[Octave-bug-tracker] [bug #39879] expm returns inaccurate results

[Marco Caliari]

Update of bug #39879 (project octave):

                  Status:                    None => Confirmed              

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Follow-up Comment #1:

The problem is in the balancing of the matrix. 
For instance, the first row of the "balanced" matrix has 1-norm 5e-2 and the
first column 9e14 (for the original matrix they are 3.5e-1 and 1e-1).
I think balance uses xGEBAL and that the problem is there (I'm using LAPACK
3.4.1 ang getting similar results with Matlab, where it is written "Balancing
can destroy the properties of certain matrices; use it with some care. If a
matrix contains small elements that are due to roundoff error [our case],
balancing might scale them up to make them as significant as the other
elements of the original matrix.").
I see here http://www.netlib.org/lapack/Errata/index2.html that xGEBAL still
has some problems in LAPACK 3.4.2.
If you remove the balancing stage, expm is fine. Possible solutions:

1) remove balancing from expm (anyone has a counterexample?)
2) try to fix balance: if, after balancing, the matrix is more unbalanced than
the original (for whatever reason), give back the original matrix and a
warning.

Marco

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