void
factor_U(const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>& U,
Eigen::Array<T, Eigen::Dynamic, 1>& CPCs) {
size_t K = U.rows();
size_t position = 0;
size_t pull = K - 1;
if (K == 2) {
CPCs(0) = atanh(U(0, 1));
return;
}
Eigen::Array<T, 1, Eigen::Dynamic> temp = U.row(0).tail(pull);
CPCs.head(pull) = temp;
Eigen::Array<T, Eigen::Dynamic, 1> acc(K);
acc(0) = -0.0;
acc.tail(pull) = 1.0 - temp.square();
for (size_t i = 1; i < (K - 1); i++) {
position += pull;
pull--;
temp = U.row(i).tail(pull);
temp /= sqrt(acc.tail(pull) / acc(i));
CPCs.segment(position, pull) = temp;
acc.tail(pull) *= 1.0 - temp.square();
}
CPCs = 0.5 * ( (1.0 + CPCs) / (1.0 - CPCs) ).log(); // now unbounded
}
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>
read_corr_L(const Eigen::Array<T, Eigen::Dynamic, 1>& CPCs, // on (-1, 1)
size_t K) {
Eigen::Array<T, Eigen::Dynamic, 1> temp;
Eigen::Array<T, Eigen::Dynamic, 1> acc(K-1);
acc.setOnes();
// Cholesky factor of correlation matrix
Eigen::Array<T, Eigen::Dynamic, Eigen::Dynamic> L(K, K);
L.setZero();
size_t position = 0;
size_t pull = K - 1;
L(0, 0) = 1.0;
L.col(0).tail(pull) = temp = CPCs.head(pull);
acc.tail(pull) = T(1.0) - temp.square();
for (size_t i = 1; i < (K - 1); i++) {
position += pull;
pull--;
temp = CPCs.segment(position, pull);
L(i, i) = sqrt(acc(i-1));
L.col(i).tail(pull) = temp * acc.tail(pull).sqrt();
acc.tail(pull) *= T(1.0) - temp.square();
}
L(K-1, K-1) = sqrt(acc(K-2));
return L.matrix();
}