1 #ifndef STAN_MATH_PRIM_FUN_CHOLESKY_CORR_CONSTRAIN_HPP
2 #define STAN_MATH_PRIM_FUN_CHOLESKY_CORR_CONSTRAIN_HPP
3
4 #include <stan/math/prim/err.hpp>
5 #include <stan/math/prim/fun/Eigen.hpp>
6 #include <stan/math/prim/fun/log1m.hpp>
7 #include <stan/math/prim/fun/sqrt.hpp>
8 #include <stan/math/prim/fun/square.hpp>
9 #include <stan/math/prim/fun/corr_constrain.hpp>
10 #include <cmath>
11
12 namespace stan {
13 namespace math {
14
15 template <typename EigVec, require_eigen_col_vector_t<EigVec>* = nullptr>
16 inline Eigen::Matrix<value_type_t<EigVec>, Eigen::Dynamic, Eigen::Dynamic>
cholesky_corr_constrain(const EigVec & y,int K)17 cholesky_corr_constrain(const EigVec& y, int K) {
18 using Eigen::Dynamic;
19 using Eigen::Matrix;
20 using std::sqrt;
21 using T_scalar = value_type_t<EigVec>;
22 int k_choose_2 = (K * (K - 1)) / 2;
23 check_size_match("cholesky_corr_constrain", "constrain size", y.size(),
24 "k_choose_2", k_choose_2);
25 Matrix<T_scalar, Dynamic, 1> z = corr_constrain(y);
26 Matrix<T_scalar, Dynamic, Dynamic> x(K, K);
27 if (K == 0) {
28 return x;
29 }
30 x.setZero();
31 x.coeffRef(0, 0) = 1;
32 int k = 0;
33 for (int i = 1; i < K; ++i) {
34 x.coeffRef(i, 0) = z.coeff(k++);
35 T_scalar sum_sqs = square(x.coeff(i, 0));
36 for (int j = 1; j < i; ++j) {
37 x.coeffRef(i, j) = z.coeff(k++) * sqrt(1.0 - sum_sqs);
38 sum_sqs += square(x.coeff(i, j));
39 }
40 x.coeffRef(i, i) = sqrt(1.0 - sum_sqs);
41 }
42 return x;
43 }
44
45 // FIXME to match above after debugged
46 template <typename EigVec, require_eigen_vector_t<EigVec>* = nullptr>
47 inline Eigen::Matrix<value_type_t<EigVec>, Eigen::Dynamic, Eigen::Dynamic>
cholesky_corr_constrain(const EigVec & y,int K,return_type_t<EigVec> & lp)48 cholesky_corr_constrain(const EigVec& y, int K, return_type_t<EigVec>& lp) {
49 using Eigen::Dynamic;
50 using Eigen::Matrix;
51 using std::sqrt;
52 using T_scalar = value_type_t<EigVec>;
53 int k_choose_2 = (K * (K - 1)) / 2;
54 check_size_match("cholesky_corr_constrain", "y.size()", y.size(),
55 "k_choose_2", k_choose_2);
56 Matrix<T_scalar, Dynamic, 1> z = corr_constrain(y, lp);
57 Matrix<T_scalar, Dynamic, Dynamic> x(K, K);
58 if (K == 0) {
59 return x;
60 }
61 x.setZero();
62 x.coeffRef(0, 0) = 1;
63 int k = 0;
64 for (int i = 1; i < K; ++i) {
65 x.coeffRef(i, 0) = z.coeff(k++);
66 T_scalar sum_sqs = square(x.coeff(i, 0));
67 for (int j = 1; j < i; ++j) {
68 lp += 0.5 * log1m(sum_sqs);
69 x.coeffRef(i, j) = z.coeff(k++) * sqrt(1.0 - sum_sqs);
70 sum_sqs += square(x.coeff(i, j));
71 }
72 x.coeffRef(i, i) = sqrt(1.0 - sum_sqs);
73 }
74 return x;
75 }
76
77 /**
78 * Return The cholesky of a `KxK` correlation matrix. If the `Jacobian`
79 * parameter is `true`, the log density accumulator is incremented with the log
80 * absolute Jacobian determinant of the transform. All of the transforms are
81 * specified with their Jacobians in the *Stan Reference Manual* chapter
82 * Constraint Transforms.
83 * @tparam Jacobian if `true`, increment log density accumulator with log
84 * absolute Jacobian determinant of constraining transform
85 * @tparam T A type inheriting from `Eigen::DenseBase` or a `var_value` with
86 * inner type inheriting from `Eigen::DenseBase` with compile time dynamic rows
87 * and 1 column
88 * @param y Linearly Serialized vector of size `(K * (K - 1))/2` holding the
89 * column major order elements of the lower triangurlar
90 * @param K The size of the matrix to return
91 * @param[in,out] lp log density accumulator
92 */
93 template <bool Jacobian, typename T, require_not_std_vector_t<T>* = nullptr>
cholesky_corr_constrain(const T & y,int K,return_type_t<T> & lp)94 inline auto cholesky_corr_constrain(const T& y, int K, return_type_t<T>& lp) {
95 if (Jacobian) {
96 return cholesky_corr_constrain(y, K, lp);
97 } else {
98 return cholesky_corr_constrain(y, K);
99 }
100 }
101
102 /**
103 * Return The cholesky of a `KxK` correlation matrix. If the `Jacobian`
104 * parameter is `true`, the log density accumulator is incremented with the log
105 * absolute Jacobian determinant of the transform. All of the transforms are
106 * specified with their Jacobians in the *Stan Reference Manual* chapter
107 * Constraint Transforms.
108 * @tparam Jacobian if `true`, increment log density accumulator with log
109 * absolute Jacobian determinant of constraining transform
110 * @tparam T A standard vector with inner type inheriting from
111 * `Eigen::DenseBase` or a `var_value` with inner type inheriting from
112 * `Eigen::DenseBase` with compile time dynamic rows and 1 column
113 * @param y Linearly Serialized vector of size `(K * (K - 1))/2` holding the
114 * column major order elements of the lower triangurlar
115 * @param K The size of the matrix to return
116 * @param[in,out] lp log density accumulator
117 */
118 template <bool Jacobian, typename T, require_std_vector_t<T>* = nullptr>
cholesky_corr_constrain(const T & y,int K,return_type_t<T> & lp)119 inline auto cholesky_corr_constrain(const T& y, int K, return_type_t<T>& lp) {
120 return apply_vector_unary<T>::apply(y, [&lp, K](auto&& v) {
121 return cholesky_corr_constrain<Jacobian>(v, K, lp);
122 });
123 }
124
125 } // namespace math
126 } // namespace stan
127 #endif
128