dirichlet_rng.hpp

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#ifndef STAN_MATH_PRIM_PROB_DIRICHLET_RNG_HPP
#define STAN_MATH_PRIM_PROB_DIRICHLET_RNG_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/log_sum_exp.hpp>
#include <boost/math/special_functions/gamma.hpp>
#include <boost/random/gamma_distribution.hpp>
#include <boost/random/uniform_real_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <class RNG>
inline Eigen::VectorXd dirichlet_rng(
    const Eigen::Matrix<double, Eigen::Dynamic, 1>& alpha, RNG& rng) {
  using boost::gamma_distribution;
  using boost::variate_generator;
  using boost::random::uniform_real_distribution;
  using Eigen::VectorXd;
  using std::exp;
  using std::log;
 
  // separate algorithm if any parameter is less than 1
  if (alpha.minCoeff() < 1) {
    variate_generator<RNG&, uniform_real_distribution<> > uniform_rng(
        rng, uniform_real_distribution<>(0.0, 1.0));
    VectorXd log_y(alpha.size());
    for (int i = 0; i < alpha.size(); ++i) {
      variate_generator<RNG&, gamma_distribution<> > gamma_rng(
          rng, gamma_distribution<>(alpha(i) + 1, 1));
      double log_u = log(uniform_rng());
      log_y(i) = log(gamma_rng()) + log_u / alpha(i);
    }
    double log_sum_y = log_sum_exp(log_y);
    VectorXd theta(alpha.size());
    for (int i = 0; i < alpha.size(); ++i) {
      theta(i) = exp(log_y(i) - log_sum_y);
    }
    return theta;
  }
 
  // standard normalized gamma algorithm
  Eigen::VectorXd y(alpha.rows());
  for (int i = 0; i < alpha.rows(); i++) {
    variate_generator<RNG&, gamma_distribution<> > gamma_rng(
        rng, gamma_distribution<>(alpha(i, 0), 1e-7));
    y(i) = gamma_rng();
  }
  return y / y.sum();
}
 
}  // namespace math
}  // namespace stan
#endif