# [R] Exponentiate a matrix

Dimitrios Rizopoulos Dimitris.Rizopoulos at med.kuleuven.be
Thu Sep 21 20:58:27 CEST 2006

```Quoting Douglas Bates <bates at stat.wisc.edu>:

> On 9/21/06, Dimitrios Rizopoulos <Dimitris.Rizopoulos at med.kuleuven.be> wrote:
>>
>> Quoting Duncan Murdoch <murdoch at stats.uwo.ca>:
>>
>> > On 9/21/2006 10:40 AM, Doran, Harold wrote:
>> >> Suppose I have a square matrix P
>> >>
>> >> P <- matrix(c(.3,.7, .7, .3), ncol=2)
>> >>
>> >> I know that
>> >>
>> >>> P * P
>> >>
>> >> Returns the element by element product, whereas
>> >>
>> >>> P%*%P
>> >>
>> >> Returns the matrix product.
>> >>
>> >> Now, P^2 also returns the element by element product. But, is there a
>> >> slick way to write
>> >>
>> >> P %*% P %*% P
>> >>
>> >> Obviously, P^3 does not return the result I expect.
>> >
>> >
>> > I don't think there's anything built in, but it's easy to write your own:
>>
>> I think there was function mtx.exp() in the Malmig package, but it
>> seems that this package has been withdrawn from CRAN. An old version
>> appears to exist in:
>>
>> http://r.meteo.uni.wroc.pl/src/contrib/Descriptions/Malmig.html
>>
>> Best,
>> Dimitris
>
> Is that function for matrix powers or for the exponential of a matrix
> (which is what I initally thought that Harold wanted)?  There is a
> function expm in the Matrix package, patterned on the octave function
> of the same name, the calculates the matrix exponential for a square
> matrix.

this function calculates the n-th power of a matrix, and this is what
I thought Harold wanted, i.e.,

P %*% P %*% P %*% P

should be equal to

mtx.exp(P, 4)

>>
>>
>> > "%^%" <- function(mat, pow) {
>> >    stopifnot(length(pow) == 1, all.equal(pow, round(pow)), nrow(mat) ==
>> > ncol(mat))
>> >    pow <- round(pow)
>> >    if (pow < 0) {
>> >      mat <- solve(mat)
>> >      pow <- abs(pow)
>> >    }
>> >    result <- diag(nrow(mat))
>> >    while (pow > 0) {
>> >      result <- result %*% mat
>> >      pow <- pow - 1
>> >    }
>> >    result
>> > }
>> >
>> > Now P %^% 3 will give you the matrix cube.
>> >
>> > Duncan Murdoch
>> >
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