Performs a (modified) Cholesky factorization of the form
cholSE(matrix, tol = (.Machine$double.eps)^(1/3))Matrix to be Factorized.
Tolerance; Algorithm suggests (.Machine$double.eps) ^ (1 / 3), default
Generalized Cholesky decomposed matrix.
t(P) %*% A %*% P + E = t(R) %*% R
As detailed in Schnabel/Eskow (1990)
matlab source: http://www.dynare.org/dynare-matlab-m2html/matlab/chol_SE.html; Slightly different return values
Robert B. Schnabel and Elizabeth Eskow. 1990. "A New Modified Cholesky Factorization," SIAM Journal of Scientific Statistical Computing, 11, 6: 1136-58.
Elizabeth Eskow and Robert B. Schnabel 1991. "Algorithm 695 - Software for a New Modified Cholesky Factorization," ACM Transactions on Mathematical Software, Vol 17, No 3: 306-312