Non negative matrix (NMF) implementation

Hello

I try to work on the traditional NMF with the paper http://www.columbia.edu/~jwp2128/Teaching/E4903/papers/nmf_nature.pdf

I have V matrix (nxm) , W(nxr), and H(rxn)

Updating rules:

                W (i,a) <- W(i,a)* Sum over mill ( V(i,mill)/(WH)(i,mill) * H(a,mill))

                H (a,mill) <- H(a,mill)* sum over i (W(i,a)* V(i,mill)/(WH)(i,mill))

in which i from 1 : n, a from 1:r, and mill from 1:m

How should we convert the equation above into matrix manipulation without using loop?

Thanks