| matrixpower {spatstat.sparse} | R Documentation |
Evaluate a specified power of a matrix.
matrixpower(x, power, complexOK = TRUE) matrixsqrt(x, complexOK = TRUE) matrixinvsqrt(x, complexOK = TRUE)
x |
A square matrix containing numeric or complex values. |
power |
A numeric value giving the power (exponent) to which |
complexOK |
Logical value indicating whether the result is allowed to be complex. |
These functions raise the matrix x to the desired power:
matrixsqrt takes the square root, matrixinvsqrt takes
the inverse square root, and matrixpower takes the specified
power of x.
Up to numerical error, matrixpower(x, 2) should be equivalent
to x %*% x, and matrixpower(x, -1) should be
equivalent to solve(x), the inverse of x.
The square root y <- matrixsqrt(x) should satisfy
y %*% y = x. The inverse square root
z <- matrixinvsqrt(x) should satisfy z %*% z = solve(x).
Computations are performed using the eigen decomposition
(eigen).
A matrix of the same size as x containing
numeric or complex values.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au.
x <- matrix(c(10,2,2,1), 2, 2) y <- matrixsqrt(x) y y %*% y z <- matrixinvsqrt(x) z %*% y matrixpower(x, 0.1)