[petsc-users] Orthogonality of eigenvectors in SLEPC

Lucas Banting bantingl at myumanitoba.ca
Wed Nov 24 09:50:15 CST 2021


Hi Kuang-Chung Wang ,

It says your eigenvalue problem type is:
problem type: non-hermitian eigenvalue problem

While the email chain you refer to is for a hermitian eigenvalue problem.
Try changing your eigenvalue problem type to a hermitian or generalized hermitian problem and it should produce orthogonal eigenvectors.

Lucas
________________________________
From: petsc-users <petsc-users-bounces at mcs.anl.gov> on behalf of Wang, Kuang-chung <kuang-chung.wang at intel.com>
Sent: Wednesday, November 24, 2021 12:15 AM
To: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
Cc: Obradovic, Borna <borna.obradovic at intel.com>; Cea, Stephen M <stephen.m.cea at intel.com>
Subject: Re: [petsc-users] Orthogonality of eigenvectors in SLEPC


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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20211124/265b7120/attachment-0001.html>


More information about the petsc-users mailing list