modifChol | R Documentation |
Computes the revised modified Cholesky factorization described in Schnabel and Eskow (1999).
modifChol(x, tau = .Machine$double.eps^(1 / 3), tau_bar = .Machine$double.eps^(2 / 3), mu = 0.1)
x |
a symmetric matrix. |
tau |
(machine epsilon)^(1/3). |
tau_bar |
(machine epsilon^(2/3)). |
mu |
numeric, 0 < μ ≤ 1. |
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.
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.
Sheila Görz
Schnabel, R. B., & Eskow, E. (1999). "A revised modified Cholesky factorization algorithm" SIAM Journal on optimization, 9(4), 1135-1148.
y <- matrix(runif(9), ncol = 3) x <- psi(y) modifChol(lrv(x))
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