[petsc-users] Orthogonality of eigenvectors in SLEPC

Wang, Kuang-chung kuang-chung.wang at intel.com
Wed Nov 24 00:15:11 CST 2021


Dear Jose :
I came across this thread describing issue using   krylovschur and finding eigenvectors non-orthogonal.
https://lists.mcs.anl.gov/pipermail/petsc-users/2014-October/023360.html

I furthermore have tested by reducing the tolerance as highlighted below from 1e-12 to 1e-16 with no luck.
Could you please suggest options/sources to try out ?
Thanks a lot for sharing your knowledge!

Sincere,
Kuang-Chung Wang

=======================================================
Kuang-Chung Wang
Computational and Modeling Technology
Intel Corporation
Hillsboro OR 97124
=======================================================

Here are more info:

  1.  slepc/3.7.4
  2.  output message from by doing  EPSView(eps,PETSC_NULL):
EPS Object: 1 MPI processes
  type: krylovschur
    Krylov-Schur: 50% of basis vectors kept after restart
    Krylov-Schur: using the locking variant
  problem type: non-hermitian eigenvalue problem
  selected portion of the spectrum: closest to target: 20.1161 (in magnitude)
  number of eigenvalues (nev): 40
  number of column vectors (ncv): 81
  maximum dimension of projected problem (mpd): 81
  maximum number of iterations: 1000
  tolerance: 1e-12
  convergence test: relative to the eigenvalue
BV Object: 1 MPI processes
  type: svec
  82 columns of global length 2988
  vector orthogonalization method: classical Gram-Schmidt
  orthogonalization refinement: always
  block orthogonalization method: Gram-Schmidt
  doing matmult as a single matrix-matrix product
DS Object: 1 MPI processes
  type: nhep
ST Object: 1 MPI processes
  type: sinvert
  shift: 20.1161
  number of matrices: 1
  KSP Object:  (st_)   1 MPI processes
    type: preonly
    maximum iterations=1000, initial guess is zero
    tolerances:  relative=1.12005e-09, absolute=1e-50, divergence=10000.
    left preconditioning
    using NONE norm type for convergence test
  PC Object:  (st_)   1 MPI processes
    type: lu
      LU: out-of-place factorization
      tolerance for zero pivot 2.22045e-14
      matrix ordering: nd
      factor fill ratio given 0., needed 0.
        Factored matrix follows:
          Mat Object:           1 MPI processes
            type: seqaij
            rows=2988, cols=2988
            package used to perform factorization: mumps
            total: nonzeros=614160, allocated nonzeros=614160
            total number of mallocs used during MatSetValues calls =0
              MUMPS run parameters:
                SYM (matrix type):                   0
                PAR (host participation):            1
                ICNTL(1) (output for error):         6
                ICNTL(2) (output of diagnostic msg): 0
                ICNTL(3) (output for global info):   0
                ICNTL(4) (level of printing):        0
                ICNTL(5) (input mat struct):         0
                ICNTL(6) (matrix prescaling):        7
                ICNTL(7) (sequential matrix ordering):7
                ICNTL(8) (scaling strategy):        77
                ICNTL(10) (max num of refinements):  0
                ICNTL(11) (error analysis):          0
                ICNTL(12) (efficiency control):                         1
                ICNTL(13) (efficiency control):                         0
                ICNTL(14) (percentage of estimated workspace increase): 20
                ICNTL(18) (input mat struct):                           0
                ICNTL(19) (Schur complement info):                       0
                ICNTL(20) (rhs sparse pattern):                         0
                ICNTL(21) (solution struct):                            0
                ICNTL(22) (in-core/out-of-core facility):               0
                ICNTL(23) (max size of memory can be allocated locally):0
                ICNTL(24) (detection of null pivot rows):               0
                ICNTL(25) (computation of a null space basis):          0
                ICNTL(26) (Schur options for rhs or solution):          0
                ICNTL(27) (experimental parameter):                     -24
                ICNTL(28) (use parallel or sequential ordering):        1
                ICNTL(29) (parallel ordering):                          0
                ICNTL(30) (user-specified set of entries in inv(A)):    0
                ICNTL(31) (factors is discarded in the solve phase):    0
                ICNTL(33) (compute determinant):                        0
                CNTL(1) (relative pivoting threshold):      0.01
                CNTL(2) (stopping criterion of refinement): 1.49012e-08
                CNTL(3) (absolute pivoting threshold):      0.
                CNTL(4) (value of static pivoting):         -1.
                CNTL(5) (fixation for null pivots):         0.
                RINFO(1) (local estimated flops for the elimination after analysis):
                  [0] 8.15668e+07
                RINFO(2) (local estimated flops for the assembly after factorization):
                  [0]  892584.
                RINFO(3) (local estimated flops for the elimination after factorization):
                  [0]  8.15668e+07
                INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):
                [0] 16
                INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):
                  [0] 16
                INFO(23) (num of pivots eliminated on this processor after factorization):
                  [0] 2988
                RINFOG(1) (global estimated flops for the elimination after analysis): 8.15668e+07
                RINFOG(2) (global estimated flops for the assembly after factorization): 892584.
                RINFOG(3) (global estimated flops for the elimination after factorization): 8.15668e+07
                (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.,0.)*(2^0)
                INFOG(3) (estimated real workspace for factors on all processors after analysis): 614160
                INFOG(4) (estimated integer workspace for factors on all processors after analysis): 31971
                INFOG(5) (estimated maximum front size in the complete tree): 246
                INFOG(6) (number of nodes in the complete tree): 197
                INFOG(7) (ordering option effectively use after analysis): 2
                INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): 100
                INFOG(9) (total real/complex workspace to store the matrix factors after factorization): 614160
                INFOG(10) (total integer space store the matrix factors after factorization): 31971
                INFOG(11) (order of largest frontal matrix after factorization): 246
                INFOG(12) (number of off-diagonal pivots): 0
                INFOG(13) (number of delayed pivots after factorization): 0
                INFOG(14) (number of memory compress after factorization): 0
                INFOG(15) (number of steps of iterative refinement after solution): 0
                INFOG(16) (estimated size (in MB) of all MUMPS internal data for factorization after analysis: value on the most memory consuming processor): 16
                INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): 16
                INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): 16
                INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): 16
                INFOG(20) (estimated number of entries in the factors): 614160
                INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): 14
                INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): 14
                INFOG(23) (after analysis: value of ICNTL(6) effectively used): 0
                INFOG(24) (after analysis: value of ICNTL(12) effectively used): 1
                INFOG(25) (after factorization: number of pivots modified by static pivoting): 0
                INFOG(28) (after factorization: number of null pivots encountered): 0
                INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): 614160
                INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): 13, 13
                INFOG(32) (after analysis: type of analysis done): 1
                INFOG(33) (value used for ICNTL(8)): 7
                INFOG(34) (exponent of the determinant if determinant is requested): 0
    linear system matrix = precond matrix:
    Mat Object:     1 MPI processes
      type: seqaij
      rows=2988, cols=2988
      total: nonzeros=151488, allocated nonzeros=151488
      total number of mallocs used during MatSetValues calls =0
        using I-node routines: found 996 nodes, limit used is 5
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