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Simone Scaringi

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29 May 2008 nCtwo All combinations of N elements taken two at the time. Author: Simone Scaringi pairs, nchoose2, nchoosek, combinations, matrices 0 4
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01 Jun 2008 nCtwo All combinations of N elements taken two at the time. Author: Simone Scaringi D'Errico, John

Interestingly, I can do better than the triu code, still in an entirely vectorized solution. The code below has no additional memory allocation. But it is no faster than the other versions. According to profile, most of the time consumed is mainly in the very last line, just the simple lookup.

function IJ = nc2(nvec)
nvec = nvec(:);
n = length(nvec);
IJ = ones(n*(n-1)/2,1)*[0 1];
ind = cumsum([1;((n-1):-1:2)']);
IJ(ind,1) = 1;
IJ(1,2) = 2;
IJ(ind(2:end),2) = 2+((1-n):1:-2)';
IJ = nvec(cumsum(IJ,1));

01 Jun 2008 nCtwo All combinations of N elements taken two at the time. Author: Simone Scaringi x@y.z, Jos

As for the present submission, it is pretty good and indeed fast. It contains help (including a H1 line). It unfortunately lacks internal comments and examples, and can be improved in this respect.
    
The following version of JD's excellent engine directly returns the rightly order output, and is a little less memory consuming (2*N-1 elements less...) :
 [c2,c1] = find(tril(ones(numel(x)-1)));
 y = x([c1(:) c2(:)+1]);
     
I have just submitted my own fast, vectorized alternative of nchoosek(x,2) to the FEX, which is also not memory consuming.
30 May 2008 nCtwo All combinations of N elements taken two at the time. Author: Simone Scaringi Scaringi, Simone

Very clever and elegant solution John!

However when dealing with large N the step

 [I,J] = find(triu(ones(length(nvec)),1));

requires lot's of ram, and nCtwo.m performs faster (even for small N)...

I know for loops are not appropriate within matlab, however one has to include some when dealing with big datasets...

Thanks...
Simo
29 May 2008 nCtwo All combinations of N elements taken two at the time. Author: Simone Scaringi D'Errico, John

Cleaner is just this simple solution.

[I,J] = find(triu(ones(length(nvec)),1));
IJ = [I(:),J(:)];
IJ = nvec(IJ);
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combinations, differentiation, matrices, nchoose2, nchoosek
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29 May 2008 nCtwo All combinations of N elements taken two at the time. Author: Simone Scaringi pairs, nchoose2, nchoosek, combinations, matrices 0 4
11 Nov 2005 2-D Savitzky-Golay Smoothing and Differentiation Filter Obtain the coefficients of the 2-D Savitzky-Golay smoothing and differentiation filter, ... Author: Jianwen Luo differentiation, leastsquares, savitzkygolay, filter analysis, smoothing, filter design 2 1

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