/* randist/poisson.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 <config.h>

#include <math.h>

#include <gsl/gsl_sf_gamma.h>

#include <gsl/gsl_rng.h>

#include <gsl/gsl_randist.h>

/* The poisson distribution has the form

   p(n) = (mu^n / n!) exp(-mu) 

   for n = 0, 1, 2, ... . The method used here is the one from Knuth. */

unsigned int

gsl_ran_poisson (const gsl_rng * r, double mu)

{

  double emu;

  double prod = 1.0;

  unsigned int k = 0;

  while (mu > 10)

    {

      unsigned int m = mu * (7.0 / 8.0);

      double X = gsl_ran_gamma_int (r, m);

      if (X >= mu)

        {

          return k + gsl_ran_binomial (r, mu / X, m - 1);

        }

      else

        {

          k += m;

          mu -= X; 

        }

    }

  /* This following method works well when mu is small */

  emu = exp (-mu);

  do

    {

      prod *= gsl_rng_uniform (r);

      k++;

    }

  while (prod > emu);

  return k - 1;

}

void

gsl_ran_poisson_array (const gsl_rng * r, size_t n, unsigned int array[],

                       double mu)

{

  size_t i;

  for (i = 0; i < n; i++)

    {

      array[i] = gsl_ran_poisson (r, mu);

    }

  return;

}

double

gsl_ran_poisson_pdf (const unsigned int k, const double mu)

{

  double p;

  double lf = gsl_sf_lnfact (k); 

  p = exp (log (mu) * k - lf - mu);

  return p;

}