/* randist/multinomial.c

 * 

 * Copyright (C) 2002 Gavin E. Crooks <gec@compbio.berkeley.edu>

 * 

 * 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 multinomial distribution has the form

                                      N!           n_1  n_2      n_K

   prob(n_1, n_2, ... n_K) = -------------------- p_1  p_2  ... p_K

                             (n_1! n_2! ... n_K!) 

   where n_1, n_2, ... n_K are nonnegative integers, sum_{k=1,K} n_k = N,

   and p = (p_1, p_2, ..., p_K) is a probability distribution. 

   Random variates are generated using the conditional binomial method.

   This scales well with N and does not require a setup step.

   Ref: 

   C.S. David, The computer generation of multinomial random variates,

   Comp. Stat. Data Anal. 16 (1993) 205-217

*/

void

gsl_ran_multinomial (const gsl_rng * r, const size_t K,

                     const unsigned int N, const double p[], unsigned int n[])

{

  size_t k;

  double norm = 0.0;

  double sum_p = 0.0;

  unsigned int sum_n = 0;

  /* p[k] may contain non-negative weights that do not sum to 1.0.

   * Even a probability distribution will not exactly sum to 1.0

   * due to rounding errors. 

   */

  for (k = 0; k < K; k++)

    {

      norm += p[k];

    }

  for (k = 0; k < K; k++)

    {

      if (p[k] > 0.0)

        {

          n[k] = gsl_ran_binomial (r, p[k] / (norm - sum_p), N - sum_n);

        }

      else

        {

          n[k] = 0;

        }

      sum_p += p[k];

      sum_n += n[k];

    }

}

double

gsl_ran_multinomial_pdf (const size_t K,

                         const double p[], const unsigned int n[])

{

  return exp (gsl_ran_multinomial_lnpdf (K, p, n));

}

double

gsl_ran_multinomial_lnpdf (const size_t K,

                           const double p[], const unsigned int n[])

{

  size_t k;

  unsigned int N = 0;

  double log_pdf = 0.0;

  double norm = 0.0;

  for (k = 0; k < K; k++)

    {

      N += n[k];

    }

  for (k = 0; k < K; k++)

    {

      norm += p[k];

    }

  log_pdf = gsl_sf_lnfact (N);

  for (k = 0; k < K; k++)

    {

      /* Handle case where n[k]==0 and p[k]==0 */

      if (n[k] > 0) 

        {

          log_pdf += log (p[k] / norm) * n[k] - gsl_sf_lnfact (n[k]);

        }

    }

  return log_pdf;

}