ; |
| double p = (u / sigma) * exp(-u * u / 2.0) ; |
| |
| return p; |
| } |
| } |
| |
| /* The Rayleigh tail distribution has the form |
| |
| p(x) dx = (x / sigma^2) exp((a^2 - x^2)/(2 sigma^2)) dx |
| |
| for x = a ... +infty */ |
| |
| double |
| gsl_ran_rayleigh_tail (const gsl_rng * r, const double a, const double sigma) |
| { |
| double u = gsl_rng_uniform_pos (r); |
| |
| return sqrt(a * a - 2.0 * sigma * sigma * log (u)); |
| } |
| |
| double |
| gsl_ran_rayleigh_tail_pdf (const double x, const double a, const double sigma) |
| { |
| if (x < a) |
| { |
| return 0 ; |
| } |
| else |
| { |
| double u = x / sigma ; |
| double v = a / sigma ; |
| |
| double p = (u / sigma) * exp((v + u) * (v - u) / 2.0) ; |
| |
| return p; |
| } |
| } |