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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 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 "gsl__config.h"
- #include <math.h>
- #include "gsl_rng.h"
- #include "gsl_randist.h"
- #include "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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