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/* 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., 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++)
{
log_pdf -= gsl_sf_lnfact (n[k]);
}
for (k = 0; k < K; k++)
{
log_pdf += log (p[k] / norm) * n[k];
}
return log_pdf;
}
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