[R] Row-wise kronecker product with Matrix package

[Ally]

I'm trying to calculate the row-wise kronecker product A \Box B of two
sparse matrices A and B, and am struggling to find a quick way to do this
that takes advantage of sparseness.  I thought a good idea would be to use
"rep" to construct 2 matrices of the same dimension of the end product, and
multiply these two together: 

library(Matrix)
A<-Matrix(c(1,0,0,0,0,1,2,0), 2, 4)
B<-Matrix(c(2,5,0,0,0,1,0,0,0,0), 2, 5)

A[, rep(seq(ncol(A)), each = ncol(B))] * B[, rep(seq(ncol(B)),ncol(A))]
		
This works, but for much larger problems is slow (compared to keeping A and
B dense).  I was wondering why this happens, and whether there might be a
way around it?  

Thanks in advance for any advice, 

Alastair

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