multi_student_t_rng.hpp

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#ifndef STAN_MATH_PRIM_PROB_MULTI_STUDENT_T_RNG_HPP
#define STAN_MATH_PRIM_PROB_MULTI_STUDENT_T_RNG_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/as_column_vector_or_scalar.hpp>
#include <stan/math/prim/fun/size_mvt.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
#include <stan/math/prim/fun/vector_seq_view.hpp>
#include <stan/math/prim/prob/inv_gamma_rng.hpp>
#include <boost/random/normal_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <typename T_loc, class RNG>
inline typename StdVectorBuilder<true, Eigen::VectorXd, T_loc>::type
multi_student_t_rng(
    double nu, const T_loc& mu,
    const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>& S, RNG& rng) {
  using boost::normal_distribution;
  using boost::variate_generator;
  using boost::random::gamma_distribution;
 
  static constexpr const char* function = "multi_student_t_rng";
  check_not_nan(function, "Degrees of freedom parameter", nu);
  check_positive(function, "Degrees of freedom parameter", nu);
  check_positive(function, "Covariance matrix rows", S.rows());
  vector_seq_view<T_loc> mu_vec(mu);
  size_t size_mu = mu_vec[0].size();
 
  size_t N = size_mvt(mu);
  for (size_t i = 1; i < N; i++) {
    check_size_match(function,
                     "Size of one of the vectors of "
                     "the location variable",
                     mu_vec[i].size(),
                     "Size of the first vector of the "
                     "location variable",
                     size_mu);
  }
 
  check_size_match(function, "Size of random variable", size_mu,
                   "rows of scale parameter", S.rows());
 
  for (size_t i = 0; i < N; i++) {
    check_finite(function, "Location parameter", mu_vec[i]);
  }
  const auto& S_ref = to_ref(S);
  check_not_nan(function, "Covariance matrix", S_ref);
  check_symmetric(function, "Covariance matrix", S_ref);
  Eigen::LLT<Eigen::MatrixXd> llt_of_S = S_ref.llt();
  check_pos_definite(function, "covariance matrix argument", llt_of_S);
 
  StdVectorBuilder<true, Eigen::VectorXd, T_loc> output(N);
 
  variate_generator<RNG&, normal_distribution<> > std_normal_rng(
      rng, normal_distribution<>(0, 1));
 
  double w = inv_gamma_rng(nu / 2, nu / 2, rng);
  for (size_t n = 0; n < N; ++n) {
    Eigen::VectorXd z(S.cols());
    for (int i = 0; i < S.cols(); i++) {
      z(i) = std_normal_rng();
    }
    z *= std::sqrt(w);
    output[n] = as_column_vector_or_scalar(mu_vec[n]) + llt_of_S.matrixL() * z;
  }
 
  return output.data();
}
 
}  // namespace math
}  // namespace stan
#endif