[R] better way to iterate matrix multiplication?

[Martyn Byng]

Hi,

If you only want the final matrix, i.e. in this case the pm at 10
months, then you might be better off looking at something like the
square-and-multiply algorithm
(http://en.wikipedia.org/wiki/Exponentiation_by_squaring) rather than a
brute force multiplication.

Martyn

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Jonathan Knibb
Sent: 01 February 2011 14:05
To: r-help at r-project.org
Subject: [R] better way to iterate matrix multiplication?

I'm simulating a Markov process using a vector of proportions. Each 
value in the vector represents the proportion of the population who are 
in a particular state (so the vector sums to 1). I have a square matrix 
of transition probabilities, and for each tick of the Markov clock the 
vector is multiplied by the transition matrix.

To illustrate the sort of thing I mean:

pm <- c(0.5,0.5,0)  # half of cases start in state 1, half in state 2
tm <- matrix(runif(9),nrow=3)  # random transition matrix for
illustration
tm <- t(apply(tm,1,function (x) x/sum(x)))  # make its rows sum to 1
total.months = 10
for(month in 1:total.months) {pm <- pm %*% tm}  # slow!
pm  # now contains the proportion of cases in each state after 10 months

My question is: is there a quicker, more R-idiomatic way of doing it, 
avoiding 'for'? I've been trying to use apply() to fill a matrix with 
the vectors, but I can't get this to act iteratively.

Suggestions gratefully received!

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