How to fastly calculate this real number matrix manipulation?

I have a matrix X with dimensional . I want to calculate a matrix M with the same dimension as X. The element of M is calculated as follows

, where . In this equation, is the element of the matrix M and represents the product of a bunch of factors.

I know using for loop by extracting the element of X can obtain this matrix M but it is not efficient. Is there any other way to fastly calculate this matrix from X?

Answer 1

[Matt J]

e=(1:A)';
I=reshape(e,1,1,[]) == repmat( e,1,B);

Xp=permute(X,[3,2,1]);
D=X./(X-Xp);
D(I)=1;

M = ipermute( prod(D,1) ,[3,2,1]);