MATLAB: How to avoid for loops when generating index arrays

for loopindexingloopMATLABvectorization

I often find myself coding nested for loops to generate vectors of integer indices. For example:
n = 4;
i = 1;
for L = 0:n
    for M = -L:L
        l(i) = L;
        m(i) = M;
        i = i+1;
    end
end
All I need are the vectors "l" and "m". I can preallocate to save some speed, but my real problem is having to use the for loops as sometimes the index vectors I need to create have many more nested for loops whose (note that the inner loop index depends on the outer loop index).
Is there a simple way to avoid using loops to generate index vectors like these?

Best Answer

Here's another method, less memory consuming than NDGRID
    mm=sparse(-n:n);
    ll=sparse(0:n);
    map=bsxfun(@le,abs(mm.'),ll);
    idx=nonzeros(bsxfun(@times,map,1:length(ll)  ));
       l=full(ll(idx));
    idx=nonzeros(bsxfun(@times,map,(1:length(mm)).'))  ;
       m=full(mm(idx));
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