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/* randist/rayleigh.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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#include <config.h>
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#include <math.h>
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#include <gsl/gsl_rng.h>
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#include <gsl/gsl_randist.h>
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/* The Rayleigh distribution has the form
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p(x) dx = (x / sigma^2) exp(-x^2/(2 sigma^2)) dx
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for x = 0 ... +infty */
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double
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gsl_ran_rayleigh (const gsl_rng * r, const double sigma)
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{
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double u = gsl_rng_uniform_pos (r);
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return sigma * sqrt(-2.0 * log (u));
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}
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double
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gsl_ran_rayleigh_pdf (const double x, const double sigma)
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{
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if (x < 0)
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{
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return 0 ;
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}
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else
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{
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double u = x / sigma ;
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double p = (u / sigma) * exp(-u * u / 2.0) ;
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return p;
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}
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}
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/* The Rayleigh tail distribution has the form
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p(x) dx = (x / sigma^2) exp((a^2 - x^2)/(2 sigma^2)) dx
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for x = a ... +infty */
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double
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gsl_ran_rayleigh_tail (const gsl_rng * r, const double a, const double sigma)
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{
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double u = gsl_rng_uniform_pos (r);
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return sqrt(a * a - 2.0 * sigma * sigma * log (u));
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}
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double
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gsl_ran_rayleigh_tail_pdf (const double x, const double a, const double sigma)
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{
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if (x < a)
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{
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return 0 ;
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}
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else
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{
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double u = x / sigma ;
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double v = a / sigma ;
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double p = (u / sigma) * exp((v + u) * (v - u) / 2.0) ;
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return p;
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}
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}
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