robcp (version 0.2.5)

modifChol: Revised Modified Cholesky Factorization

Description

Computes the revised modified Cholesky factorization described in Schnabel and Eskow (1999).

Usage

modifChol(x, tau = .Machine$double.eps^(1 / 3), 
           tau_bar = .Machine$double.eps^(2 / 3), mu = 0.1)

Arguments

x

a symmetric matrix.

tau

(machine epsilon)^(1/3).

tau_bar

(machine epsilon^(2/3)).

mu

numeric, \(0 < \mu \le 1\).

Value

Lower triangular matrix \(L\) of the form \(LL' = x + E\). The attribute swaps is a vector of the lenght of dimension of x. It cointains the indices of the rows and columns that were swapped in x in order to compute the modified Cholesky factorization. For example if the i-th element of swaps is the number j, then the i-th and the j-th row and column were swapped. To reconstruct the original matrix swaps has to be read backwards.

Details

modif.chol computes the revised modified Cholesky Factorization of a symmetric, not neccessarily positive definite matrix x + E such that \(LL' = x + E\) for \(E \ge 0\).

References

Schnabel, R. B., & Eskow, E. (1999). "A revised modified Cholesky factorization algorithm" SIAM Journal on optimization, 9(4), 1135-1148.

Examples

# NOT RUN {
y <- matrix(runif(9), ncol = 3)
x <- psi(y)
modifChol(sigma2(x))
# }