Stan Math Library  2.14.0
reverse mode automatic differentiation
read_corr_L.hpp
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1 #ifndef STAN_MATH_PRIM_MAT_FUN_READ_CORR_L_HPP
2 #define STAN_MATH_PRIM_MAT_FUN_READ_CORR_L_HPP
3 
8 #include <cstddef>
9 #include <iostream>
10 
11 namespace stan {
12  namespace math {
13 
35  template <typename T>
36  Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>
37  read_corr_L(const Eigen::Array<T, Eigen::Dynamic, 1>& CPCs, // on (-1, 1)
38  size_t K) {
39  Eigen::Array<T, Eigen::Dynamic, 1> temp;
40  Eigen::Array<T, Eigen::Dynamic, 1> acc(K-1);
41  acc.setOnes();
42  // Cholesky factor of correlation matrix
43  Eigen::Array<T, Eigen::Dynamic, Eigen::Dynamic> L(K, K);
44  L.setZero();
45 
46  size_t position = 0;
47  size_t pull = K - 1;
48 
49  L(0, 0) = 1.0;
50  L.col(0).tail(pull) = temp = CPCs.head(pull);
51  acc.tail(pull) = T(1.0) - temp.square();
52  for (size_t i = 1; i < (K - 1); i++) {
53  position += pull;
54  pull--;
55  temp = CPCs.segment(position, pull);
56  L(i, i) = sqrt(acc(i-1));
57  L.col(i).tail(pull) = temp * acc.tail(pull).sqrt();
58  acc.tail(pull) *= T(1.0) - temp.square();
59  }
60  L(K-1, K-1) = sqrt(acc(K-2));
61  return L.matrix();
62  }
63 
88  template <typename T>
89  Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>
90  read_corr_L(const Eigen::Array<T, Eigen::Dynamic, 1>& CPCs,
91  size_t K,
92  T& log_prob) {
93  Eigen::Matrix<T, Eigen::Dynamic, 1> values(CPCs.rows() - 1);
94  size_t pos = 0;
95  // no need to abs() because this Jacobian determinant
96  // is strictly positive (and triangular)
97  // see inverse of Jacobian in equation 11 of LKJ paper
98  for (size_t k = 1; k <= (K - 2); k++)
99  for (size_t i = k + 1; i <= K; i++) {
100  values(pos) = (K - k - 1) * log1m(square(CPCs(pos)));
101  pos++;
102  }
103 
104  log_prob += 0.5 * sum(values);
105  return read_corr_L(CPCs, K);
106  }
107 
108  }
109 }
110 #endif
fvar< T > sum(const std::vector< fvar< T > > &m)
Return the sum of the entries of the specified standard vector.
Definition: sum.hpp:20
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:14
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:13
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > read_corr_L(const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, size_t K)
Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to...
Definition: read_corr_L.hpp:37

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