VCA (version 1.2.1)

Solve: Solve System of Linear Equations using Inverse of Cholesky-Root.

Description

This function is intended to reduce the computational time in function solveMME which computes the inverse of the square variance- covariance Matrix of observations. It is considerably faster than function solve (see example). Whenever an error occurs, which is the case for non positive definite matrices 'X', function MPinv is called automatically yielding a generalized inverse (Moore-Penrose inverse) of 'X'.

Usage

Solve(X)

Arguments

X

(matrix, Matrix) object to be inverted

Value

• (matrix, Matrix) corresponding to the inverse of X

Examples

# following complex (nonsense) model takes pretty long to fit
system.time(res.sw <- anovaVCA(y~(sample+lot+device)/day/run, VCAdata1))
# solve mixed model equations (not automatically done to be more efficient)
system.time(res.sw <- solveMME(res.sw))
# extract covariance matrix of observations V
V1 <- getMat(res.sw, "V")
V2 <- as.matrix(V1)
system.time(V2i <- solve(V2))
system.time(V1i <- VCA:::Solve(V1))
V1i <- as.matrix(V1i)
dimnames(V1i) <- NULL
dimnames(V2i) <- NULL
all.equal(V1i, V2i)