[Octave-bug-tracker] [bug #42097] 64bit Slackware, eig returning incorrect results

[Russell Carden]

Follow-up Comment #7, bug #42097 (project octave):

I compiled octave, blas, and lapack using the scripts on slackbuild.org for
version 14.1 of slackware.  I had been using using atlas until I encountered
this problem with eig.  Since encountering this problem with eig, I removed
atlas and the packages affected by its removal and then reinstalled.

Everything seems to work for upper Hessenberg matrices.  Scaling the matrix,
computing the eigenvalues and then scaling back produces incorrect results.

For the matrix from my previous comment, using the V and D returned from eig

octave:45> V*D/V
ans =

 Columns 1 and 2:

   0.000000000000001 - 0.000000000000000i   1.000000000000000 +
0.000000000000000i
  -1.000000000000001 + 0.000000000000000i  -0.000000000000001 -
0.000000000000000i
   1.000000000000000 - 0.000000000000000i   0.000000000000000 +
0.000000000000000i

 Column 3:

  -0.000000000000000 + 0.000000000000000i
   1.000000000000000 - 0.000000000000000i
  -0.000000000000000 - 0.000000000000000i

or V*D/V=
  0 1 0 
 -1 0 0
  1 0 0 

The entry (3,1) entry seems to result in a perturbation of the (2,1) entry. 
The perturbation is not a linear function of A(3,1).  See the following

octave:115> for i=[1:38], A(3,1)=i; [V D]=eig(A);Ahat=V*D/V; disp([i
Ahat(2,1), Ahat(3,1)]), end
   1.0000 + 0.0000i  -1.0000 + 0.0000i   1.0000 + 0.0000i
   2.0000 + 0.0000i  -1.0000 - 0.0000i   2.0000 + 0.0000i
   3.0000 + 0.0000i  -2.0000 + 0.0000i   3.0000 + 0.0000i
   4.0000 + 0.0000i  -2.0000 - 0.0000i   4.0000 - 0.0000i
   5.0000 + 0.0000i  -2.0000 - 0.0000i   5.0000 + 0.0000i
   6.0000 + 0.0000i  -2.0000 + 0.0000i   6.0000 - 0.0000i
   7.0000 + 0.0000i  -2.0000 + 0.0000i   7.0000 + 0.0000i
   8.0000 + 0.0000i  -2.0000 + 0.0000i   8.0000 - 0.0000i
   9.0000 + 0.0000i  -2.0000 + 0.0000i   9.0000 + 0.0000i
   10.0000 +  0.0000i   -2.0000 -  0.0000i   10.0000 +  0.0000i
   11   -2   11
   12.0000 +  0.0000i   -2.0000 +  0.0000i   12.0000 +  0.0000i
   13.0000 +  0.0000i   -2.0000 +  0.0000i   13.0000 +  0.0000i
   14.0000 +  0.0000i   -2.0000 +  0.0000i   14.0000 -  0.0000i
   15.0000 +  0.0000i   -2.0000 +  0.0000i   15.0000 +  0.0000i
   16.0000 +  0.0000i   -2.0000 +  0.0000i   16.0000 +  0.0000i
   17.0000 +  0.0000i   -2.0000 +  0.0000i   17.0000 +  0.0000i
   18.0000 +  0.0000i   -2.0000 -  0.0000i   18.0000 -  0.0000i
   19.0000 +  0.0000i   -2.0000 +  0.0000i   19.0000 +  0.0000i
   20.0000 +  0.0000i   -2.0000 -  0.0000i   20.0000 +  0.0000i
   21.0000 +  0.0000i   -2.0000 +  0.0000i   21.0000 -  0.0000i
   22.0000 +  0.0000i   -2.0000 -  0.0000i   22.0000 +  0.0000i
   23.0000 +  0.0000i   -2.0000 -  0.0000i   23.0000 -  0.0000i
   24.0000 +  0.0000i   -2.0000 +  0.0000i   24.0000 -  0.0000i
   25.0000 +  0.0000i   -2.0000 -  0.0000i   25.0000 +  0.0000i
   26.0000 +  0.0000i   -2.0000 +  0.0000i   26.0000 +  0.0000i
   27.0000 +  0.0000i   -2.0000 -  0.0000i   27.0000 -  0.0000i
   28.0000 +  0.0000i   -2.0000 -  0.0000i   28.0000 +  0.0000i
   29.0000 +  0.0000i   -2.0000 +  0.0000i   29.0000 +  0.0000i
   30.0000 +  0.0000i   -2.0000 +  0.0000i   30.0000 -  0.0000i
   31.0000 +  0.0000i   -2.0000 -  0.0000i   31.0000 -  0.0000i
   32.0000 +  0.0000i   -2.0000 +  0.0000i   32.0000 +  0.0000i
   33.0000 +  0.0000i   -2.0000 +  0.0000i   33.0000 +  0.0000i
   34.0000 +  0.0000i   -2.0000 +  0.0000i   34.0000 +  0.0000i
   35.0000 +  0.0000i   -2.0000 +  0.0000i   35.0000 +  0.0000i
   36.0000 +  0.0000i   -2.0000 -  0.0000i   36.0000 +  0.0000i
   37.0000 +  0.0000i   -2.0000 +  0.0000i   37.0000 +  0.0000i
   38.0000 +  0.0000i   -4.0000 -  0.0000i   38.0000 +  0.0000i



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