Stan Math Library  2.14.0
reverse mode automatic differentiation
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 
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>
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 
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 
124  lp -= (0.5 * size_y) * LOG_PI * size_vec;
125 
126  using Eigen::Array;
127 
129  lp -= 0.5 * log_determinant_ldlt(ldlt_Sigma) * size_vec;
130  }
131 
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
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
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)
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:20
size_t max_size_mvt(const T1 &x1, const T2 &x2)
const double LOG_PI
Definition: constants.hpp:167
void check_ldlt_factor(const char *function, const char *name, LDLT_factor< T, R, C > &A)
Check if the argument is a valid LDLT_factor.
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
scalar_type_helper< is_vector< T >::value, T >::type type
Definition: scalar_type.hpp:34
void check_size_match(const char *function, const char *name_i, T_size1 i, const char *name_j, T_size2 j)
Check if the provided sizes match.
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
size_t size_
Definition: dot_self.hpp:18
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.
void check_symmetric(const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
Check if the specified matrix is symmetric.
int is_inf(const fvar< T > &x)
Returns 1 if the input&#39;s value is infinite and 0 otherwise.
Definition: is_inf.hpp:21
return_type< T_y, T_loc, T_covar >::type multi_normal_log(const T_y &y, const T_loc &mu, const T_covar &Sigma)
VectorViewMvt is a template expression that wraps either an Eigen::Matrix or a std::vector<Eigen::Mat...
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:11
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
size_t length_mvt(const Eigen::Matrix< T, R, C > &)
Definition: length_mvt.hpp:12
T log_determinant_ldlt(LDLT_factor< T, R, C > &A)

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