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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 <boost/math/special_functions/gamma.hpp>
5 #include <boost/math/special_functions/fpclassify.hpp>
6 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 #include <cstdlib>
23 
24 namespace stan {
25 
26  namespace math {
27  using Eigen::Dynamic;
34  template <bool propto,
35  typename T_y, typename T_dof, typename T_loc, typename T_scale>
36  typename return_type<T_y, T_dof, T_loc, T_scale>::type
37  multi_student_t_log(const T_y& y,
38  const T_dof& nu,
39  const T_loc& mu,
40  const T_scale& Sigma) {
41  static const char* function("stan::math::multi_student_t");
42 
48  using boost::math::lgamma;
52  using stan::math::log1p;
53  using std::log;
54 
55  typedef typename scalar_type<T_scale>::type T_scale_elem;
56  typedef typename return_type<T_y, T_dof, T_loc, T_scale>::type lp_type;
57  lp_type lp(0.0);
58 
59  // allows infinities
60  check_not_nan(function, "Degrees of freedom parameter", nu);
61  check_positive(function, "Degrees of freedom parameter", nu);
62 
63  using boost::math::isinf;
64 
65  if (isinf(nu)) // already checked nu > 0
66  return multi_normal_log(y, mu, Sigma);
67 
68  using Eigen::Matrix;
69  using std::vector;
70  VectorViewMvt<const T_y> y_vec(y);
71  VectorViewMvt<const T_loc> mu_vec(mu);
72  // size of std::vector of Eigen vectors
73  size_t size_vec = max_size_mvt(y, mu);
74 
75 
76  // Check if every vector of the array has the same size
77  int size_y = y_vec[0].size();
78  int size_mu = mu_vec[0].size();
79  if (size_vec > 1) {
80  int size_y_old = size_y;
81  int size_y_new;
82  for (size_t i = 1, size_ = length_mvt(y); i < size_; i++) {
83  int size_y_new = y_vec[i].size();
84  check_size_match(function,
85  "Size of one of the vectors of the random variable",
86  size_y_new,
87  "Size of another vector of the random variable",
88  size_y_old);
89  size_y_old = size_y_new;
90  }
91  int size_mu_old = size_mu;
92  int size_mu_new;
93  for (size_t i = 1, size_ = length_mvt(mu); i < size_; i++) {
94  int size_mu_new = mu_vec[i].size();
95  check_size_match(function,
96  "Size of one of the vectors "
97  "of the location variable",
98  size_mu_new,
99  "Size of another vector of "
100  "the location variable",
101  size_mu_old);
102  size_mu_old = size_mu_new;
103  }
104  (void) size_y_old;
105  (void) size_y_new;
106  (void) size_mu_old;
107  (void) size_mu_new;
108  }
109 
110 
111  check_size_match(function,
112  "Size of random variable", size_y,
113  "size of location parameter", size_mu);
114  check_size_match(function,
115  "Size of random variable", size_y,
116  "rows of scale parameter", Sigma.rows());
117  check_size_match(function,
118  "Size of random variable", size_y,
119  "columns of scale parameter", Sigma.cols());
120 
121  for (size_t i = 0; i < size_vec; i++) {
122  check_finite(function, "Location parameter", mu_vec[i]);
123  check_not_nan(function, "Random variable", y_vec[i]);
124  }
125  check_symmetric(function, "Scale parameter", Sigma);
126 
127 
129  check_ldlt_factor(function, "LDLT_Factor of scale parameter", ldlt_Sigma);
130 
131  if (size_y == 0) // y_vec[0].size() == 0
132  return lp;
133 
135  lp += lgamma(0.5 * (nu + size_y)) * size_vec;
136  lp -= lgamma(0.5 * nu) * size_vec;
137  lp -= (0.5 * size_y) * log(nu) * size_vec;
138  }
139 
141  lp -= (0.5 * size_y) * LOG_PI * size_vec;
142 
143  using stan::math::multiply;
145  using stan::math::subtract;
146  using Eigen::Array;
147 
148 
150  lp -= 0.5 * log_determinant_ldlt(ldlt_Sigma) * size_vec;
151  }
152 
154  lp_type sum_lp_vec(0.0);
155  for (size_t i = 0; i < size_vec; i++) {
156  Eigen::Matrix<typename return_type<T_y, T_loc>::type, Dynamic, 1>
157  y_minus_mu(size_y);
158  for (int j = 0; j < size_y; j++)
159  y_minus_mu(j) = y_vec[i](j)-mu_vec[i](j);
160  sum_lp_vec += log1p(trace_inv_quad_form_ldlt(ldlt_Sigma, y_minus_mu)
161  / nu);
162  }
163  lp -= 0.5 * (nu + size_y) * sum_lp_vec;
164  }
165  return lp;
166  }
167 
168  template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
169  inline
171  multi_student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu,
172  const T_scale& Sigma) {
173  return multi_student_t_log<false>(y, nu, mu, Sigma);
174  }
175 
176  }
177 }
178 #endif
int isinf(const stan::math::var &a)
Checks if the given number is infinite.
Definition: std_isinf.hpp:18
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
size_t max_size_mvt(const T1 &x1, const T2 &x2)
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > subtract(const Eigen::Matrix< T1, R, C > &m1, const Eigen::Matrix< T2, R, C > &m2)
Return the result of subtracting the second specified matrix from the first specified matrix...
Definition: subtract.hpp:27
const double LOG_PI
Definition: constants.hpp:170
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
Eigen::Matrix< fvar< T >, R1, C1 > multiply(const Eigen::Matrix< fvar< T >, R1, C1 > &m, const fvar< T > &c)
Definition: multiply.hpp:20
bool check_symmetric(const char *function, const char *name, const Eigen::Matrix< T_y, Dynamic, Dynamic > &y)
Return true if the specified matrix is symmetric.
scalar_type_helper< is_vector< T >::value, T >::type type
Definition: scalar_type.hpp:38
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 stan::math::LDLT_factor< T1, R2, C2 > &A, const Eigen::Matrix< T2, R3, C3 > &B)
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
bool isinf(const stan::math::var &v)
Checks if the given number is infinite.
Definition: boost_isinf.hpp:22
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.
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
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.
size_t length_mvt(const T &)
Definition: length_mvt.hpp:12
fvar< T > dot_product(const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2)
Definition: dot_product.hpp:20
return_type< T_y, T_loc, T_covar >::type multi_normal_log(const T_y &y, const T_loc &mu, const T_covar &Sigma)
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:16
T log_determinant_ldlt(stan::math::LDLT_factor< T, R, C > &A)
bool check_ldlt_factor(const char *function, const char *name, stan::math::LDLT_factor< T, R, C > &A)
Return true if the argument is a valid stan::math::LDLT_factor.

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