/* randist/hyperg.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_rng.h>

#include <gsl/gsl_randist.h>

#include <gsl/gsl_sf_gamma.h>

/* The hypergeometric distribution has the form,

   prob(k) =  choose(n1,t) choose(n2, t-k) / choose(n1+n2,t)

   where choose(a,b) = a!/(b!(a-b)!) 

   n1 + n2 is the total population (tagged plus untagged)

   n1 is the tagged population

   t is the number of samples taken (without replacement)

   k is the number of tagged samples found

*/

unsigned int

gsl_ran_hypergeometric (const gsl_rng * r, unsigned int n1, unsigned int n2, 

                        unsigned int t)

{

  const unsigned int n = n1 + n2;

  unsigned int i = 0;

  unsigned int a = n1;

  unsigned int b = n1 + n2;

  unsigned int k = 0;

  if (t > n)

    {

      t = n ;

    }

  if (t < n / 2) 

    {

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

        {

          double u = gsl_rng_uniform(r) ;

          if (b * u < a)

            {

              k++ ;

              if (k == n1)

                return k ;

              a-- ;

            }

          b-- ;

        }

      return k;

    }

  else

    {

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

        {

          double u = gsl_rng_uniform(r) ;

          if (b * u < a)

            {

              k++ ;

              if (k == n1)

                return n1 - k ;

              a-- ;

            }

          b-- ;

        }

      return n1 - k;

    }

}

double

gsl_ran_hypergeometric_pdf (const unsigned int k, 

                            const unsigned int n1, 

                            const unsigned int n2, 

                            unsigned int t)

{

  if (t > n1 + n2)

    {

      t = n1 + n2 ;

    }

  if (k > n1 || k > t)

    {

      return 0 ;

    }

  else if (t > n2 && k + n2 < t )

    {

      return 0 ;

    }

  else 

    {

      double p;

      double c1 = gsl_sf_lnchoose(n1,k);

      double c2 = gsl_sf_lnchoose(n2,t-k);

      double c3 = gsl_sf_lnchoose(n1+n2,t);

      p = exp(c1 + c2 - c3) ;

      return p;

    }

}