[Octave-bug-tracker] [bug #60357] Failing test for `qz` with LAPACK 3.9.1

[Markus Mützel]

Follow-up Comment #15, bug #60357 (project octave):

Looks like I misspelled some tags. Next attempt:

Re comment #12:
With LAPACK 3.9.1, I see the following:

> a = [ 10 1 2;
1 2 -1;
1 1 2];
b = reshape (1:9,3,3);
[aa, bb, q, z, v, w, lambda] = qz (a, b);
>> a*v

ans =

5.000000 7.659527 -1.273807
-2.000000 3.806974 -1.526360
0.500000 -0.045579 -1.778912

>> b*v*diag(lambda)

ans =

-3.101857 7.659527 -1.273807
-4.652786 3.806974 -1.526360
-6.203714 -0.045579 -1.778912


If I read the documentation of `qz` correctly, the last two matrices should be
the same. But the first column differs by a large amount.
IIUC, that column corresponds to the eigenvalue that differs by several orders
of magnitude from the other two values.

`b*v` is close to double `eps` for that eigenvalue:

>> b*v
ans =

-8.8818e-16 -1.7998e+00 -6.8665e+00
-1.3323e-15 -8.9456e-01 -8.2279e+00
-1.7764e-15 1.0710e-02 -9.5893e+00


It might be good if someone with a background in linear algebra could have a
look.
Should we postprocess the results from LAPACK and discard the "outlier"
eigenvalue?


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