Symmetric Matrix Power
Raise symmetric matrix to specified power. Default calculates symmetric square root.
smpower(X, power = 0.5, tol = NULL)
X |
Symmetric real-valued matrix. |
power |
Power to apply to eigenvalues of |
tol |
Stability tolerance for eigenvalues. |
Basically returns tcrossprod(Y$vec%*%diag(Y$val^power),Y$vec) where Y = eigen(X,symmetric=TRUE).
Returns X raised to specified power.
Default tolerance is tol = max(dim(X)) * .Machine$double.eps.
Nathaniel E. Helwig <helwig@umn.edu>
########## EXAMPLE ########## X <- crossprod(matrix(rnorm(2000),100,20)) Xsqrt <- smpower(X) # square root Xinv <- smpower(X,-1) # inverse Xisqrt <- smpower(X,-0.5) # inverse square root
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