Stan Math Library  2.9.0
reverse mode automatic differentiation
multi_normal_prec_log.hpp
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1 #ifndef STAN_MATH_PRIM_MAT_PROB_MULTI_NORMAL_PREC_LOG_HPP
2 #define STAN_MATH_PRIM_MAT_PROB_MULTI_NORMAL_PREC_LOG_HPP
3 
27 
28 namespace stan {
29 
30  namespace math {
31 
32  template <bool propto,
33  typename T_y, typename T_loc, typename T_covar>
34  typename return_type<T_y, T_loc, T_covar>::type
35  multi_normal_prec_log(const T_y& y,
36  const T_loc& mu,
37  const T_covar& Sigma) {
38  static const char* function("stan::math::multi_normal_prec_log");
39  typedef typename scalar_type<T_covar>::type T_covar_elem;
40  typedef typename return_type<T_y, T_loc, T_covar>::type lp_type;
41  lp_type lp(0.0);
42 
48  using stan::math::sum;
53 
54  check_positive(function, "Precision matrix rows", Sigma.rows());
55  check_symmetric(function, "Precision matrix", Sigma);
56 
57  LDLT_factor<T_covar_elem,
58  Eigen::Dynamic, Eigen::Dynamic> ldlt_Sigma(Sigma);
59  check_ldlt_factor(function, "LDLT_Factor of precision parameter",
60  ldlt_Sigma);
61 
62  using Eigen::Matrix;
63  using std::vector;
64  VectorViewMvt<const T_y> y_vec(y);
65  VectorViewMvt<const T_loc> mu_vec(mu);
66  // size of std::vector of Eigen vectors
67  size_t size_vec = max_size_mvt(y, mu);
68 
69 
70  // Check if every vector of the array has the same size
71  int size_y = y_vec[0].size();
72  int size_mu = mu_vec[0].size();
73  if (size_vec > 1) {
74  int size_y_old = size_y;
75  int size_y_new;
76  for (size_t i = 1, size_ = length_mvt(y); i < size_; i++) {
77  int size_y_new = y_vec[i].size();
78  check_size_match(function,
79  "Size of one of the vectors "
80  "of the random variable", size_y_new,
81  "Size of another vector of "
82  "the random variable", size_y_old);
83  size_y_old = size_y_new;
84  }
85  int size_mu_old = size_mu;
86  int size_mu_new;
87  for (size_t i = 1, size_ = length_mvt(mu); i < size_; i++) {
88  int size_mu_new = mu_vec[i].size();
89  check_size_match(function,
90  "Size of one of the vectors "
91  "of the location variable", size_mu_new,
92  "Size of another vector of "
93  "the location variable", size_mu_old);
94  size_mu_old = size_mu_new;
95  }
96  (void) size_y_old;
97  (void) size_y_new;
98  (void) size_mu_old;
99  (void) size_mu_new;
100  }
101 
102  check_size_match(function,
103  "Size of random variable", size_y,
104  "size of location parameter", size_mu);
105  check_size_match(function,
106  "Size of random variable", size_y,
107  "rows of covariance parameter", Sigma.rows());
108  check_size_match(function,
109  "Size of random variable", size_y,
110  "columns of covariance parameter", Sigma.cols());
111 
112  for (size_t i = 0; i < size_vec; i++) {
113  check_finite(function, "Location parameter", mu_vec[i]);
114  check_not_nan(function, "Random variable", y_vec[i]);
115  }
116 
117  if (size_y == 0) // y_vec[0].size() == 0
118  return lp;
119 
121  lp += 0.5 * log_determinant_ldlt(ldlt_Sigma) * size_vec;
122 
124  lp += NEG_LOG_SQRT_TWO_PI * size_y * size_vec;
125 
127  lp_type sum_lp_vec(0.0);
128  for (size_t i = 0; i < size_vec; i++) {
129  Eigen::Matrix<typename return_type<T_y, T_loc>::type,
130  Eigen::Dynamic, 1> y_minus_mu(size_y);
131  for (int j = 0; j < size_y; j++)
132  y_minus_mu(j) = y_vec[i](j) - mu_vec[i](j);
133  sum_lp_vec += trace_quad_form(Sigma, y_minus_mu);
134  }
135  lp -= 0.5*sum_lp_vec;
136  }
137  return lp;
138  }
139 
140  template <typename T_y, typename T_loc, typename T_covar>
141  inline
143  multi_normal_prec_log(const T_y& y, const T_loc& mu, const T_covar& Sigma) {
144  return multi_normal_prec_log<false>(y, mu, Sigma);
145  }
146 
147  }
148 }
149 #endif
150 
fvar< T > sum(const std::vector< fvar< T > > &m)
Return the sum of the entries of the specified standard vector.
Definition: sum.hpp:20
size_t max_size_mvt(const T1 &x1, const T2 &x2)
fvar< T > trace_quad_form(const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, CB > &B)
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
scalar_type_helper< is_vector< T >::value, T >::type type
Definition: scalar_type.hpp:38
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
return_type< T_y, T_loc, T_covar >::type multi_normal_prec_log(const T_y &y, const T_loc &mu, const T_covar &Sigma)
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
size_t size_
Definition: dot_self.hpp:18
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
const double NEG_LOG_SQRT_TWO_PI
Definition: constants.hpp:184
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
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.
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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