corpcor (version 1.6.9)

mpower: Compute the Power of a Real Symmetric Matrix

Description

mpower computes \(m^alpha\), i.e. the alpha-th power of the real symmetric matrix m.

Usage

mpower(m, alpha, pseudo=FALSE, tol)

Arguments

m

a real-valued symmetric matrix.

alpha

exponent.

pseudo

if pseudo=TRUE then all zero eigenvalues are dropped (e.g. for computing the pseudoinverse). The default is to use all eigenvalues.

tol

tolerance - eigenvalues with absolute value smaller or equal to tol are considered identically zero (default: tol = max(dim(m))*max(abs(eval))*.Machine$double.eps).

Value

mpower returns a matrix of the same dimensions as m.

Details

The matrix power of m is obtained by first computing the spectral decomposition of m, and subsequent modification of the resulting eigenvalues.

Note that m is assumed to by symmetric, and only its lower triangle (diagonal included) is used in eigen.

For computing the matrix power of cor.shrink use the vastly more efficient function powcor.shrink.

See Also

powcor.shrink, eigen.

Examples

# NOT RUN {
# load corpcor library
library("corpcor")

# generate symmetric matrix
p = 10
n = 20
X = matrix(rnorm(n*p), nrow = n, ncol = p)
m = cor(X)

m %*% m
mpower(m, 2)

solve(m)
mpower(m, -1)

msq = mpower(m, 0.5)
msq %*% msq
m

mpower(m, 1.234)
# }