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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
4 #include <stan/math/prim/mat/fun/Eigen.hpp>
5 #include <stan/math/prim/scal/fun/log1m.hpp>
6 #include <stan/math/prim/scal/fun/square.hpp>
7 #include <stan/math/prim/mat/fun/sum.hpp>
8 #include <cstddef>
9 #include <iostream>
10
11 namespace stan {
12
13 namespace math {
14
15
16 // MATRIX TRANSFORMS +/- JACOBIANS
17
39 template <typename T>
40 Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>
41 read_corr_L(const Eigen::Array<T, Eigen::Dynamic, 1>& CPCs, // on (-1, 1)
42 const size_t K) {
43 Eigen::Array<T, Eigen::Dynamic, 1> temp;
44 Eigen::Array<T, Eigen::Dynamic, 1> acc(K-1);
45 acc.setOnes();
46 // Cholesky factor of correlation matrix
47 Eigen::Array<T, Eigen::Dynamic, Eigen::Dynamic> L(K, K);
48 L.setZero();
49
50 size_t position = 0;
51 size_t pull = K - 1;
52
53 L(0, 0) = 1.0;
54 L.col(0).tail(pull) = temp = CPCs.head(pull);
55 acc.tail(pull) = T(1.0) - temp.square();
56 for (size_t i = 1; i < (K - 1); i++) {
57 position += pull;
58 pull--;
59 temp = CPCs.segment(position, pull);
60 L(i, i) = sqrt(acc(i-1));
61 L.col(i).tail(pull) = temp * acc.tail(pull).sqrt();
62 acc.tail(pull) *= T(1.0) - temp.square();
63 }
64 L(K-1, K-1) = sqrt(acc(K-2));
65 return L.matrix();
66 }
67
68
93 template <typename T>
94 Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>
95 read_corr_L(const Eigen::Array<T, Eigen::Dynamic, 1>& CPCs,
96 const size_t K,
97 T& log_prob) {
98 using stan::math::log1m;
99 using stan::math::square;
100 using stan::math::sum;
101
102 Eigen::Matrix<T, Eigen::Dynamic, 1> values(CPCs.rows() - 1);
103 size_t pos = 0;
104 // no need to abs() because this Jacobian determinant
105 // is strictly positive (and triangular)
106 // see inverse of Jacobian in equation 11 of LKJ paper
107 for (size_t k = 1; k <= (K - 2); k++)
108 for (size_t i = k + 1; i <= K; i++) {
109 values(pos) = (K - k - 1) * log1m(square(CPCs(pos)));
110 pos++;
111 }
112
113 log_prob += 0.5 * sum(values);
114 return read_corr_L(CPCs, K);
115 }
116
117 }
118
119 }
120
121 #endif
stan::math::sum
fvar< T > sum(const std::vector< fvar< T > > &m)
Return the sum of the entries of the specified standard vector.
Definition: sum.hpp:20
stan::math::sqrt
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:15
stan
Definition: log_sum_exp.hpp:8
square.hpp
stan::math::square
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:15
log1m.hpp
Eigen.hpp
stan::math::read_corr_L
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > read_corr_L(const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const size_t K)
Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to...
Definition: read_corr_L.hpp:41
sum.hpp
stan::math::log1m
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:16

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