Stan Math Library  2.20.0
reverse mode automatic differentiation
multi_normal_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_MAT_PROB_MULTI_NORMAL_LPDF_HPP
2 #define STAN_MATH_PRIM_MAT_PROB_MULTI_NORMAL_LPDF_HPP
3 
15 
16 namespace stan {
17 namespace math {
18 
19 template <bool propto, typename T_y, typename T_loc, typename T_covar>
21  const T_y& y, const T_loc& mu, const T_covar& Sigma) {
22  static const char* function = "multi_normal_lpdf";
23  typedef typename scalar_type<T_covar>::type T_covar_elem;
24  typedef typename return_type<T_y, T_loc, T_covar>::type lp_type;
25 
26  using Eigen::Dynamic;
27 
28  check_positive(function, "Covariance matrix rows", Sigma.rows());
29  check_symmetric(function, "Covariance matrix", Sigma);
30 
32  check_ldlt_factor(function, "LDLT_Factor of covariance parameter",
33  ldlt_Sigma);
34 
35  size_t number_of_y = length_mvt(y);
36  size_t number_of_mu = length_mvt(mu);
37  if (number_of_y == 0 || number_of_mu == 0)
38  return 0.0;
39  check_consistent_sizes_mvt(function, "y", y, "mu", mu);
40 
41  lp_type lp(0.0);
42  vector_seq_view<T_y> y_vec(y);
43  vector_seq_view<T_loc> mu_vec(mu);
44  size_t size_vec = max_size_mvt(y, mu);
45 
46  int size_y = y_vec[0].size();
47  int size_mu = mu_vec[0].size();
48  if (size_vec > 1) {
49  int size_y_old = size_y;
50  int size_y_new;
51  for (size_t i = 1, size_ = length_mvt(y); i < size_; i++) {
52  int size_y_new = y_vec[i].size();
53  check_size_match(function,
54  "Size of one of the vectors of "
55  "the random variable",
56  size_y_new,
57  "Size of another vector of the "
58  "random variable",
59  size_y_old);
60  size_y_old = size_y_new;
61  }
62  int size_mu_old = size_mu;
63  int size_mu_new;
64  for (size_t i = 1, size_ = length_mvt(mu); i < size_; i++) {
65  int size_mu_new = mu_vec[i].size();
66  check_size_match(function,
67  "Size of one of the vectors of "
68  "the location variable",
69  size_mu_new,
70  "Size of another vector of the "
71  "location variable",
72  size_mu_old);
73  size_mu_old = size_mu_new;
74  }
75  (void)size_y_old;
76  (void)size_y_new;
77  (void)size_mu_old;
78  (void)size_mu_new;
79  }
80 
81  check_size_match(function, "Size of random variable", size_y,
82  "size of location parameter", size_mu);
83  check_size_match(function, "Size of random variable", size_y,
84  "rows of covariance parameter", Sigma.rows());
85  check_size_match(function, "Size of random variable", size_y,
86  "columns of covariance parameter", Sigma.cols());
87 
88  for (size_t i = 0; i < size_vec; i++) {
89  check_finite(function, "Location parameter", mu_vec[i]);
90  check_not_nan(function, "Random variable", y_vec[i]);
91  }
92 
93  if (size_y == 0)
94  return lp;
95 
97  lp += NEG_LOG_SQRT_TWO_PI * size_y * size_vec;
98 
100  lp -= 0.5 * log_determinant_ldlt(ldlt_Sigma) * size_vec;
101 
103  lp_type sum_lp_vec(0.0);
104  for (size_t i = 0; i < size_vec; i++) {
105  Eigen::Matrix<typename return_type<T_y, T_loc>::type, Dynamic, 1>
106  y_minus_mu(size_y);
107  for (int j = 0; j < size_y; j++)
108  y_minus_mu(j) = y_vec[i](j) - mu_vec[i](j);
109  sum_lp_vec += trace_inv_quad_form_ldlt(ldlt_Sigma, y_minus_mu);
110  }
111  lp -= 0.5 * sum_lp_vec;
112  }
113  return lp;
114 }
115 
116 template <typename T_y, typename T_loc, typename T_covar>
118  const T_y& y, const T_loc& mu, const T_covar& Sigma) {
119  return multi_normal_lpdf<false>(y, mu, Sigma);
120 }
121 
122 } // namespace math
123 } // namespace stan
124 #endif
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
size_t max_size_mvt(const T1 &x1, const T2 &x2)
return_type< T_y, T_loc, T_covar >::type multi_normal_lpdf(const T_y &y, const T_loc &mu, const T_covar &Sigma)
void check_ldlt_factor(const char *function, const char *name, LDLT_factor< T, R, C > &A)
Raise domain error if the specified LDLT factor is invalid.
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...
LDLT_factor is a thin wrapper on Eigen::LDLT to allow for reusing factorizations and efficient autodi...
Definition: LDLT_factor.hpp:63
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
std::enable_if< !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)
const double NEG_LOG_SQRT_TWO_PI
Definition: constants.hpp:156
This class provides a low-cost wrapper for situations where you either need an Eigen Vector or RowVec...
void check_consistent_sizes_mvt(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
void check_symmetric(const char *function, const char *name, const matrix_cl &y)
Check if the matrix_cl is symmetric.
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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