modifChol: Revised Modified Cholesky Factorization

In robcp: Robust Change-Point Tests

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 < μ ≤ 1.

Details

modif.chol computes the revised modified Cholesky Factorization of a symmetric, not necessarily positive definite matrix x + E such that L'L = x + E for E ≥ 0.

Value

Upper triangular matrix L of the form L'L = x + E. The attribute swaps is a vector of the length of dimension of x. It contains 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.

Author(s)

Sheila Görz

References

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

Examples

y <- matrix(runif(9), ncol = 3)
x <- psi(y)
modifChol(lrv(x))

robcp documentation built on Sept. 16, 2022, 5:05 p.m.