<div dir="ltr"><div class="gmail_quote"><div dir="ltr">On Tue, Nov 13, 2018 at 7:48 AM Ale Foggia via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div>Thanks Jose for the answer. I tried it an it worked! I send the output of -eps_view again, just in case:</div><div><br></div><div>EPS Object: 1024 MPI processes<br> type: krylovschur<br> 50% of basis vectors kept after restart<br> using the locking variant<br> problem type: non-symmetric eigenvalue problem<br> selected portion of the spectrum: smallest real parts<br> number of eigenvalues (nev): 1<br> number of column vectors (ncv): 16<br> maximum dimension of projected problem (mpd): 16<br> maximum number of iterations: 291700777<br> tolerance: 1e-09<br> convergence test: relative to the eigenvalue<br>BV Object: 1024 MPI processes<br> type: svec<br> 17 columns of global length 2333606220<br> vector orthogonalization method: classical Gram-Schmidt<br> orthogonalization refinement: if needed (eta: 0.7071)<br> block orthogonalization method: GS<br> doing matmult as a single matrix-matrix product<br>DS Object: 1024 MPI processes<br> type: nhep<br> parallel operation mode: REDUNDANT<br>ST Object: 1024 MPI processes<br> type: shift<br> shift: 0.<br> number of matrices: 1</div><div><br></div><div> k ||Ax-kx||/||kx||<br> ----------------- ------------------<br> -15.048025 1.85112e-10<br> -15.047159 3.13104e-10<br></div><div><br></div><div>Iterations performed 18<br></div><div><br></div><div>Why does treating it as non-Hermitian help the convergence? Why doesn't this happen with Lanczos? I'm lost :/<br></div></div></div></div></div></blockquote><div><br></div><div>Are you sure your matrix is Hermitian? Lanczos will work for non-Hermitian things (I believe).</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div></div><div><br></div><div>Ale<br></div></div></div></div></div><br><div class="gmail_quote"><div dir="ltr">El mar., 13 nov. 2018 a las 12:34, Jose E. Roman (<<a href="mailto:jroman@dsic.upv.es" target="_blank">jroman@dsic.upv.es</a>>) escribió:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">This is really strange. We cannot say what is going on, everything seems fine.<br>
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.<br>
Jose<br>
<br>
<br>
> El 13 nov 2018, a las 10:58, Ale Foggia via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>> escribió:<br>
> <br>
> Hello,<br>
> <br>
> 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:<br>
> <br>
> EPS Object: 2048 MPI processes<br>
> type: krylovschur<br>
> 50% of basis vectors kept after restart<br>
> using the locking variant<br>
> problem type: symmetric eigenvalue problem<br>
> selected portion of the spectrum: smallest real parts<br>
> number of eigenvalues (nev): 1<br>
> number of column vectors (ncv): 101<br>
> maximum dimension of projected problem (mpd): 100<br>
> maximum number of iterations: 46210024<br>
> tolerance: 1e-09<br>
> convergence test: relative to the eigenvalue<br>
> BV Object: 2048 MPI processes<br>
> type: svec<br>
> 102 columns of global length 2333606220<br>
> vector orthogonalization method: classical Gram-Schmidt<br>
> orthogonalization refinement: if needed (eta: 0.7071)<br>
> block orthogonalization method: GS<br>
> doing matmult as a single matrix-matrix product<br>
> DS Object: 2048 MPI processes<br>
> type: hep<br>
> parallel operation mode: REDUNDANT<br>
> solving the problem with: Implicit QR method (_steqr)<br>
> ST Object: 2048 MPI processes<br>
> type: shift<br>
> shift: 0.<br>
> number of matrices: 1<br>
> <br>
> k ||Ax-kx||/||kx||<br>
> ----------------- ------------------<br>
> -15.093051 0.00323917 (with KS)<br>
> -15.087320 0.00265215 (with KS)<br>
> -15.048025 8.67204e-09 (with Lanczos)<br>
> Iterations performed 2<br>
> <br>
> Ale<br>
<br>
</blockquote></div>
</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>