Stan Math Library  2.12.0
reverse mode automatic differentiation
factor_U.hpp
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1 #ifndef STAN_MATH_PRIM_MAT_FUN_FACTOR_U_HPP
2 #define STAN_MATH_PRIM_MAT_FUN_FACTOR_U_HPP
3 
6 
7 #include <cmath>
8 #include <cstddef>
9 #include <iostream>
10 #include <limits>
11 #include <stdexcept>
12 #include <sstream>
13 #include <vector>
14 
15 namespace stan {
16  namespace math {
17 
25  template<typename T>
26  void
27  factor_U(const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>& U,
28  Eigen::Array<T, Eigen::Dynamic, 1>& CPCs) {
29  size_t K = U.rows();
30  size_t position = 0;
31  size_t pull = K - 1;
32 
33  if (K == 2) {
34  CPCs(0) = atanh(U(0, 1));
35  return;
36  }
37 
38  Eigen::Array<T, 1, Eigen::Dynamic> temp = U.row(0).tail(pull);
39 
40  CPCs.head(pull) = temp;
41 
42  Eigen::Array<T, Eigen::Dynamic, 1> acc(K);
43  acc(0) = -0.0;
44  acc.tail(pull) = 1.0 - temp.square();
45  for (size_t i = 1; i < (K - 1); i++) {
46  position += pull;
47  pull--;
48  temp = U.row(i).tail(pull);
49  temp /= sqrt(acc.tail(pull) / acc(i));
50  CPCs.segment(position, pull) = temp;
51  acc.tail(pull) *= 1.0 - temp.square();
52  }
53  CPCs = 0.5 * ( (1.0 + CPCs) / (1.0 - CPCs) ).log(); // now unbounded
54  }
55 
56  }
57 
58 }
59 
60 #endif
fvar< T > atanh(const fvar< T > &x)
Definition: atanh.hpp:13
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
void factor_U(const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &U, Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs)
This function is intended to make starting values, given a unit upper-triangular matrix U such that U...
Definition: factor_U.hpp:27

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