Pair-wise operation on two vectors that avoids double calculation

I have 1 vector and I would like to calculate the pair-wise difference.

This does the job, but it unnecessarily performs the calculation twice.

bsxfun(@minus, A, A')

Is there a way to do this only outputs a lower triangular matrix?

Answer 1

[Matt J]

I doubt there's a way that makes the effort worthwhile, but here is one possibility,

      N=length(A);

      map=tril(true(N));
      [i,j]=find(map);

      out=double(map);
      out(map)=A(i)-A(j);

[Sam Li]

Hi Matt thanks for your answer. This does work indeed but it seems to run 10 times slower than using bsxfun directly. I guess I will just have to stick with the array manipulation in this case.

Answer 2

[Bjorn Gustavsson]

This made me curious about how the JIT-compiler performs. This function shouldn't do too many extra operations:

function Adiffs = AAprimedifferences(A)

for i1 = length(A):-1:2,
  for i2 = (i1-1):-1:1,   
    Adiffs(i1,i2) = A(i1) - A(i2);
  end
end

I don't have time to do timings or such properly...

[Sam Li]

Hi Bjorn, this one runs about 4 times slower than bfxfun. The test code is here:

A = rand(10000,10000);
method == 0;
tic
if method == 0 

      out = AAprimedifferences(A);

else

      out = bsxfun(@minus, A, A');

end
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