mpower {corpcor} | R Documentation |
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 |
tol |
tolerance - eigenvalues with absolute value smaller or equal
to |
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
.
Value
mpower
returns
a matrix of the same dimensions as m
.
Author(s)
Korbinian Strimmer (https://strimmerlab.github.io).
See Also
Examples
# 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)