Run your code with -eps_view_mat0 binary:amatrix.bin This will save the A matrix of the EPS solver in file "amatrix.bin" at the end of EPSSolve(). I cannot say which is the best method, it depends on the distribution of the spectrum. Let's see how it goes.
Jose > El 11 oct 2018, a las 20:13, Moritz Cygorek <mcygo...@uottawa.ca> escribió: > > Thank you for the response. This example is exactly the kind of thing I > thought about. > But, as you say, convergence is indeed not better. > > > What's the best format to send the matrix to slepc-maint? > My small test case is a sparse matrix of dimension 30720. I currently read it > from three files (containing IA, JA, and the values in CSR format). Because > everything is contained in a larger framework, it's not very easy to extract > the reader. Is there a generic way to read in sparse matrices from files for > PETSc? > > > > Maybe you can already give me a hint about the best method if I tell you the > properties of the spectrum: > The problem is the calculation of electronic states in a quantum dot. There > is a band gap from around 0 to 2 and I am interested in the first 20 or 40 > eigenvectors above and below the gap. > The first few states are separated by about 0.1 but for higher states the > energies come closer and closer together. > Additionally, there are a number of states with energies around 1000, which > are artificial and originate from the way we treat the boundary conditions. > Also, I know that all states come in pairs with the same energy (Kramers > degeneracy). > > For the small test case, the conduction band states, i.e. eigenvectors with > energies close to 2, converge very fast (about 5 min on a laptop computer). > However, the states with energies around 0 converge much more slowly and > that's one of my major problems. > For those states harmonic extraction seems to be better suited, but I have > the impression that it is not extremely stable. For example, applied to the > states close to 2 I see that some states are skipped, which can be seen by > the fact that the degeneracies are sometimes wrong. > Also, with harmonic extraction, the program sometimes stops claiming the > number of requested eigenpairs are reached, but the calculated relative error > of most states is way larger than the tolerance. > > Maybe you know from experience which method is better suited to tackle these > kinds of problems? > > > Eventually, I intend to do calculates with dimensions of ~ 10 million > distributed of a few 100 CPUs. > > Regards, > Moritz > > > > > From: Jose E. Roman <jro...@dsic.upv.es> > Sent: Thursday, October 11, 2018 5:55 AM > To: Matthew Knepley; Moritz Cygorek > Cc: PETSc; Carmen Campos > Subject: Re: [petsc-users] STFILTER in slepc > > The filter technique must be used with an interval in EPS, e.g. > -eps_interval 2.,2.7 > (This interval will be passed to STFILTER, so no need to specify > -st_filter_interval). > Therefore, it does not require -eps_target_magnitude or similar. > > Regarding the simpler (A-tau*I)^2, we call it "spectrum folding" (see section > 3.4.6 of SLEPc's manual) and it is implemented in ex24.c > http://slepc.upv.es/documentation/current/src/eps/examples/tutorials/ex24.c.html > > My experience is that spectrum folding will not give good convergence except > for easy problems. For more difficult problems with clustered eigenvalues you > need a polynomial filter. The technique of polynomial filter trades > iterations of the Krylov subspace for matrix-vector products required by a > high-degree polynomial. > > If you want, send us the matrix to slepc-maint and we will have a try. > > Jose > > > > El 11 oct 2018, a las 2:43, Matthew Knepley <knep...@gmail.com> escribió: > > > > On Wed, Oct 10, 2018 at 8:41 PM Moritz Cygorek <mcygo...@uottawa.ca> wrote: > > Thank you very much. Apparently, I've misunderstood what the filter > > actually does. I thought about the much simpler process, where you > > diagonalize > > > > > > > > -(A- tau*I)^2 +offset*I > > > > > > > > where tau is my target an offset is large enough so that the global maximum > > is reached for eigenvalues around tau. > > > > > > Is this different from -eps_target_magnitude? > > > > Thanks, > > > > Matt > > > > Then you look for the largest eigenvalue of the modified problem and either > > calculate the Ritz value of the original matrix or calculate back from the > > eigenvalues of the modified problem. > > > > > > > > Now, it looks to me like -st_type filter activates something like the > > package FILTLAN. > > > > > > > > I guess I can define a MatShell to do the thing I intended in the first > > place. > > > > But, I guess, this is a common thing, so I am wondering whether it is > > already implemented somewhere and I just didn't find it in the > > documentation. Can you say something about this? > > > > > > > > Regards, > > > > Moritz > > > > > > > > > > > > From: Jose E. Roman <jro...@dsic.upv.es> > > Sent: Wednesday, October 10, 2018 3:48 PM > > To: Moritz Cygorek > > Cc: petsc-users@mcs.anl.gov > > Subject: Re: [petsc-users] STFILTER in slepc > > > > This type of method requires a very high degree polynomial; suggest using > > degree=100 at least (this is the default value), but larger values may be > > necessary. Also, for this particular filter the "range" must be > > approximately equal to the numerical range; if you have no clue where your > > first and last eigenvalues are, you may use EPSSolve() calls with > > EPS_LARGEST_REAL and EPS_SMALLEST_REAL. > > > > Jose > > > > > El 10 oct 2018, a las 21:10, Moritz Cygorek <mcygo...@uottawa.ca> > > > escribió: > > > > > > Thank you for the fast reply. > > > > > > I've tried running my program (using the defaul Krylov-Schur method for > > > sparse MPI matrices) with the additional options: > > > > > > -st_type filter -st_filter_degree 2 -st_filter_interval 2.,2.7 > > > -st_filter_range -2000,2000 > > > > > > and I get the following error message: > > > > > > [0]PETSC ERROR: STFILTER cannot get the filter specified; please adjust > > > your filter parameters (e.g. increasing the polynomial degree) > > > .... > > > [0]PETSC ERROR: #1 FILTLAN_GetIntervals() line 451 in > > > /home/applications/sources/libraries/slepc-3.9.2/src/sys/classes/st/impls/filter/filtlan.c > > > [0]PETSC ERROR: #2 STFilter_FILTLAN_setFilter() line 1016 in > > > /home/applications/sources/libraries/slepc-3.9.2/src/sys/classes/st/impls/filter/filtlan.c > > > [0]PETSC ERROR: #3 STSetUp_Filter() line 42 in > > > /home/applications/sources/libraries/slepc-3.9.2/src/sys/classes/st/impls/filter/filter.c > > > [0]PETSC ERROR: #4 STSetUp() line 271 in > > > /home/applications/sources/libraries/slepc-3.9.2/src/sys/classes/st/interface/stsolve.c > > > [0]PETSC ERROR: #5 EPSSetUp() line 263 in > > > /home/applications/sources/libraries/slepc-3.9.2/src/eps/interface/epssetup.c > > > [0]PETSC ERROR: #6 EPSSolve() line 135 in > > > /home/applications/sources/libraries/slepc-3.9.2/src/eps/interface/epssolve.c > > > > > > > > > > > > Do you have a clue what I've missed? > > > > > > > > > Moritz > > > > > > > > > From: Jose E. Roman <jro...@dsic.upv.es> > > > Sent: Wednesday, October 10, 2018 2:30 PM > > > To: Moritz Cygorek > > > Cc: petsc-users@mcs.anl.gov > > > Subject: Re: [petsc-users] STFILTER in slepc > > > > > > > > > > El 10 oct 2018, a las 19:54, Moritz Cygorek <mcygo...@uottawa.ca> > > > > escribió: > > > > > > > > Hi, > > > > > > > > in the list of changes to SLEPc version 3.8, it is stated that there is > > > > a preliminary implementation of polynomial filtering using STFILTER. > > > > > > > > Because I am struggling to obtain interior eigenvalues and harmonic > > > > extraction seems not to be stable enough in my case, I wanted to give > > > > it a try, but I could not find any documentation yet. > > > > > > > > Does anybody have an example of how to use STFILTER or any > > > > documentation about it? > > > > > > > > Thanks in advance, > > > > Moritz > > > > > > There are no examples. You just set the type to STFILTER and set some > > > parameters such as the interval of interest or the polynomial degree. See > > > functions starting with STFilter > > > here:http://slepc.upv.es/documentation/current/docs/manualpages/ST/index.html > > > > > > In some problems it works well, but don't expect too much. It is still in > > > our to-do list to make it more usable. It will be good to have your > > > feedback. If you want, send results to slepc-maint, maybe we can help > > > tuning the parameters. > > > > > > 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 > > > > https://www.cse.buffalo.edu/~knepley/
