Counting number of common elements between the rows of two different matrices

Hello

I'm trying to solve this problem without using a for loop but I have so
far failed to find a solution.

I have two matrices of K columns each, e.g. (K=5), and with numbers of
row N_A and N_B respectively

A = ? ? (1 5 3 8 15;
? ? ? ? 2 7 20 11 13;
? ? ? ? 12 19 20 21 43)

B = ? ? (2 6 30 8 16;
? ? ? ? 3 8 19 11 13)

(the actual matrices have hundreds of thousands of entry, that's why I'm
keen to avoid "for" loops)

And what I need to do is to apply a function which counts the number of
common elements between ANY row of A and ANY row of B, giving a result
like this:


A1 vs B1: ?1 ?# (8 is a common element)
A1 vs B2: ?1 ?# (8 is a common element)
A2 vs B1: ?1 ?# (2 is a common element)
A2 vs B2: ?1 ?# 11, 13 are common elements
Etc.

I've built a function that counts the number of common elements between
two vectors, based on the intersect function in the R manual

common_elements <- function(x,y) length(y[match(x,y,nomatch=0)])

And a double loop who solves my problem would be something like
(pseudo-code)

For(i in 1:N_A){
? ? ? ?for(j in 1:N_B){
? ? ? ? ? ? ? ?ce(i,j)=common_elements(a(i),b(j))
? ? ? ? ? ? ? ?}
? ? ? ?}

Is there an efficient, clean way to do the same job and give as an
output a matrix N_A x N_B such as that above?

Thanks a lot for your help

Regards

Pietro