matrixPower {lavaSearch2}

Power of a Matrix

Description

Compute the power of a matrix.

Usage

matrixPower(object, power, symmetric, tol = 1e-12, print.warning = TRUE)

Arguments

object

a matrix.

power

[numeric] power to be applied to the matrix.

symmetric

[logical] is the matrix symmetric? Argument passed to the function eigen.

tol

[numeric >0] the threshold under which the eigenvalues are set to 0.

print.warning

[logical] should a warning be print when some or the eigenvalues are not strictly positive.

Value

A matrix.

Examples

## symmetric matrix
set.seed(10)
M <- matrix(rnorm(20*6),20,6)
Sigma <- var(M)
Sigma.half <- matrixPower(Sigma, power = 1/2, symmetric = TRUE)
round(Sigma.half %*% Sigma.half - Sigma,5)

iSigma <- matrixPower(Sigma, power = -1, symmetric = TRUE)
round(iSigma %*% Sigma,5)

iSigma.half <- matrixPower(Sigma, power = -1/2, symmetric = TRUE)
round(iSigma.half %*% iSigma.half - iSigma,5)

## non symmetric matrix
set.seed(10)
M <- matrix(abs(rnorm(9)), 3, 3) + diag(1,3,3)
M-t(M)

iM <- matrixPower(M, power = -1, symmetric = FALSE)
round(iM %*% M,5)

iM.half <- matrixPower(M, power = -1/2, symmetric = FALSE)
round(iM.half %*% iM.half %*% M,5)