[Octave-bug-tracker] [bug #49470] [MXE] eig.cc-tst failure in __run_test_suite__.m with 64-bit-Octave

[Avinoam Kalma]

Follow-up Comment #5, bug #49470 (project octave):

The problem is with


function chol_qz_accuracy (A, B, is_qz_accurate, is_chol_accurate)
  [V1,D1] = eig (A,B, 'qz');
  [V2,D2] = eig (A,B); %default is chol
  assert (isequal (A*V1,A*V1*D1), is_qz_accurate)
  assert (isequal (A*V2, A*V2*D2), is_chol_accurate)
endfunction


The test is


>> A = diag([10^-16, 10^-15]);
>> chol_qz_accuracy (A, A, true, false);
error: ASSERT errors for:  assert (isequal (A * V2, A * V2 *
D2),is_chol_accurate)

  Location  |  Observed  |  Expected  |  Reason
     ()           1            0         Abs err 1 exceeds tol 0


In 32 bit version


debug> D1
D1 =

Diagonal Matrix

   1   0
   0   1

debug> D2
D2 =

Diagonal Matrix

   1.00000         0
         0   1.00000

debug> D2 - [1 0; 0 1]
ans =

  -1.1102e-016  -0.0000e+000
  -0.0000e+000  2.2204e-016


So 


assert (isequal (A*V2, A*V2*D2), is_chol_accurate)


pass.

In 64 bit


debug> D1
D1 =

Diagonal Matrix

   1   0
   0   1

debug> D2
D2 =

Diagonal Matrix

   1   0
   0   1

debug> D2 - [1 0; 0 1]
ans =

   0  -0
  -0   0


so A*V2 = A*V2*D2 and the test *fails*.

Actually this test looks wrong. it does not check the correct values of V1,
V2. It checks if D1, D2 are close enough to the unit matrix, and if D2 is
close enough, the test fails.

I suggest to replace the test with checking the values of V1, V2 with
tolernce, something like


 assert (V1, diag ([1,1]), 0)
 assert (V2, diag([10^8,3.16227766016838*10^7]),10^(-7))



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