Two arrays defining 2D coordinates, as array indices

A faster way is to use linear indexing directly without calling SUB2IND:

output = A( size(A,1)*(iy-1) + ix )

... think of the matrix A as a 1D array (column-wise order)

This is the one-line method which is not very efficient for large matrices

reshape(diag(A(ix(:),iy(:))),[ny nx])

A clearer and more efficient method would be to use sub2ind. I've incorporated yuk's comment for situations (like yours) when ix and iy have the same number of elements:

newA = A(sub2ind(size(A),ix,iy));

Also, don't confuse x and y for i and j in notation - j and x generally represent columns and i and y represent rows.