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multi_student_t_log.hpp
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1 #ifndef STAN_MATH_PRIM_MAT_PROB_MULTI_STUDENT_T_LOG_HPP
2 #define STAN_MATH_PRIM_MAT_PROB_MULTI_STUDENT_T_LOG_HPP
3
4 #include <stan/math/prim/mat/err/check_ldlt_factor.hpp>
5 #include <stan/math/prim/mat/err/check_symmetric.hpp>
6 #include <stan/math/prim/mat/fun/multiply.hpp>
7 #include <stan/math/prim/mat/fun/dot_product.hpp>
8 #include <stan/math/prim/mat/fun/subtract.hpp>
9 #include <stan/math/prim/mat/meta/VectorViewMvt.hpp>
10 #include <stan/math/prim/mat/prob/multi_normal_log.hpp>
11 #include <stan/math/prim/scal/err/check_size_match.hpp>
12 #include <stan/math/prim/scal/err/check_finite.hpp>
13 #include <stan/math/prim/scal/err/check_not_nan.hpp>
14 #include <stan/math/prim/scal/err/check_positive.hpp>
15 #include <stan/math/prim/scal/fun/constants.hpp>
16 #include <stan/math/prim/scal/fun/is_inf.hpp>
17 #include <stan/math/prim/scal/fun/log1p.hpp>
18 #include <stan/math/prim/scal/meta/include_summand.hpp>
19 #include <boost/math/special_functions/gamma.hpp>
20 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 #include <cstdlib>
23
24 namespace stan {
25 namespace math {
26
33 template <bool propto,
34 typename T_y, typename T_dof, typename T_loc, typename T_scale>
35 typename return_type<T_y, T_dof, T_loc, T_scale>::type
36 multi_student_t_log(const T_y& y,
37 const T_dof& nu,
38 const T_loc& mu,
39 const T_scale& Sigma) {
40 static const char* function("multi_student_t");
41
42 using boost::math::lgamma;
43 using std::log;
44
45 typedef typename scalar_type<T_scale>::type T_scale_elem;
46 typedef typename return_type<T_y, T_dof, T_loc, T_scale>::type lp_type;
47 lp_type lp(0.0);
48
49 check_not_nan(function, "Degrees of freedom parameter", nu);
50 check_positive(function, "Degrees of freedom parameter", nu);
51
52 if (is_inf(nu))
53 return multi_normal_log(y, mu, Sigma);
54
55 using Eigen::Matrix;
56 using std::vector;
57 VectorViewMvt<const T_y> y_vec(y);
58 VectorViewMvt<const T_loc> mu_vec(mu);
59 size_t size_vec = max_size_mvt(y, mu);
60
61 int size_y = y_vec[0].size();
62 int size_mu = mu_vec[0].size();
63 if (size_vec > 1) {
64 int size_y_old = size_y;
65 int size_y_new;
66 for (size_t i = 1, size_ = length_mvt(y); i < size_; i++) {
67 int size_y_new = y_vec[i].size();
68 check_size_match(function,
69 "Size of one of the vectors of the random variable",
70 size_y_new,
71 "Size of another vector of the random variable",
72 size_y_old);
73 size_y_old = size_y_new;
74 }
75 int size_mu_old = size_mu;
76 int size_mu_new;
77 for (size_t i = 1, size_ = length_mvt(mu); i < size_; i++) {
78 int size_mu_new = mu_vec[i].size();
79 check_size_match(function,
80 "Size of one of the vectors "
81 "of the location variable",
82 size_mu_new,
83 "Size of another vector of "
84 "the location variable",
85 size_mu_old);
86 size_mu_old = size_mu_new;
87 }
88 (void) size_y_old;
89 (void) size_y_new;
90 (void) size_mu_old;
91 (void) size_mu_new;
92 }
93
94 check_size_match(function,
95 "Size of random variable", size_y,
96 "size of location parameter", size_mu);
97 check_size_match(function,
98 "Size of random variable", size_y,
99 "rows of scale parameter", Sigma.rows());
100 check_size_match(function,
101 "Size of random variable", size_y,
102 "columns of scale parameter", Sigma.cols());
103
104 for (size_t i = 0; i < size_vec; i++) {
105 check_finite(function, "Location parameter", mu_vec[i]);
106 check_not_nan(function, "Random variable", y_vec[i]);
107 }
108 check_symmetric(function, "Scale parameter", Sigma);
109
110 LDLT_factor<T_scale_elem,
111 Eigen::Dynamic, Eigen::Dynamic> ldlt_Sigma(Sigma);
112 check_ldlt_factor(function, "LDLT_Factor of scale parameter", ldlt_Sigma);
113
114 if (size_y == 0)
115 return lp;
116
117 if (include_summand<propto, T_dof>::value) {
118 lp += lgamma(0.5 * (nu + size_y)) * size_vec;
119 lp -= lgamma(0.5 * nu) * size_vec;
120 lp -= (0.5 * size_y) * log(nu) * size_vec;
121 }
122
123 if (include_summand<propto>::value)
124 lp -= (0.5 * size_y) * LOG_PI * size_vec;
125
126 using Eigen::Array;
127
128 if (include_summand<propto, T_scale_elem>::value) {
129 lp -= 0.5 * log_determinant_ldlt(ldlt_Sigma) * size_vec;
130 }
131
132 if (include_summand<propto, T_y, T_dof, T_loc, T_scale_elem>::value) {
133 lp_type sum_lp_vec(0.0);
134 for (size_t i = 0; i < size_vec; i++) {
135 Eigen::Matrix<typename return_type<T_y, T_loc>::type,
136 Eigen::Dynamic, 1> y_minus_mu(size_y);
137 for (int j = 0; j < size_y; j++)
138 y_minus_mu(j) = y_vec[i](j)-mu_vec[i](j);
139 sum_lp_vec += log1p(trace_inv_quad_form_ldlt(ldlt_Sigma, y_minus_mu)
140 / nu);
141 }
142 lp -= 0.5 * (nu + size_y) * sum_lp_vec;
143 }
144 return lp;
145 }
146
147 template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
148 inline
149 typename return_type<T_y, T_dof, T_loc, T_scale>::type
150 multi_student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu,
151 const T_scale& Sigma) {
152 return multi_student_t_log<false>(y, nu, mu, Sigma);
153 }
154
155 }
156 }
157 #endif
check_not_nan.hpp
multiply.hpp
stan::math::trace_inv_quad_form_ldlt
boost::enable_if_c<!stan::is_var< T1 >::value &&!stan::is_var< T2 >::value, typename boost::math::tools::promote_args< T1, T2 >::type >::type trace_inv_quad_form_ldlt(const LDLT_factor< T1, R2, C2 > &A, const Eigen::Matrix< T2, R3, C3 > &B)
Definition: trace_inv_quad_form_ldlt.hpp:27
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:14
stan::max_size_mvt
size_t max_size_mvt(const T1 &x1, const T2 &x2)
Definition: max_size_mvt.hpp:10
stan::math::check_not_nan
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
Definition: check_not_nan.hpp:60
check_size_match.hpp
check_positive.hpp
stan
Definition: log_sum_exp.hpp:8
stan::math::LOG_PI
const double LOG_PI
Definition: constants.hpp:167
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
VectorViewMvt.hpp
is_inf.hpp
stan::scalar_type::type
scalar_type_helper< is_vector< T >::value, T >::type type
Definition: scalar_type.hpp:34
check_symmetric.hpp
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:35
stan::math::check_ldlt_factor
bool check_ldlt_factor(const char *function, const char *name, LDLT_factor< T, R, C > &A)
Return true if the argument is a valid LDLT_factor.
Definition: check_ldlt_factor.hpp:34
stan::return_type::type
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
include_summand.hpp
check_ldlt_factor.hpp
stan::math::LDLT_factor
Definition: LDLT_factor.hpp:13
multi_normal_log.hpp
size_
size_t size_
Definition: dot_self.hpp:18
stan::math::multi_student_t_log
return_type< T_y, T_dof, T_loc, T_scale >::type multi_student_t_log(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma)
Return the log of the multivariate Student t distribution at the specified arguments.
Definition: multi_student_t_log.hpp:36
stan::math::check_positive
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
Definition: check_positive.hpp:66
stan::math::check_size_match
bool check_size_match(const char *function, const char *name_i, T_size1 i, const char *name_j, T_size2 j)
Return true if the provided sizes match.
Definition: check_size_match.hpp:30
dot_product.hpp
stan::math::is_inf
int is_inf(const fvar< T > &x)
Returns 1 if the input's value is infinite and 0 otherwise.
Definition: is_inf.hpp:21
stan::math::multi_normal_log
return_type< T_y, T_loc, T_covar >::type multi_normal_log(const T_y &y, const T_loc &mu, const T_covar &Sigma)
Definition: multi_normal_log.hpp:26
stan::math::check_finite
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
Definition: check_finite.hpp:60
constants.hpp
check_finite.hpp
stan::VectorViewMvt
VectorViewMvt is a template expression that wraps either an Eigen::Matrix or a std::vector
Definition: VectorViewMvt.hpp:29
stan::math::log1p
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:15
log1p.hpp
stan::math::check_symmetric
bool check_symmetric(const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
Return true if the specified matrix is symmetric.
Definition: check_symmetric.hpp:36
subtract.hpp
stan::length_mvt
size_t length_mvt(const Eigen::Matrix< T, R, C > &)
Definition: length_mvt.hpp:12
stan::math::log_determinant_ldlt
T log_determinant_ldlt(LDLT_factor< T, R, C > &A)
Definition: log_determinant_ldlt.hpp:12

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