[petsc-users] SLEPc: smallest eigenvalues

Sat Sep 25 01:50:38 CDT 2021

Ok, great! I will give that a try, thanks for your help!

On Fri, Sep 24, 2021 at 11:12 PM Jose E. Roman <jroman at dsic.upv.es> wrote:

> Yes, you can use PCMAT
> https://petsc.org/release/docs/manualpages/PC/PCMAT.html then pass a
> preconditioner matrix that performs the inverse via a shell matrix.
>
> > El 25 sept 2021, a las 8:07, Varun Hiremath <varunhiremath at gmail.com>
> escribió:
> >
> > Hi Jose,
> >
> > Thanks for checking my code and providing suggestions.
> >
> > In my particular case, I don't know the matrix A explicitly, I compute
> A*x in a matrix-free way within a shell matrix, so I can't use any of the
> direct factorization methods. But just a question regarding your suggestion
> to compute a (parallel) LU factorization. In our work, we do use MUMPS to
> compute the parallel factorization. For solving the generalized problem,
> A*x = lambda*B*x, we are computing inv(B)*A*x within a shell matrix, where
> factorization of B is computed using MUMPS. (We don't call MUMPS through
> SLEPc as we have our own MPI wrapper and other user settings to handle.)
> >
> > So for the preconditioning, instead of using the iterative solvers, can
> I provide a shell matrix that computes inv(P)*x corrections (where P is the
> preconditioner matrix) using MUMPS direct solver?
> >
> > And yes, thanks, #define PETSC_USE_COMPLEX 1 is not needed, it works
> without it.
> >
> > Regards,
> > Varun
> >
> > On Fri, Sep 24, 2021 at 9:14 AM Jose E. Roman <jroman at dsic.upv.es>
> wrote:
> > If you do
> > $ ./acoustic_matrix_test.o -shell 0 -st_type sinvert -deflate 1
> > then it is using an LU factorization (the default), which is fast.
> >
> > Use -eps_view to see which solver settings are you using.
> >
> > BiCGStab with block Jacobi does not work for you matrix, it exceeds the
> maximum 10000 iterations. So this is not viable unless you can find a
> better preconditioner for your problem. If not, just using
> EPS_SMALLEST_MAGNITUDE will be faster.
> >
> > Computing smallest magnitude eigenvalues is a difficult task. The most
> robust way is to compute a (parallel) LU factorization if you can afford it.
> >
> >
> > A side note: don't add this to your source code
> > #define PETSC_USE_COMPLEX 1
> > This define is taken from PETSc's include files, you should not mess
> with it. Instead, you probably want to add something like this AFTER
> #include <slepceps.h>:
> > #if !defined(PETSC_USE_COMPLEX)
> > #error "Requires complex scalars"
> > #endif
> >
> > Jose
> >
> >
> > > El 22 sept 2021, a las 19:38, Varun Hiremath <varunhiremath at gmail.com>
> escribió:
> > >
> > > Hi Jose,
> > >
> > > Thank you, that explains it and my example code works now without
> specifying "-eps_target 0" in the command line.
> > >
> > > However, both the Krylov inexact shift-invert and JD solvers are
> struggling to converge for some of my actual problems. The issue seems to
> be related to non-symmetric general matrices. I have extracted one such
> matrix attached here as MatA.gz (size 100k), and have also included a short
> program that loads this matrix and then computes the smallest eigenvalues
> as I described earlier.
> > >
> > > For this matrix, if I compute the eigenvalues directly (without using
> the shell matrix) using shift-and-invert (as below) then it converges in
> less than a minute.
> > > $ ./acoustic_matrix_test.o -shell 0 -st_type sinvert -deflate 1
> > >
> > > However, if I use the shell matrix and use any of the preconditioned
> solvers JD or Krylov shift-invert (as shown below) with the same matrix as
> the preconditioner, then they struggle to converge.
> > > $ ./acoustic_matrix_test.o -usejd 1 -deflate 1
> > > $ ./acoustic_matrix_test.o -sinvert 1 -deflate 1
> > >
> > > Could you please check the attached code and suggest any changes in
> settings that might help with convergence for these kinds of matrices? I
> appreciate your help!
> > >
> > > Thanks,
> > > Varun
> > >
> > > On Tue, Sep 21, 2021 at 11:14 AM Jose E. Roman <jroman at dsic.upv.es>
> wrote:
> > > I will have a look at your code when I have more time. Meanwhile, I am
> answering 3) below...
> > >
> > > > El 21 sept 2021, a las 0:23, Varun Hiremath <varunhiremath at gmail.com>
> escribió:
> > > >
> > > > Hi Jose,
> > > >
> > > > Sorry, it took me a while to test these settings in the new builds.
> I am getting good improvement in performance using the preconditioned
> solvers, so thanks for the suggestions! But I have some questions related
> to the usage.
> > > >
> > > > We are using SLEPc to solve the acoustic modal eigenvalue problem.
> Attached is a simple standalone program that computes acoustic modes in a
> simple rectangular box. This program illustrates the general setup I am
> using, though here the shell matrix and the preconditioner matrix are the
> same, while in my actual program the shell matrix computes A*x without
> explicitly forming A, and the preconditioner is a 0th order approximation
> of A.
> > > >
> > > > In the attached program I have tested both
> > > > 1) the Krylov-Schur with inexact shift-and-invert (implemented under
> the option sinvert);
> > > > 2) the JD solver with preconditioner (implemented under the option
> usejd)
> > > >
> > > > Both the solvers seem to work decently, compared to no
> preconditioning. This is how I run the two solvers (for a mesh size of
> 1600x400):
> > > > $ ./acoustic_box_test.o -nx 1600 -ny 400 -usejd 1 -deflate 1
> -eps_target 0
> > > > $ ./acoustic_box_test.o -nx 1600 -ny 400 -sinvert 1 -deflate 1
> -eps_target 0
> > > > Both finish in about ~10 minutes on my system in serial. JD seems to
> be slightly faster and more accurate (for the imaginary part of eigenvalue).
> > > > The program also runs in parallel using mpiexec. I use complex
> builds, as in my main program the matrix can be complex.
> > > >
> > > > Now here are my questions:
> > > > 1) For this particular problem type, could you please check if these
> are the best settings that one could use? I have tried different
> combinations of KSP/PC types e.g. GMRES, GAMG, etc, but BCGSL + BJACOBI
> seems to work the best in serial and parallel.
> > > >
> > > > 2) When I tested these settings in my main program, for some reason
> the JD solver was not converging. After further testing, I found the issue
> was related to the setting of "-eps_target 0". I have included
> "EPSSetTarget(eps,0.0);" in the program and I assumed this is equivalent to
> passing "-eps_target 0" from the command line, but that doesn't seem to be
> the case. For instance, if I run the attached program without "-eps_target
> 0" in the command line then it doesn't converge.
> > > > $ ./acoustic_box_test.o -nx 1600 -ny 400 -usejd 1 -deflate 1
> -eps_target 0
> > > >  the above finishes in about 10 minutes
> > > > $ ./acoustic_box_test.o -nx 1600 -ny 400 -usejd 1 -deflate 1
> > > >  the above doesn't converge even though "EPSSetTarget(eps,0.0);" is
> included in the code
> > > >
> > > > This only seems to affect the JD solver, not the Krylov
> shift-and-invert (-sinvert 1) option. So is there any difference between
> passing "-eps_target 0" from the command line vs using
> "EPSSetTarget(eps,0.0);" in the code? I cannot pass any command line
> arguments in my actual program, so need to set everything internally.
> > > >
> > > > 3) Also, another minor related issue. While using the inexact
> shift-and-invert option, I was running into the following error:
> > > >
> > > > ""
> > > > Missing or incorrect user input
> > > > Shift-and-invert requires a target 'which' (see
> EPSSetWhichEigenpairs), for instance -st_type sinvert -eps_target 0
> -eps_target_magnitude
> > > > ""
> > > >
> > > > I already have the below two lines in the code:
> > > > EPSSetWhichEigenpairs(eps,EPS_SMALLEST_MAGNITUDE);
> > > > EPSSetTarget(eps,0.0);
> > > >
> > > > so shouldn't these be enough? If I comment out the first line
> "EPSSetWhichEigenpairs", then the code works fine.
> > >
> > > You should either do
> > >
> > > EPSSetWhichEigenpairs(eps,EPS_SMALLEST_MAGNITUDE);
> > >
> > > without shift-and-invert or
> > >
> > > EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE);
> > > EPSSetTarget(eps,0.0);
> > >
> > > with shift-and-invert. The latter can also be used without
> shift-and-invert (e.g. in JD).
> > >
> > > I have to check, but a possible explanation why in your comment above
> (2) the command-line option -eps_target 0 works differently is that it also
> sets -eps_target_magnitude if omitted, so to be equivalent in source code
> you have to call both
> > > EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE);
> > > EPSSetTarget(eps,0.0);
> > >
> > > Jose
> > >
> > > > I have some more questions regarding setting the preconditioner for
> a quadratic eigenvalue problem, which I will ask in a follow-up email.
> > > >
> > > > Thanks for your help!
> > > >
> > > > -Varun
> > > >
> > > >
> > > > On Thu, Jul 1, 2021 at 5:01 AM Varun Hiremath <
> varunhiremath at gmail.com> wrote:
> > > > Thank you very much for these suggestions! We are currently using
> version 3.12, so I'll try to update to the latest version and try your
> suggestions. Let me get back to you, thanks!
> > > >
> > > > On Thu, Jul 1, 2021, 4:45 AM Jose E. Roman <jroman at dsic.upv.es>
> wrote:
> > > > Then I would try Davidson methods https://doi.org/10.1145/2543696
> > > > You can also try Krylov-Schur with "inexact" shift-and-invert, for
> instance, with preconditioned BiCGStab or GMRES, see section 3.4.1 of the
> users manual.
> > > >
> > > > In both cases, you have to pass matrix A in the call to
> EPSSetOperators() and the preconditioner matrix via
> STSetPreconditionerMat() - note this function was introduced in version
> 3.15.
> > > >
> > > > Jose
> > > >
> > > >
> > > >
> > > > > El 1 jul 2021, a las 13:36, Varun Hiremath <
> varunhiremath at gmail.com> escribió:
> > > > >
> > > > > Thanks. I actually do have a 1st order approximation of matrix A,
> that I can explicitly compute and also invert. Can I use that matrix as
> preconditioner to speed things up? Is there some example that explains how
> to setup and call SLEPc for this scenario?
> > > > >
> > > > > On Thu, Jul 1, 2021, 4:29 AM Jose E. Roman <jroman at dsic.upv.es>
> wrote:
> > > > > For smallest real parts one could adapt ex34.c, but it is going to
> be costly
> https://slepc.upv.es/documentation/current/src/eps/tutorials/ex36.c.html
> > > > > Also, if eigenvalues are clustered around the origin, convergence
> may still be very slow.
> > > > >
> > > > > It is a tough problem, unless you are able to compute a good
> preconditioner of A (no need to compute the exact inverse).
> > > > >
> > > > > Jose
> > > > >
> > > > >
> > > > > > El 1 jul 2021, a las 13:23, Varun Hiremath <
> varunhiremath at gmail.com> escribió:
> > > > > >
> > > > > > I'm solving for the smallest eigenvalues in magnitude. Though is
> it cheaper to solve smallest in real part, as that might also work in my
> case? Thanks for your help.
> > > > > >
> > > > > > On Thu, Jul 1, 2021, 4:08 AM Jose E. Roman <jroman at dsic.upv.es>
> wrote:
> > > > > > Smallest eigenvalue in magnitude or real part?
> > > > > >
> > > > > >
> > > > > > > El 1 jul 2021, a las 11:58, Varun Hiremath <
> varunhiremath at gmail.com> escribió:
> > > > > > >
> > > > > > > Sorry, no both A and B are general sparse matrices
> (non-hermitian). So is there anything else I could try?
> > > > > > >
> > > > > > > On Thu, Jul 1, 2021 at 2:43 AM Jose E. Roman <
> jroman at dsic.upv.es> wrote:
> > > > > > > Is the problem symmetric (GHEP)? In that case, you can try
> LOBPCG on the pair (A,B). But this will likely be slow as well, unless you
> can provide a good preconditioner.
> > > > > > >
> > > > > > > Jose
> > > > > > >
> > > > > > >
> > > > > > > > El 1 jul 2021, a las 11:37, Varun Hiremath <
> varunhiremath at gmail.com> escribió:
> > > > > > > >
> > > > > > > > Hi All,
> > > > > > > >
> > > > > > > > I am trying to compute the smallest eigenvalues of a
> generalized system A*x= lambda*B*x. I don't explicitly know the matrix A
> (so I am using a shell matrix with a custom matmult function) however, the
> matrix B is explicitly known so I compute inv(B)*A within the shell matrix
> and solve inv(B)*A*x = lambda*x.
> > > > > > > >
> > > > > > > > To compute the smallest eigenvalues it is recommended to
> solve the inverted system, but since matrix A is not explicitly known I
> can't invert the system. Moreover, the size of the system can be really
> big, and with the default Krylov solver, it is extremely slow. So is there
> a better way for me to compute the smallest eigenvalues of this system?
> > > > > > > >
> > > > > > > > Thanks,
> > > > > > > > Varun
> > > > > > >
> > > > > >
> > > > >
> > > >
> > > > <acoustic_box_test.cpp>
> > >
> > > <acoustic_matrix_test.cpp><MatA.gz>
> >
>
>
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