matpow: Matrix Power

In expm: Matrix Exponential, Log, 'etc'

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

Arguments

x	a square matrix, numeric or complex.
k	an integer, k \ge 0.

Details

Argument k is coerced to integer using as.integer.

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

Value

A matrix of the same dimension as x.

Note

If you think you need x^k for k < 0, then consider instead solve(x %^% (-k)).

Author(s)

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

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)

expm documentation built on Sept. 11, 2024, 8:58 p.m.