Stan Math Library  2.9.0
reverse mode automatic differentiation
dirichlet_rng.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_MAT_PROB_DIRICHLET_RNG_HPP
2 #define STAN_MATH_PRIM_MAT_PROB_DIRICHLET_RNG_HPP
3 
4 #include <boost/math/special_functions/gamma.hpp>
5 #include <boost/random/gamma_distribution.hpp>
6 #include <boost/random/uniform_real_distribution.hpp>
7 #include <boost/random/variate_generator.hpp>
8 
16 
17 #include <cmath>
18 
19 namespace stan {
20 
21  namespace math {
22 
44  template <class RNG>
45  inline Eigen::VectorXd
46  dirichlet_rng(const Eigen::Matrix<double, Eigen::Dynamic, 1>& alpha,
47  RNG& rng) {
48  using boost::variate_generator;
49  using boost::gamma_distribution;
50  using boost::random::uniform_real_distribution;
51  using Eigen::VectorXd;
52  using std::exp;
53  using std::log;
54 
55  // separate algorithm if any parameter is less than 1
56  if (alpha.minCoeff() < 1) {
57  variate_generator<RNG&, uniform_real_distribution<> >
58  uniform_rng(rng, uniform_real_distribution<>(0.0, 1.0));
59  VectorXd log_y(alpha.size());
60  for (int i = 0; i < alpha.size(); ++i) {
61  variate_generator<RNG&, gamma_distribution<> >
62  gamma_rng(rng, gamma_distribution<>(alpha(i) + 1, 1));
63  double log_u = log(uniform_rng());
64  log_y(i) = log(gamma_rng()) + log_u / alpha(i);
65  }
66  double log_sum_y = log_sum_exp(log_y);
67  VectorXd theta(alpha.size());
68  for (int i = 0; i < alpha.size(); ++i)
69  theta(i) = exp(log_y(i) - log_sum_y);
70  return theta;
71  }
72 
73  // standard normalized gamma algorithm
74  Eigen::VectorXd y(alpha.rows());
75  for (int i = 0; i < alpha.rows(); i++) {
76  variate_generator<RNG&, gamma_distribution<> >
77  gamma_rng(rng, gamma_distribution<>(alpha(i, 0), 1e-7));
78  y(i) = gamma_rng();
79  }
80  return y / y.sum();
81  }
82 
83  }
84 }
85 #endif
double gamma_rng(const double alpha, const double beta, RNG &rng)
Definition: gamma_rng.hpp:33
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
fvar< T > log_sum_exp(const std::vector< fvar< T > > &v)
Definition: log_sum_exp.hpp:14
Eigen::VectorXd dirichlet_rng(const Eigen::Matrix< double, Eigen::Dynamic, 1 > &alpha, RNG &rng)
Return a draw from a Dirichlet distribution with specified parameters and pseudo-random number genera...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
double uniform_rng(const double alpha, const double beta, RNG &rng)
Definition: uniform_rng.hpp:22
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:95

     [ Stan Home Page ] © 2011–2015, Stan Development Team.