/* randist/dirichlet.c *  * 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_math.h>#include <gsl/gsl_rng.h>#include <gsl/gsl_randist.h>#include <gsl/gsl_sf_gamma.h>/* The Dirichlet probability distribution of order K-1 is      p(\theta_1,...,\theta_K) d\theta_1 ... d\theta_K =         (1/Z) \prod_i=1,K \theta_i^{alpha_i - 1} \delta(1 -\sum_i=1,K \theta_i)   The normalization factor Z can be expressed in terms of gamma functions:      Z = {\prod_i=1,K \Gamma(\alpha_i)} / {\Gamma( \sum_i=1,K \alpha_i)}     The K constants, \alpha_1,...,\alpha_K, must be positive. The K parameters,    \theta_1,...,\theta_K are nonnegative and sum to 1.   The random variates are generated by sampling K values from gamma   distributions with parameters a=\alpha_i, b=1, and renormalizing.    See A.M. Law, W.D. Kelton, Simulation Modeling and Analysis (1991).   Gavin E. Crooks <gec@compbio.berkeley.edu> (2002)*/voidgsl_ran_dirichlet (const gsl_rng * r, const size_t K,                   const double alpha[], double theta[]){  size_t i;  double norm = 0.0;  for (i = 0; i < K; i++)    {      theta[i] = gsl_ran_gamma (r, alpha[i], 1.0);    }  for (i = 0; i < K; i++)    {      norm += theta[i];    }  for (i = 0; i < K; i++)    {      theta[i] /= norm;    }}doublegsl_ran_dirichlet_pdf (const size_t K,                       const double alpha[], const double theta[]){  return exp (gsl_ran_dirichlet_lnpdf (K, alpha, theta));}doublegsl_ran_dirichlet_lnpdf (const size_t K,                         const double alpha[], const double theta[]){  /*We calculate the log of the pdf to minimize the possibility of overflow */  size_t i;  double log_p = 0.0;  double sum_alpha = 0.0;  for (i = 0; i < K; i++)    {      log_p += (alpha[i] - 1.0) * log (theta[i]);    }  for (i = 0; i < K; i++)    {      sum_alpha += alpha[i];    }  log_p += gsl_sf_lngamma (sum_alpha);  for (i = 0; i < K; i++)    {      log_p -= gsl_sf_lngamma (alpha[i]);    }  return log_p;}