[Octave-bug-tracker] [bug #63787] test pcg may fail at high optimization

[Dmitri A. Sergatskov]

URL:
  <https://savannah.gnu.org/bugs/?63787>

                 Summary: test pcg may fail at high optimization
                 Project: GNU Octave
               Submitter: dasergatskov
               Submitted: Fri 10 Feb 2023 09:19:45 PM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Unexpected Error or Warning
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
                 Release: 8.0.90
         Discussion Lock: Any
        Operating System: Any
           Fixed Release: None
         Planned Release: None


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Follow-up Comments:


-------------------------------------------------------
Date: Fri 10 Feb 2023 09:19:45 PM UTC By: Dmitri A. Sergatskov <dasergatskov>
With gcc 11 or gcc 12 and (_O2 -mavx -mavx2 -flto) 
"test pcg" fails:


octave:1> test pcg
***** testif HAVE_CHOLMOD
 ## pcg solves preconditioned linear system with A HPD
 N = 20;
 A = sparse (toeplitz ([4, 1, zeros(1, 18)])) + ...
     i * sparse (toeplitz ([0, 1, zeros(1, 18)], [0, -1, zeros(1,18)]));
 b = A * ones (N, 1);
 M2 = chol (A + 0.1 * eye (N));  # Factor of a perturbed matrix
 M = M2' * M2;
 Hermitian_A = ishermitian (A);
 Hermitian_M = ishermitian (M);
 [x, flag] = pcg (A, b, [], 2*N, M);
 assert (Hermitian_A, true);
 assert (Hermitian_M, true);
 assert (flag, 0);
 assert (x, ones (N, 1), -1e-4);
!!!!! test failed
ASSERT errors for:  assert (Hermitian_M,true)

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

due to :


octave:2> N = 20;
 A = sparse (toeplitz ([4, 1, zeros(1, 18)])) + ...
     i * sparse (toeplitz ([0, 1, zeros(1, 18)], [0, -1, zeros(1,18)]));
 b = A * ones (N, 1);
 M2 = chol (A + 0.1 * eye (N));  # Factor of a perturbed matrix
 M = M2' * M2;
octave:7> ishermitian (M)
ans = 0
octave:8> Z = M - M'
Z =

Compressed Column Sparse (rows = 20, cols = 20, nnz = 19 [4.8%])

  (2, 2) ->           0 - 5.0446e-18i
  (3, 3) ->           0 - 5.1973e-17i
  (4, 4) ->           0 + 2.0610e-17i
  (5, 5) ->           0 + 1.6595e-17i
  (6, 6) ->           0 - 4.0964e-17i
  (7, 7) ->           0 - 2.9936e-18i
  (8, 8) ->           0 - 3.1185e-17i
  (9, 9) ->           0 - 5.5264e-17i
  (10, 10) ->           0 - 6.4907e-19i
  (11, 11) ->           0 + 5.3025e-17i
  (12, 12) ->           0 - 2.8965e-17i
  (13, 13) ->           0 - 2.2264e-17i
  (14, 14) ->           0 + 5.3442e-18i
  (15, 15) ->           0 - 2.1381e-18i
  (16, 16) ->           0 - 3.6669e-17i
  (17, 17) ->           0 - 4.4072e-17i
  (18, 18) ->           0 - 2.9208e-18i
  (19, 19) ->           0 + 5.4313e-17i
  (20, 20) ->           0 + 4.2576e-17i



I think the "Hermitian_M = ishermitian (M);" should be 
replaced with relaxed version "Hermitian_M = ishermitian (M, eps);" or
similar.

Dmitri.
-- 








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