[R] vectorized nested loop: apply a function that takes two rows

Jose Quesada quesada at gmail.com
Tue Jan 23 21:40:50 CET 2007

Dear R users,

I want to apply a function that takes two vectors as input to all pairs
(combinations (nrow(X), 2))of matrix rows in a matrix.
I know that ideally, one should avoid loops in R, but after reading the docs for
do.call, apply, etc, I still don't know how to write the nested loop in a
vectorized way.

Example data:
x 		= matrix(rnorm(1000), 100, 100)
zeros	= runif(90)
# this is actually a very large sparse matrix, but it doesn't matter for the
# example
x = as(dat,"CsparseMatrix")

# cosine function
cosine = function (x, y){
	if (is.vector(x) && is.vector(y)) {
		return(crossprod(x, y)/sqrt(crossprod(x) * crossprod(y)))
	} else {stop("cosine: argument mismatch. Two vectors needed as input.")}

# The loop-based solution I have is:
		if (is(x, "Matrix") ) {
			cos 	= array(NA, c(ncol(x), ncol(x))) # preallocate memory
			for (i in 2:ncol(x)) {
				for (j in 1:(i - 1)) {
					cos[i, j] = cosine(x[, i], x[, j])

This solution seems inneficient. Is there an easy way of achieving this with a
clever do.call + apply combination?
Thanks in advance,

Jose Quesada, PhD
Research fellow, Psychology Dept.
Sussex University, Brighton, UK

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