[petsc-users] eigensolution error with slepc

Mon Apr 4 11:18:01 CDT 2016

> 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