[petsc-users] Orthogonality of eigenvectors in SLEPC

Wang, Kuang-chung kuang-chung.wang at intel.com
Thu Dec 2 14:06:21 CST 2021


Thanks Jose for your prompt reply.
I did find my matrix highly non-hermitian.  By forcing the solver to be hermtian, the orthogonality was restored. 
But I do need to root cause why my matrix is non-hermitian in the first place. 
Along the way, I highly recommend MatIsHermitian() function or combining functions like MatHermitianTranspose () MatAXPY MatNorm to determine the hermiticity to safeguard our program. 

Best,
Kuang  

-----Original Message-----
From: Jose E. Roman <jroman at dsic.upv.es> 
Sent: Wednesday, November 24, 2021 6:20 AM
To: Wang, Kuang-chung <kuang-chung.wang at intel.com>
Cc: petsc-users at mcs.anl.gov; 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

In Hermitian eigenproblems orthogonality of eigenvectors is guaranteed/enforced. But you are solving the problem as non-Hermitian.

If your matrix is Hermitian, make sure you solve it as a HEP, and make sure that your matrix is numerically Hermitian.

If your matrix is non-Hermitian, then you cannot expect the eigenvectors to be orthogonal. What you can do in this case is get an orthogonal basis of the computed eigenspace, see https://slepc.upv.es/documentation/current/docs/manualpages/EPS/EPSGetInvariantSubspace.html


By the way, version 3.7 is more than 5 years old, it is better if you can upgrade to a more recent version.

Jose



> El 24 nov 2021, a las 7:15, Wang, Kuang-chung <kuang-chung.wang at intel.com> escribió:
> 
> 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.ht
> ml
>  
> 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: 
> 	• slepc/3.7.4
> 	• 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



More information about the petsc-users mailing list