Greetings,

My goal is to create a Markov transition matrix (probability of moving from
one state to another) with the 'highest traffic' portion of the matrix
occupying the top-left section. Consider the following sample:

inputData <- c(
    c(5, 3, 1, 6, 7),
    c(9, 7, 3, 10, 11),
    c(1, 2, 3, 4, 5),
    c(2, 4, 6, 8, 10),
    c(9, 5, 2, 1, 1)
    )

MAT <- matrix(inputData, nrow = 5, ncol = 5, byrow = TRUE)
colnames(MAT) <- c("A", "B", "C", "D", "E")
rownames(MAT) <- c("A", "B", "C", "D", "E")

rowSums(MAT)

I wan to re-arrange the elements of this matrix such that the elements with
the largest row sums are placed to the top-left, in descending order. Does
this make sense? In this case the order I'm looking for would be B, D, A, E,
C Any thoughts?

As an aside, here is the function I've written to construct the transition
matrix. Is there a more elegant way to do this that doesn't involve a double
transpose?

TMAT <- apply(t(MAT), 2, function(X) X/sum(X))
TMAT <- t(TMAT)

I tried the following:

TMAT <- apply(MAT, 1, function(X) X/sum(X))

But my the custom function is still getting applied over the columns of the
array, rather than the rows. For a check try:

rowSums(TMAT)
colSums(TMAT)

Row sums here should equal 1...

Many thanks in advance,
Aaron

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