/* 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 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., 675 Mass Ave, Cambridge, MA 02139, 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*/voidgsl_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];    }}doublegsl_ran_multinomial_pdf (const size_t K,                         const double p[], const unsigned int n[]){  return exp (gsl_ran_multinomial_lnpdf (K, p, n));}doublegsl_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];    }  /* Note: n! == gamma(n+1) */  log_pdf = gsl_sf_lngamma (N + 1);  for (k = 0; k < K; k++)    {      log_pdf -= gsl_sf_lngamma (n[k] + 1);    }  for (k = 0; k < K; k++)    {      log_pdf += log (p[k] / norm) * n[k];    }  return log_pdf;}