Matlab: need some help for a seemingly simple vectorization of an operation

Question

I would like to optimize this piece of Matlab code but so far I have failed. I have tried different combinations of repmat and sums and cumsums, but all my attempts seem to

Answer 1

The nchoosek(v,k) function generates all combinations of the elements in v taken k at a time. We can use this to generate all possible pairs of indicies then use this to vectorize the loops. It appears that in this case the vectorization doesn't actually improve performance (at least on my machine with 2017a). Maybe someone will come up with a more efficient approach.

idx = nchoosek(1:T,2);
d = bsxfun(@minus,(X(idx(:,2),:) - X(idx(:,1),:)), (idx(:,2)-idx(:,1))/T);
Result = sum(abs(d),1)';