[petsc-users] Slepc JD and GD converge to wrong eigenpair
Matthew Knepley
knepley at gmail.com
Tue Apr 4 06:40:39 CDT 2017
On Tue, Apr 4, 2017 at 2:20 AM, Toon Weyens <toon.weyens at gmail.com> wrote:
> Dear Jose and Matthew,
>
> Thank you so much for the effort!
>
> I still don't manage to converge using the range interval technique to
> filter out the positive eigenvalues, but using shift-invert combined with a
> target eigenvalue does true miracles. I get extremely fast convergence.
>
> The truth of the matter is that we are mainly interested in negative
> eigenvalues (unstable modes), and from physical considerations they are
> more or less situated in -0.2<lambda<0 in the normalized quantities that we
> use. So we will just use guesses.
>
> Thank you so much again!
>
> Also, I have finally managed to run streams (the cluster is quite full
> atm). These are the outputs:
>
1) This shows you have a bad process mapping. You could get much more
speedup for 1-4 procs by properly mapping processes to cores, perhaps with
numactl.
2) Essentially 3 processes can saturate your memory bandwidth, so I would
not expect much gain from using more than 4.
Thanks,
Matt
> 1 processes
> Number of MPI processes 1 Processor names c04b27
> Triad: 12352.0825 Rate (MB/s)
> 2 processes
> Number of MPI processes 2 Processor names c04b27 c04b27
> Triad: 18968.0226 Rate (MB/s)
> 3 processes
> Number of MPI processes 3 Processor names c04b27 c04b27 c04b27
> Triad: 21106.8580 Rate (MB/s)
> 4 processes
> Number of MPI processes 4 Processor names c04b27 c04b27 c04b27 c04b27
> Triad: 21655.5885 Rate (MB/s)
> 5 processes
> Number of MPI processes 5 Processor names c04b27 c04b27 c04b27 c04b27
> c04b27
> Triad: 21627.5559 Rate (MB/s)
> 6 processes
> Number of MPI processes 6 Processor names c04b27 c04b27 c04b27 c04b27
> c04b27 c04b27
> Triad: 21394.9620 Rate (MB/s)
> 7 processes
> Number of MPI processes 7 Processor names c04b27 c04b27 c04b27 c04b27
> c04b27 c04b27 c04b27
> Triad: 24952.7076 Rate (MB/s)
> 8 processes
> Number of MPI processes 8 Processor names c04b27 c04b27 c04b27 c04b27
> c04b27 c04b27 c04b27 c04b27
> Triad: 28357.1062 Rate (MB/s)
> 9 processes
> Number of MPI processes 9 Processor names c04b27 c04b27 c04b27 c04b27
> c04b27 c04b27 c04b27 c04b27 c04b27
> Triad: 31720.4545 Rate (MB/s)
> 10 processes
> Number of MPI processes 10 Processor names c04b27 c04b27 c04b27 c04b27
> c04b27 c04b27 c04b27 c04b27 c04b27 c04b27
> Triad: 35198.7412 Rate (MB/s)
> 11 processes
> Number of MPI processes 11 Processor names c04b27 c04b27 c04b27 c04b27
> c04b27 c04b27 c04b27 c04b27 c04b27 c04b27 c04b27
> Triad: 38616.0615 Rate (MB/s)
> 12 processes
> Number of MPI processes 12 Processor names c04b27 c04b27 c04b27 c04b27
> c04b27 c04b27 c04b27 c04b27 c04b27 c04b27 c04b27 c04b27
> Triad: 41939.3994 Rate (MB/s)
>
> I attach a figure.
>
> Thanks again!
>
> On Mon, Apr 3, 2017 at 8:29 PM Jose E. Roman <jroman at dsic.upv.es> wrote:
>
>>
>> > El 1 abr 2017, a las 0:01, Toon Weyens <toon.weyens at gmail.com>
>> escribió:
>> >
>> > Dear jose,
>> >
>> > I have saved the matrices in Matlab format and am sending them to you
>> using pCloud. If you want another format, please tell me. Please also note
>> that they are about 1.4GB each.
>> >
>> > I also attach a typical output of eps_view and log_view in output.txt,
>> for 8 processes.
>> >
>> > Thanks so much for helping me out! I think Petsc and Slepc are amazing
>> inventions that really have saved me many months of work!
>> >
>> > Regards
>>
>> I played a little bit with your matrices.
>>
>> With Krylov-Schur I can solve the problem quite easily. Note that in
>> generalized eigenvalue problems it is always better to use STSINVERT
>> because you have to invert a matrix anyway. So instead of setting
>> which=smallest_real, use shift-and-invert with a target that is close to
>> the wanted eigenvalue. For instance, with target=-0.005 I get convergence
>> with just one iteration:
>>
>> $ ./ex7 -f1 A.bin -f2 B.bin -st_ksp_type preonly -st_pc_type lu
>> -st_pc_factor_mat_solver_package mumps -eps_tol 1e-5 -st_type sinvert
>> -eps_target -0.005
>>
>> Generalized eigenproblem stored in file.
>>
>> Reading COMPLEX 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-05, maxit=7500
>> Linear eigensolve converged (1 eigenpair) due to CONVERGED_TOL;
>> iterations 1
>> ---------------------- --------------------
>> k ||Ax-kBx||/||kx||
>> ---------------------- --------------------
>> -0.004809-0.000000i 8.82085e-05
>> ---------------------- --------------------
>>
>>
>> Of course, you don't know a priori where your eigenvalue is.
>> Alternatively, you can set the target at 0 and get rid of positive
>> eigenvalues with a region filtering. For instance:
>>
>> $ ./ex7 -f1 A.bin -f2 B.bin -st_ksp_type preonly -st_pc_type lu
>> -st_pc_factor_mat_solver_package mumps -eps_tol 1e-5 -st_type sinvert
>> -eps_target 0 -rg_type interval -rg_interval_endpoints -1,0,-.05,.05
>> -eps_nev 2
>>
>> Generalized eigenproblem stored in file.
>>
>> Reading COMPLEX matrices from binary files...
>> Number of iterations of the method: 8
>> Number of linear iterations of the method: 74
>> Solution method: krylovschur
>>
>> Number of requested eigenvalues: 2
>> Stopping condition: tol=1e-05, maxit=7058
>> Linear eigensolve converged (2 eigenpairs) due to CONVERGED_TOL;
>> iterations 8
>> ---------------------- --------------------
>> k ||Ax-kBx||/||kx||
>> ---------------------- --------------------
>> -0.000392-0.000000i 2636.4
>> -0.004809+0.000000i 318441
>> ---------------------- --------------------
>>
>> In this case, the residuals seem very bad. But this is due to the fact
>> that your matrices have huge norms. Adding the option -eps_error_backward
>> ::ascii_info_detail will show residuals relative to the matrix norms:
>> ---------------------- --------------------
>> k eta(x,k)
>> ---------------------- --------------------
>> -0.000392-0.000000i 3.78647e-11
>> -0.004809+0.000000i 5.61419e-08
>> ---------------------- --------------------
>>
>>
>> Regarding the GD solver, I am also getting the correct solution. I don't
>> know why you are not getting convergence to the wanted eigenvalue:
>>
>> $ ./ex7 -f1 A.bin -f2 B.bin -st_ksp_type preonly -st_pc_type lu
>> -st_pc_factor_mat_solver_package mumps -eps_tol 1e-5 -eps_smallest_real
>> -eps_ncv 32 -eps_type gd
>>
>> Generalized eigenproblem stored in file.
>>
>> Reading COMPLEX matrices from binary files...
>> Number of iterations of the method: 132
>> Number of linear iterations of the method: 0
>> Solution method: gd
>>
>> Number of requested eigenvalues: 1
>> Stopping condition: tol=1e-05, maxit=120000
>> Linear eigensolve converged (1 eigenpair) due to CONVERGED_TOL;
>> iterations 132
>> ---------------------- --------------------
>> k ||Ax-kBx||/||kx||
>> ---------------------- --------------------
>> -0.004809+0.000000i 2.16223e-05
>> ---------------------- --------------------
>>
>>
>> Again, it is much better to use a target instead of smallest_real:
>>
>> $ ./ex7 -f1 A.bin -f2 B.bin -st_ksp_type preonly -st_pc_type lu
>> -st_pc_factor_mat_solver_package mumps -eps_tol 1e-5 -eps_type gd
>> -eps_target -0.005
>>
>> Generalized eigenproblem stored in file.
>>
>> Reading COMPLEX matrices from binary files...
>> Number of iterations of the method: 23
>> Number of linear iterations of the method: 0
>> Solution method: gd
>>
>> Number of requested eigenvalues: 1
>> Stopping condition: tol=1e-05, maxit=120000
>> Linear eigensolve converged (1 eigenpair) due to CONVERGED_TOL;
>> iterations 23
>> ---------------------- --------------------
>> k ||Ax-kBx||/||kx||
>> ---------------------- --------------------
>> -0.004809-0.000000i 2.06572e-05
>> ---------------------- --------------------
>>
>>
>> Jose
>>
>>
>>
--
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
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