Behaviour of backslash operator for non-square matrices least-squares fitting
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Matt O'Donnell
on 24 Feb 2020
Commented: Matt O'Donnell
on 24 Feb 2020
I am currently trying to reproduce a set of results from a pre-existing project and can't get to the bottom of the following difference.
Phi = design matrix of input data size(29507x97)
Ref = reference values to fit to, six data sets, size(29507x6)
Phi = rand(29507,97);
Ref = rand(29507,6);
c1 = Phi\Ref;
for ii = 1:6
c2(:,ii) = Phi\Ref(:,ii);
end
all(all(c1==c2))
I would have expected c1 to give identical results to c2. I can't find detailed information on what the "\" algorithm is doing differently between these case.
Any help appreciated!
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Accepted Answer
the cyclist
on 24 Feb 2020
They are equal, to within floating-point precision. Notice that
max(abs(c1(:)-c2(:)))
is around 1e-16.
4 Comments
Matt J
on 24 Feb 2020
Edited: Matt J
on 24 Feb 2020
Also, internal parallelization of mldivide and other linear algebra operations is different depending on the size of the inputs. So, when you perform the mldivide column-by-column, the inputs are divided up into parallel chunks in a different way, leading to floating point differences.
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