Calculate Euclidean distances between all rows in matrices A and B

Question

I have two matrices, A and B, with N_a and N_b rows, respectively. I need to calculate the Euclidean distance between all pairwise combinations of an element in A (a) and another in B (b), such that the output of the calculation is an N_a by N_b matrix, where cell [a, b] is the distance from a to b. I've started an example below.

# Example
set.seed(1)
A <- matrix(rnorm(1000, 5, 50), ncol = 5)
B <- matrix(rnorm(10000, 0, 50), ncol = 5)

# Return N_a x N_b matrix of euclidean distances, where [a,b] is the
# distance from a to b

Answer 1

A one-liner without loops, without additional packages, and a little bit faster:

euklDist <- sqrt(apply(array(apply(B,1,function(x){(x-t(A))^2}),c(ncol(A),nrow(A),nrow(B))),2:3,sum))

Speed comparison:

> microbenchmark(jogo  = for (i in 1:nrow(A)) for (j in 1:nrow(B)) d[i,j] <- sqrt(sum((A[i,]-B[j,])^2)),
+                mra68 = sqrt(apply(array(app .... [TRUNCATED] 
Unit: seconds
  expr      min       lq     mean   median       uq      max neval
  jogo 3.601533 4.724619 5.403420 5.549199 6.098734 6.470888    10
 mra68 1.334661 1.635258 2.473297 2.542550 3.247981 3.348365    10