[petsc-users] eigensolution error with slepc
David Knezevic
david.knezevic at akselos.com
Mon Apr 4 11:32:02 CDT 2016
Hi Jose,
I'm interested to know more about this comment from your email below:
"You can also try the symmetric-indefinite solver, but this is not
recommended since it is not numerically stable."
I frequently use SLEPc's symmetric-indefinite solver for buckling
eigenvalue problems (which are naturally symmetric and indefinite), and
this works well in my experience. But, based on your comment, I was
wondering if you would recommend a different solver for this case?
Thanks,
David
On Mon, Apr 4, 2016 at 12:18 PM, Jose E. Roman <jroman at dsic.upv.es> wrote:
>
> > El 4 abr 2016, a las 18:06, Manav Bhatia <bhatiamanav at gmail.com>
> escribió:
> >
> > Hi Jose,
> >
> > I also read these matrices into matlab and found the eigenvalues as
> >
> > >>A = PetscBinaryRead('A.petsc’);
> > >>B = PetscBinaryRead(‘B.petsc’);
> > >> [v,d] = eigs(A,B)
> > (*** got a lot of output about poor-conditioning ***)
> > >> diag(d)
> >
> > ans =
> >
> > 1.0e-05 *
> >
> > -0.2219
> > 0.0229
> > 0.0229
> > 0.0025
> > 0.0019
> > 0.0014
> >
> > >> So, one of these is turning out to be negative, but I am still
> getting numbers.
> >
> >
> >
> > Using these matrices with ex7 produces an error:
> >
> > Dhcp-90-243:T_400_V_0 manav$
> /Users/manav/Documents/codes/numerical_lib/slepc/slepc-3.6.2/src/eps/examples/tutorials/ex7
> -f1 A.petsc -f2 B.petsc -eps_gen_hermitian -eps_view -eps_nev 1
> >
> > Generalized eigenproblem stored in file.
> >
> > Reading REAL matrices from binary files...
> > [0]PETSC ERROR: --------------------- Error Message
> --------------------------------------------------------------
> > [0]PETSC ERROR: Error in external library
> > [0]PETSC ERROR: Error in Lapack xSTEQR 15
> > [0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html
> for trouble shooting.
> > [0]PETSC ERROR: Petsc Release Version 3.6.3, Dec, 03, 2015
> > [0]PETSC ERROR:
> /Users/manav/Documents/codes/numerical_lib/slepc/slepc-3.6.2/src/eps/examples/tutorials/ex7
> on a arch-darwin-cxx-opt named ws243-49.walker.dynamic.msstate.edu by
> manav Mon Apr 4 11:05:30 2016
> > [0]PETSC ERROR: Configure options
> --prefix=/Users/manav/Documents/codes/numerical_lib/petsc/petsc-3.6.3/../
> --CC=mpicc --CXX=mpicxx --FC=mpif90 --with-clanguage=c++ --with-fortran=0
> --with-mpiexec=/opt/local/bin/mpiexec --with-shared-libraries=1 --with-x=1
> --with-x-dir=/opt/X11 --with-debugging=0
> --with-lapack-lib=/usr/lib/liblapack.dylib
> --with-blas-lib=/usr/lib/libblas.dylib --download-superlu=yes
> --download-superlu_dist=yes --download-suitesparse=yes --download-mumps=yes
> --download-scalapack=yes --download-parmetis=yes
> --download-parmetis-shared=1 --download-metis=yes --download-metis-shared=1
> --download-hypre=yes --download-hypre-shared=1 --download-ml=yes
> --download-ml-shared=1 --download-sundials=yes --download-sundials-shared=1
> > [0]PETSC ERROR: #1 DSSolve_HEP_QR() line 495 in
> /Users/manav/Documents/codes/numerical_lib/slepc/slepc-3.6.2/src/sys/classes/ds/impls/hep/dshep.c
> > [0]PETSC ERROR: #2 DSSolve() line 543 in
> /Users/manav/Documents/codes/numerical_lib/slepc/slepc-3.6.2/src/sys/classes/ds/interface/dsops.c
> > [0]PETSC ERROR: #3 EPSSolve_KrylovSchur_Symm() line 68 in
> /Users/manav/Documents/codes/numerical_lib/slepc/slepc-3.6.2/src/eps/impls/krylov/krylovschur/ks-symm.c
> > [0]PETSC ERROR: #4 EPSSolve() line 101 in
> /Users/manav/Documents/codes/numerical_lib/slepc/slepc-3.6.2/src/eps/interface/epssolve.c
> > [0]PETSC ERROR: #5 main() line 147 in
> /Users/manav/Documents/codes/numerical_lib/slepc/slepc-3.6.2/src/eps/examples/tutorials/ex7.c
> > [0]PETSC ERROR: PETSc Option Table entries:
> > [0]PETSC ERROR: -eps_gen_hermitian
> > [0]PETSC ERROR: -eps_nev 1
> > [0]PETSC ERROR: -eps_view
> > [0]PETSC ERROR: -f1 A.petsc
> > [0]PETSC ERROR: -f2 B.petsc
> > [0]PETSC ERROR: -matload_block_size 1
> > [0]PETSC ERROR: ----------------End of Error Message -------send entire
> error message to petsc-maint at mcs.anl.gov----------
> >
> --------------------------------------------------------------------------
> > MPI_ABORT was invoked on rank 0 in communicator MPI_COMM_WORLD
> > with errorcode 76.
> >
> > NOTE: invoking MPI_ABORT causes Open MPI to kill all MPI processes.
> > You may or may not see output from other processes, depending on
> > exactly when Open MPI kills them.
> >
> --------------------------------------------------------------------------
> >
>
> The problem is that now K is indefinite. The check for indefinite B-matrix
> was not done correctly. This is fixed in 3.6.3, where you should get a more
> informative error:
>
> [0]PETSC ERROR: The inner product is not well defined: indefinite matrix
>
> When considered as a non-symmetric problem, the solver returns reasonable
> output:
>
> $ ./ex7 -f1 ~/tmp/bhatia/A.petsc -f2 ~/tmp/bhatia/B.petsc
>
> Generalized eigenproblem stored in file.
>
> Reading REAL matrices from binary files...
> Number of iterations of the method: 1
> Number of linear iterations of the method: 16
> Solution method: krylovschur
>
> Number of requested eigenvalues: 1
> Stopping condition: tol=1e-08, maxit=768
> Linear eigensolve converged (6 eigenpairs) due to CONVERGED_TOL;
> iterations 1
> ---------------------- --------------------
> k ||Ax-kBx||/||kx||
> ---------------------- --------------------
> -22.185956 8.66397e-08
> 2.291422 1.32466e-07
> 2.291422 1.55081e-07
> 0.252494 8.88997e-05
> 0.192453 0.000780395
> 0.141618 0.00113141
> ---------------------- --------------------
>
> The large residuals are due to bad scaling/conditioning of your matrices.
> You can also try the symmetric-indefinite solver, but this is not
> recommended since it is not numerically stable.
>
> $ ./ex7 -f1 ~/tmp/bhatia/A.petsc -f2 ~/tmp/bhatia/B.petsc
> -eps_gen_indefinite
>
> Generalized eigenproblem stored in file.
>
> Reading REAL matrices from binary files...
> Number of iterations of the method: 1
> Number of linear iterations of the method: 17
> Solution method: krylovschur
>
> Number of requested eigenvalues: 1
> Stopping condition: tol=1e-08, maxit=768
> Linear eigensolve converged (6 eigenpairs) due to CONVERGED_TOL;
> iterations 1
> ---------------------- --------------------
> k ||Ax-kBx||/||kx||
> ---------------------- --------------------
> -22.185956 7.08858e-09
> 2.291422 5.87577e-09
> 2.291422 6.39304e-09
> 0.252494 1.7497e-07
> 0.192453 1.63916e-06
> 0.141618 1.75568e-06
> ---------------------- --------------------
>
>
> Jose
>
>
>
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