Row-wise correlations in R

Question

I have two matrices of the same size. I would like to calculate the correlation coefficient between each pair of rows in these matrices; row 1 from A with row 1 B, row 2 from A with row 2 from B etc.

A <- matrix(runif(1:200), nrow=20)
B <- matrix(runif(1:200), nrow=20)

Best I could come up with is

ret <- sapply(1:20, function(i) cor(A[i,], B[i,]))

but it is terribly inefficient (the matrices have tens of thousands of rows). Is there a better, faster way?

Answer 1

This should be fast:

cA <- A - rowMeans(A)
cB <- B - rowMeans(B)
sA <- sqrt(rowMeans(cA^2))
sB <- sqrt(rowMeans(cB^2))

rowMeans(cA * cB) / (sA * sB)

Answer 2

You could create vectorized functions that will calculate covariance and SD for you such as,

RowSD <- function(x) {
  sqrt(rowSums((x - rowMeans(x))^2)/(dim(x)[2] - 1))
}

VecCov <- function(x, y){
  rowSums((x - rowMeans(x))*(y - rowMeans(y)))/(dim(x)[2] - 1)
}

Then, simply do

VecCov(A, B)/(RowSD(A) * RowSD(B))