[petsc-users] [SLEPc] Krylov-Schur convergence

[Ale Foggia]

Thanks Jose for the answer. I tried it an it worked! I send the output of
-eps_view again, just in case:

EPS Object: 1024 MPI processes
  type: krylovschur
    50% of basis vectors kept after restart
    using the locking variant
  problem type: non-symmetric eigenvalue problem
  selected portion of the spectrum: smallest real parts
  number of eigenvalues (nev): 1
  number of column vectors (ncv): 16
  maximum dimension of projected problem (mpd): 16
  maximum number of iterations: 291700777
  tolerance: 1e-09
  convergence test: relative to the eigenvalue
BV Object: 1024 MPI processes
  type: svec
  17 columns of global length 2333606220
  vector orthogonalization method: classical Gram-Schmidt
  orthogonalization refinement: if needed (eta: 0.7071)
  block orthogonalization method: GS
  doing matmult as a single matrix-matrix product
DS Object: 1024 MPI processes
  type: nhep
  parallel operation mode: REDUNDANT
ST Object: 1024 MPI processes
  type: shift
  shift: 0.
  number of matrices: 1

              k               ||Ax-kx||/||kx||
   -----------------       ------------------
     -15.048025        1.85112e-10
     -15.047159        3.13104e-10

Iterations performed 18

Why does treating it as non-Hermitian help the convergence? Why doesn't
this happen with Lanczos? I'm lost :/

Ale

El mar., 13 nov. 2018 a las 12:34, Jose E. Roman (<jroman at dsic.upv.es>)
escribió:

> This is really strange. We cannot say what is going on, everything seems
> fine.
> Could you try solving the problem as non-Hermitian to see what happens?
> Just run with -eps_non_hermitian. Depending on the result, we can suggest
> other things to try.
> Jose
>
>
> > El 13 nov 2018, a las 10:58, Ale Foggia via petsc-users <
> petsc-users at mcs.anl.gov> escribió:
> >
> > Hello,
> >
> > I'm using SLEPc to get the smallest real eigenvalue (EPS_SMALLEST_REAL)
> of a Hermitian problem (EPS_HEP). The linear size of the matrices I'm
> solving is around 10**9 elements and they are sparse. I've asked a few
> questions before regarding the same problem setting and you suggested me to
> use Krylov-Schur (because I was using Lanczos). I tried KS and up to a
> certain matrix size the convergence (relative to the eigenvalue) is good,
> it's around 10**-9, like with Lanczos, but when I increase the size I start
> getting the eigenvalue with only 3 correct digits. I've used the options:
> -eps_tol 1e-9 -eps_mpd 100 (16 was the default), but the only thing I got
> is one more eigenvalue with the same big error, and the iterations
> performed were only 2. Why didn't it do more in order to reach the
> convergence? Should I set other parameters? I don't know how to work out
> this problem, can you help me with this please? I send the -eps_view output
> and the eigenvalues with its errors:
> >
> > EPS Object: 2048 MPI processes
> >   type: krylovschur
> >     50% of basis vectors kept after restart
> >     using the locking variant
> >   problem type: symmetric eigenvalue problem
> >   selected portion of the spectrum: smallest real parts
> >   number of eigenvalues (nev): 1
> >   number of column vectors (ncv): 101
> >   maximum dimension of projected problem (mpd): 100
> >   maximum number of iterations: 46210024
> >   tolerance: 1e-09
> >   convergence test: relative to the eigenvalue
> > BV Object: 2048 MPI processes
> >   type: svec
> >   102 columns of global length 2333606220
> >   vector orthogonalization method: classical Gram-Schmidt
> >   orthogonalization refinement: if needed (eta: 0.7071)
> >   block orthogonalization method: GS
> >   doing matmult as a single matrix-matrix product
> > DS Object: 2048 MPI processes
> >   type: hep
> >   parallel operation mode: REDUNDANT
> >   solving the problem with: Implicit QR method (_steqr)
> > ST Object: 2048 MPI processes
> >   type: shift
> >   shift: 0.
> >   number of matrices: 1
> >
> >               k                ||Ax-kx||/||kx||
> >    -----------------        ------------------
> >      -15.093051         0.00323917 (with KS)
> >      -15.087320         0.00265215 (with KS)
> >      -15.048025         8.67204e-09 (with Lanczos)
> > Iterations performed 2
> >
> > Ale
>
>
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