1 #ifndef STAN_MATH_PRIM_PROB_MULTI_STUDENT_T_RNG_HPP
2 #define STAN_MATH_PRIM_PROB_MULTI_STUDENT_T_RNG_HPP
3
4 #include <stan/math/prim/meta.hpp>
5 #include <stan/math/prim/err.hpp>
6 #include <stan/math/prim/fun/as_column_vector_or_scalar.hpp>
7 #include <stan/math/prim/fun/size_mvt.hpp>
8 #include <stan/math/prim/fun/to_ref.hpp>
9 #include <stan/math/prim/fun/vector_seq_view.hpp>
10 #include <boost/random/normal_distribution.hpp>
11 #include <boost/random/gamma_distribution.hpp>
12 #include <boost/random/variate_generator.hpp>
13 #include <cmath>
14
15 namespace stan {
16 namespace math {
17
18 /** \ingroup multivar_dists
19 * Return a multivariate student-t random variate with the given degrees of
20 * freedom location and covariance using the specified random number generator.
21 *
22 * mu can be either an Eigen::VectorXd, an Eigen::RowVectorXd, or a std::vector
23 * of either of those types.
24 *
25 * @tparam T_loc Type of location parameter
26 * @tparam RNG Type of pseudo-random number generator
27 * @param nu degrees of freedom parameter
28 * @param mu (Sequence of) location parameter(s)
29 * @param S Covariance matrix
30 * @param rng random number generator
31 * @throw std::domain_error if S is not positive definite, any value in mu is
32 * not finite, nu is not positive, or nu is NaN
33 * @throw std::invalid_argument if the length of (each) mu is not equal to the
34 * number of rows and columns in S
35 */
36 template <typename T_loc, class RNG>
37 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)38 multi_student_t_rng(
39 double nu, const T_loc& mu,
40 const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>& S, RNG& rng) {
41 using boost::normal_distribution;
42 using boost::variate_generator;
43 using boost::random::gamma_distribution;
44
45 static const char* function = "multi_student_t_rng";
46 check_not_nan(function, "Degrees of freedom parameter", nu);
47 check_positive(function, "Degrees of freedom parameter", nu);
48 check_positive(function, "Covariance matrix rows", S.rows());
49 vector_seq_view<T_loc> mu_vec(mu);
50 size_t size_mu = mu_vec[0].size();
51
52 size_t N = size_mvt(mu);
53 for (size_t i = 1; i < N; i++) {
54 check_size_match(function,
55 "Size of one of the vectors of "
56 "the location variable",
57 mu_vec[i].size(),
58 "Size of the first vector of the "
59 "location variable",
60 size_mu);
61 }
62
63 for (size_t i = 0; i < N; i++) {
64 check_finite(function, "Location parameter", mu_vec[i]);
65 }
66 const auto& S_ref = to_ref(S);
67 check_not_nan(function, "Covariance matrix", S_ref);
68 check_symmetric(function, "Covariance matrix", S_ref);
69 Eigen::LLT<Eigen::MatrixXd> llt_of_S = S_ref.llt();
70 check_pos_definite(function, "covariance matrix argument", llt_of_S);
71
72 StdVectorBuilder<true, Eigen::VectorXd, T_loc> output(N);
73
74 variate_generator<RNG&, normal_distribution<> > std_normal_rng(
75 rng, normal_distribution<>(0, 1));
76 variate_generator<RNG&, gamma_distribution<> > gamma_rng(
77 rng, gamma_distribution<>(nu / 2.0, 2.0 / nu));
78
79 double w = 1.0 / gamma_rng();
80 for (size_t n = 0; n < N; ++n) {
81 Eigen::VectorXd z(S.cols());
82 for (int i = 0; i < S.cols(); i++) {
83 z(i) = std::sqrt(w) * std_normal_rng();
84 }
85
86 output[n] = as_column_vector_or_scalar(mu_vec[n]) + llt_of_S.matrixL() * z;
87 }
88
89 return output.data();
90 }
91
92 } // namespace math
93 } // namespace stan
94 #endif
95