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/* randist/logarithmic.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>
/* Logarithmic distribution
prob(n) = p^n / (n log(1/(1-p)) for n = 1, 2, 3, ...
We use Kemp's second accelerated generator, from Luc Devroye's book
on "Non-Uniform Random Variate Generation", Springer */
unsigned int
gsl_ran_logarithmic (const gsl_rng * r, const double p)
{
double c = log (1-p) ;
double v = gsl_rng_uniform_pos (r);
if (v >= p)
{
return 1 ;
}
else
{
double u = gsl_rng_uniform_pos (r);
double q = 1 - exp (c * u);
if (v <= q*q)
{
double x = 1 + log(v)/log(q) ;
return x ;
}
else if (v <= q)
{
return 2;
}
else
{
return 1 ;
}
}
}
double
gsl_ran_logarithmic_pdf (const unsigned int k, const double p)
{
if (k == 0)
{
return 0 ;
}
else
{
double P = pow(p, (double)k) / (double) k / log(1/(1-p)) ;
return P;
}
}
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