# Arrange elements on a matrix according to rowSums + short 'apply' Q

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...

Use rowSums and colSums more! The first problem can be done with simple:

```MAT[order(rowSums(MAT),decreasing=T),]
```

The second with:

```MAT/rep(rowSums(MAT),nrow(MAT))
```

this is a bit hacky, but becomes obvious if you recall that matrix is also a by-column vector. Taking also recycling into account it can be also done just by:

```MAT/rowSums(MAT)
```

For your first request, this gets the desired descending reordering by row sums:

```MAT[rev(order(rowSums(MAT))), ]
```

And this gets your TMAT in one step. The apply function returns a series of vectors and the column major ordering of matrices will transpose the results from what beginning users of R expect.

```> TMAT <- t(apply(MAT, 1, function(X) X/sum(X)) )
> rowSums(TMAT)
A B C D E
1 1 1 1 1
```