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

[Russell Carden]

Follow-up Comment #5, bug #42097 (project octave):

Here is a cleaner example.  Note that for this particular matrix,
a correct eigenvalue decomposition is returned for A' but not for A.  This is
probably be due to the fact that A' is already upper Hessenberg, so that the
problem may lie in bringing A to upper Hessenberg form.

octave:1> A=[ 0 1 0 ; 0 0 1 ; 1  0 0 ]
A =

   0   1   0
   0   0   1
   1   0   0

octave:2> format long
octave:3> [V D]=eig(A)
V =

 Columns 1 and 2:

  -0.158836098085991 - 0.540780260472586i  -0.158836098085991 +
0.540780260472586i
   0.682327803828019 + 0.000000000000000i   0.682327803828019 -
0.000000000000000i
  -0.391621714024374 + 0.251771732042861i  -0.391621714024374 -
0.251771732042861i

 Column 3:

  -0.526062999881448 + 0.000000000000000i
  -0.358947411384288 + 0.000000000000000i
  -0.770982798781043 + 0.000000000000000i

D =

Diagonal Matrix

 Columns 1 and 2:

  -0.341163901914010 + 1.161541399997252i                                     
  0
                                        0  -0.341163901914010 -
1.161541399997252i
                                        0                                     
  0

 Column 3:

                                        0
                                        0
   0.682327803828019 + 0.000000000000000i

octave:4> A*V-V*D
ans =

 Columns 1 and 2:

  -0.000000000000000 + 0.000000000000000i  -0.000000000000000 -
0.000000000000000i
  -0.158836098085990 - 0.540780260472587i  -0.158836098085990 +
0.540780260472587i
  -0.000000000000000 + 0.000000000000000i  -0.000000000000000 -
0.000000000000000i

 Column 3:

   0.000000000000000 + 0.000000000000000i
  -0.526062999881449 + 0.000000000000000i
   0.000000000000000 + 0.000000000000000i

octave:5> [V D]=eig(A')
V =

 Columns 1 and 2:

   0.577350269189626 + 0.000000000000000i   0.577350269189626 -
0.000000000000000i
  -0.288675134594813 - 0.500000000000000i  -0.288675134594813 +
0.500000000000000i
  -0.288675134594813 + 0.500000000000000i  -0.288675134594813 -
0.500000000000000i

 Column 3:

  -0.577350269189626 + 0.000000000000000i
  -0.577350269189626 + 0.000000000000000i
  -0.577350269189626 + 0.000000000000000i

D =

Diagonal Matrix

 Columns 1 and 2:

  -0.500000000000000 + 0.866025403784439i                                     
  0
                                        0  -0.500000000000000 -
0.866025403784439i
                                        0                                     
  0

 Column 3:

                                        0
                                        0
   1.000000000000000 + 0.000000000000000i

octave:6> A
A =

   0   1   0
   0   0   1
   1   0   0

octave:7> A'*V-V*D
ans =

 Column 1:

  -2.22044604925031e-16 - 5.55111512312578e-17i
   1.11022302462516e-16 + 2.77555756156289e-17i
  -1.11022302462516e-16 + 3.33066907387547e-16i

 Column 2:

  -2.22044604925031e-16 + 5.55111512312578e-17i
   1.11022302462516e-16 - 2.77555756156289e-17i
  -1.11022302462516e-16 - 3.33066907387547e-16i

 Column 3:

  -2.22044604925031e-16 + 0.00000000000000e+00i
   4.44089209850063e-16 + 0.00000000000000e+00i
   1.11022302462516e-16 + 0.00000000000000e+00i

octave:8> 


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