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

[Matthew Knepley]

On Tue, Nov 13, 2018 at 7:48 AM Ale Foggia via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> 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 :/
>

Are you sure your matrix is Hermitian? Lanczos will work for non-Hermitian
things (I believe).

  Thanks,

     Matt


>
> 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
>>
>>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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