Faster and More Efficient `squareform()`

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Royi Avital
Royi Avital 2019-10-2
编辑： Royi Avital 2019-10-15
I'm using squareform(pdist(mX)) fairly often.
The problem is squareform() is so slow it makes use of pdist2(mX, mX) faster.
This is basically what squareform() does in the case above:
function [ mY ] = MySquareForm( vX )
numElements = numel(vX);
numDist = (1 + sqrt(1 + (8 * numElements))) / 2;
mY = zeros(numDist, numDist, class(vX));
mY(tril(true(numDist, numDist), -1)) = vX;
mY = mY + mY.';
end
Basically, imagine you have a symmetric matrix mX then the vector vx above is it lower tringular matrix vectorized.
Something like:
mX = randn(100, 100);
mX = mX + mX.';
mL = tril(mX, -1);
vX = mL(mL ~= 0);
If the diagonal of is zerod then one could reproduce mX from vX using MySquareForm().
Any ideas how to do the same more efficiently and faster?

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