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+/* 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, 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;
+}