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- /* randist/rayleigh.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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 "gsl__config.h"
- #include <math.h>
- #include "gsl_rng.h"
- #include "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;
- }
- }
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