| /* 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; |
| } |