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 Sourcecode: gsl version 1.101.10-41.111.11+dfsg1.11+dfsg-11.11+dfsg-21.11-21.12+dfsg1.12+dfsg-11.13+dfsg1.13+dfsg-11.14+dfsg1.14+dfsg-11.15+dfsg1.15+dfsg-11.61.6-21.71.7-41.81.8-21.8-3build11.91.9-3

# dirichlet.c

/* randist/dirichlet.c
*
* This program is free software; you can redistribute it and/or modify
* 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)
*/

void
gsl_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;
}
}

double
gsl_ran_dirichlet_pdf (const size_t K,
const double alpha[], const double theta[])
{
return exp (gsl_ran_dirichlet_lnpdf (K, alpha, theta));
}

double
gsl_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;
}


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