# Sorting element pairs by differences?

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Marco Bakker on 7 Oct 2016
Commented: Jos (10584) on 7 Oct 2016
Suppose values is a vector, how to produce a matrix whose rows contain pairs of elements of this vector, ordered ascending by the differences between the elements.
For example:
values = [1,2,1.5,1.9]
I want the matrix
differences = [1.9 2; 1.5 1.9; 1 1.5; 1.5 2; 1 1.9; 1 2]

uu tsi on 7 Oct 2016
the following is my code
values = [1,2,1.5,1.9];
ss = nchoosek(values, 2);
[~, idx] = sort(abs(diff(ss')));
res = ss(idx, :)
Jos (10584) on 7 Oct 2016
Thanks for having put my answer in code. As a follow-up: diff(A,1,2) is faster than diff(A'), and A.' (transpose)is more versatile than A' (conjugate transpose).

Massimo Zanetti on 7 Oct 2016
More elegant is to use pdist, that does the bad job..

Jos (10584) on 7 Oct 2016
Take a look at NCHOOSEK, ABS, DIFF, and SORT:
• with X = nchoosek(values,2) you can get all the 6 different combinations
• use Y = abs(diff(X)) to get the absolute differences
• the second output of the function sort, applied tot these latter values, can be uses to sort the combinations accordingly.