Indexing matrix with index pairs without using linear indexing

I have a set of n row indices [r1 r2 ... rn], and n column indices [c1 c2 ... cn], and I would like to get the elements corresponding to indices (r1,c1), (r2,c2) and so on. The normal way of doing this is using linear indexing A(sub2ind(size(A),r,c)). However, I am dealing with sparse matrices of ridiculous dimensions (e.g.: [2^40, 2^10] ), meaning that I can no longer use linear indexing.

A naive alternative would be with a loop:

A = sprand(2^40,2^10, 1e-10);
r = [1 4 345 922139 2^40]';
c = [2 89 100 120 1024]';

out = zeros(length(r),1);
for i=1:length(r)
    out(i) = A(r(i), c(i));
end

Are there more efficient ways of doing this?

Answer 1

[Matt J]

Bruno Luong has a fast MEX for this,

https://www.mathworks.com/matlabcentral/fileexchange/23488-sparse-sub-access

Answer 2

[AS]

Turns out I foud the solution myself after all:

out = full(diag(A(r,c)));

[Matt J]

That will of course be inefficient if A(r,c) is not sparse.