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

[Markus Mützel]

Follow-up Comment #14, bug #60357 (project octave):

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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