Scaled Cholesky square roots of the sample covariance matrix and its inverse.
start_resids(Y, mode_rep = NULL)An array of numeric data.
A vector of integers. The modes specified by
mode_rep will be given an identity matrix instead of a
sample-based matrix.
Sig A list where Sig[[i]] is the
lower-triangular Cholesky square root of the sample covariance
matrix of the \(i\)th mode, scaled down to have determinant
1.
Sig_inv A list where Sig_inv[[i]] is the inverse of the
lower-triangular Cholesky square root of the sample covariance matrix of
the \(i\)th mode, scaled down to have determinant 1.
If mode_rep is not NULL, then the list elements in Sig
and Sig_inv specified in mode_rep will be the identity matrix
instead of sample-based matrices.
This function will take the sample covariance matrix of the
\(i\)th matricization of an input array \(Y\) and will return
(1) its lower-triangular Cholesky square root scaled down to have
determinant 1 and (2) the inverse of its lower-triangular Cholesky
square root scaled down to have determinant 1. This function is
primarily used to obtain starting values for the Gibbs sampler
implemented in equi_mcmc.