[Octave-bug-tracker] [bug #55710] svd may sometimes return -0 for exactly zero singular values

[Rik]

Update of bug #55710 (project octave):

                  Status:                    None => Confirmed              

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Follow-up Comment #2:

Matlab doesn't display the negative sign for zero, so you need to infer it
from something like taking 1/x.

Here is a sample session from R2018b showing that Matlab is returning a -0.


n = 10;
A = randn(n);
A = triu(A);

A(1) = -0;
[U,s,V] = svd(A);
1/s(end)
ans = -Inf


Also, for some reason this is dependent on the random values in A.  A more
interesting test is


n = 10;
for i = 1:20
  A = randn(n);
  A = triu(A);
  A(1) = -0;
  [U,S,V] = svd(A);
  tst(i) = (1/S(end) == -Inf);
end
fprintf ("-0 results: %d / 20\n", sum (tst));


This shows about half the time the results are -0 versus +0.

This occurs on both Matlab and Octave.

I'm pretty sure this will be found to be an upstream issue with LAPACK, but in
the meantime, we can probably do something about it.

The matrix S returned from the [U,S,V] is a diagonal matrix which in Octave
means it is stored in a space-efficient manner.  If we were to call abs(S)
before returning it would only require running abs() on the N elements of the
diagonal which would be exceedlingly quick.  Alternatively, we could fix
things up in the m-file with


S(S == 0) = 0;


which would replace any negative zeros with positive zeros.

@Tim: Is that an acceptable workaround?  Are all other singular values
guaranteed to be positive so that abs or the indexing trick would be enough?


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