Matrix (version 1.5-1)

chol2inv-methods: Inverse from Choleski or QR Decomposition -- Matrix Methods

Description

Invert a symmetric, positive definite square matrix from its Choleski decomposition. Equivalently, compute \((X'X)^{-1}\) from the (\(R\) part) of the QR decomposition of \(X\).
Even more generally, given an upper triangular matrix \(R\), compute \((R'R)^{-1}\).

Methods

x = "ANY"

the default method from base, see chol2inv, for traditional matrices.

x = "dtrMatrix"

method for the numeric triangular matrices, built on the same LAPACK DPOTRI function as the base method.

x = "denseMatrix"

if x is coercable to a triangularMatrix, call the "dtrMatrix" method above.

x = "sparseMatrix"

if x is coercable to a triangularMatrix, use solve() currently.

%% better algorithms are welcome!

See Also

chol (for Matrix objects); further, chol2inv (from the base package), solve.

Examples

(M  <- Matrix(cbind(1, 1:3, c(1,3,7))))
(cM <- chol(M)) # a "Cholesky" object, inheriting from "dtrMatrix"
chol2inv(cM) %*% M # the identity
stopifnot(all(chol2inv(cM) %*% M - Diagonal(nrow(M))) < 1e-10)