1 #ifndef STAN_MATH_PRIM_PROB_MULTI_STUDENT_T_LPDF_HPP
2 #define STAN_MATH_PRIM_PROB_MULTI_STUDENT_T_LPDF_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/constants.hpp>
8 #include <stan/math/prim/fun/is_inf.hpp>
9 #include <stan/math/prim/fun/log.hpp>
10 #include <stan/math/prim/fun/log1p.hpp>
11 #include <stan/math/prim/fun/lgamma.hpp>
12 #include <stan/math/prim/fun/max_size_mvt.hpp>
13 #include <stan/math/prim/fun/size_mvt.hpp>
14 #include <stan/math/prim/fun/to_ref.hpp>
15 #include <stan/math/prim/fun/vector_seq_view.hpp>
16 #include <stan/math/prim/prob/multi_normal_log.hpp>
17 #include <cmath>
18 #include <cstdlib>
19 
20 namespace stan {
21 namespace math {
22 
23 /** \ingroup multivar_dists
24  * Return the log of the multivariate Student t distribution
25  * at the specified arguments.
26  *
27  * @tparam propto Carry out calculations up to a proportion
28  */
29 template <bool propto, typename T_y, typename T_dof, typename T_loc,
30           typename T_scale>
multi_student_t_lpdf(const T_y & y,const T_dof & nu,const T_loc & mu,const T_scale & Sigma)31 return_type_t<T_y, T_dof, T_loc, T_scale> multi_student_t_lpdf(
32     const T_y& y, const T_dof& nu, const T_loc& mu, const T_scale& Sigma) {
33   using T_scale_elem = typename scalar_type<T_scale>::type;
34   using lp_type = return_type_t<T_y, T_dof, T_loc, T_scale>;
35   using Eigen::Matrix;
36   using std::log;
37   using std::vector;
38   static const char* function = "multi_student_t";
39   check_not_nan(function, "Degrees of freedom parameter", nu);
40   check_positive(function, "Degrees of freedom parameter", nu);
41 
42   if (is_inf(nu)) {
43     return multi_normal_log(y, mu, Sigma);
44   }
45 
46   size_t number_of_y = size_mvt(y);
47   size_t number_of_mu = size_mvt(mu);
48   if (number_of_y == 0 || number_of_mu == 0) {
49     return 0;
50   }
51   check_consistent_sizes_mvt(function, "y", y, "mu", mu);
52 
53   vector_seq_view<T_y> y_vec(y);
54   vector_seq_view<T_loc> mu_vec(mu);
55   size_t size_vec = max_size_mvt(y, mu);
56 
57   int size_y = y_vec[0].size();
58   int size_mu = mu_vec[0].size();
59   if (size_vec > 1) {
60     int size_y_old = size_y;
61     int size_y_new;
62     for (size_t i = 1, size_mvt_y = size_mvt(y); i < size_mvt_y; i++) {
63       int size_y_new = y_vec[i].size();
64       check_size_match(
65           function, "Size of one of the vectors of the random variable",
66           size_y_new, "Size of another vector of the random variable",
67           size_y_old);
68       size_y_old = size_y_new;
69     }
70     int size_mu_old = size_mu;
71     int size_mu_new;
72     for (size_t i = 1, size_mvt_mu = size_mvt(mu); i < size_mvt_mu; i++) {
73       int size_mu_new = mu_vec[i].size();
74       check_size_match(function,
75                        "Size of one of the vectors "
76                        "of the location variable",
77                        size_mu_new,
78                        "Size of another vector of "
79                        "the location variable",
80                        size_mu_old);
81       size_mu_old = size_mu_new;
82     }
83     (void)size_y_old;
84     (void)size_y_new;
85     (void)size_mu_old;
86     (void)size_mu_new;
87   }
88 
89   check_size_match(function, "Size of random variable", size_y,
90                    "size of location parameter", size_mu);
91   check_size_match(function, "Size of random variable", size_y,
92                    "rows of scale parameter", Sigma.rows());
93   check_size_match(function, "Size of random variable", size_y,
94                    "columns of scale parameter", Sigma.cols());
95 
96   for (size_t i = 0; i < size_vec; i++) {
97     check_finite(function, "Location parameter", mu_vec[i]);
98     check_not_nan(function, "Random variable", y_vec[i]);
99   }
100   const auto& Sigma_ref = to_ref(Sigma);
101   check_symmetric(function, "Scale parameter", Sigma_ref);
102 
103   auto ldlt_Sigma = make_ldlt_factor(Sigma_ref);
104   check_ldlt_factor(function, "LDLT_Factor of scale parameter", ldlt_Sigma);
105 
106   if (size_y == 0) {
107     return 0;
108   }
109 
110   lp_type lp(0);
111 
112   if (include_summand<propto, T_dof>::value) {
113     lp += lgamma(0.5 * (nu + size_y)) * size_vec;
114     lp -= lgamma(0.5 * nu) * size_vec;
115     lp -= (0.5 * size_y) * log(nu) * size_vec;
116   }
117 
118   if (include_summand<propto>::value) {
119     lp -= (0.5 * size_y) * LOG_PI * size_vec;
120   }
121 
122   using Eigen::Array;
123 
124   if (include_summand<propto, T_scale_elem>::value) {
125     lp -= 0.5 * log_determinant_ldlt(ldlt_Sigma) * size_vec;
126   }
127 
128   if (include_summand<propto, T_y, T_dof, T_loc, T_scale_elem>::value) {
129     lp_type sum_lp_vec(0.0);
130     for (size_t i = 0; i < size_vec; i++) {
131       const auto& y_col = as_column_vector_or_scalar(y_vec[i]);
132       const auto& mu_col = as_column_vector_or_scalar(mu_vec[i]);
133       sum_lp_vec
134           += log1p(trace_inv_quad_form_ldlt(ldlt_Sigma, y_col - mu_col) / nu);
135     }
136     lp -= 0.5 * (nu + size_y) * sum_lp_vec;
137   }
138   return lp;
139 }
140 
141 template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
multi_student_t_lpdf(const T_y & y,const T_dof & nu,const T_loc & mu,const T_scale & Sigma)142 inline return_type_t<T_y, T_dof, T_loc, T_scale> multi_student_t_lpdf(
143     const T_y& y, const T_dof& nu, const T_loc& mu, const T_scale& Sigma) {
144   return multi_student_t_lpdf<false>(y, nu, mu, Sigma);
145 }
146 
147 }  // namespace math
148 }  // namespace stan
149 #endif
150