expm (version 1.0-0)

matpow: Matrix Power

Description

Compute the \(k\)-th power of a matrix. Whereas x^k computes element wise powers, x %^% k corresponds to \(k - 1\) matrix multiplications, x %*% x %*% ... %*% x.

Usage

x %^% k

Value

A matrix of the same dimension as x.

Arguments

x

a square matrix, numeric or complex.

k

an integer, \(k \ge 0\).

Author

Based on an R-help posting of Vicente Canto Casasola, and Vincent Goulet's C implementation in actuar.

Details

Argument \(k\) is coerced to integer using as.integer.

The algorithm uses \(O(log_2(k))\) matrix multiplications.

See Also

%*% for matrix multiplication.

Examples

A <- cbind(1, 2 * diag(3)[,-1])
A
A %^% 2
stopifnot(identical(A, A %^% 1),
          A %^% 2 == A %*% A)

## also for complex number matrix  Z :
Z <- A + 2i*A
Z %^% 2
stopifnot(identical(Z, Z %^% 1),
          Z %^% 2 == Z %*% Z)