# Raising a matrix to a power in R

A surprising deficiency in R is the absence of an operator or built-in function for matrix exponentiation. I had to deal with this today when porting a function from MATLAB to R. Here is my quick-and-dirty solution:

```mpower = function(M,p) {
A = as.matrix(M)

if (dim(A) != dim(A)) stop("not a square matrix")

# M^{-1} = the matrix inverse of M
if (p==-1) return(solve(A))

# M^0 = I
if (p==0) return(diag(1,dim(A),dim(A)))

# M^1 = M
if (p==1) return(A)

if (p < -1) stop("only powers >= -1 allowed")
if (p != as.integer(p)) stop("only integer powers allowed")

R = A
for (i in 2:p) {
R = R %*% A
}
return(R)
}
```

Not the most efficient method, perhaps, but it works. If you know of a better alternative, please add a comment to this blog entry. One possibility might be to port MATLAB’s `expm` function, as defined in `expm1.m` in the MATLAB demos directory, to R.

For a detailed review of methods for computing the exponential of a matrix, see:

Moler, Cleve and Charles Van Loan (2003), “Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later,” Society for Industrial and Applied Mathematics, 45 (1), 3-49.