Run with -eps_type lapack Eigen is not interfaced from SLEPc.
Jose > El 8 jul 2020, a las 17:06, Aulisa, Eugenio <eugenio.aul...@ttu.edu> escribió: > > yes the size varies from 6 to 100, > > I will try EPSLAPACK or EIGEN to see how it works > > Thanks again > Eugenio > > > > > > Eugenio Aulisa > > Department of Mathematics and Statistics, > Texas Tech University > Lubbock TX, 79409-1042 > room: 226 > http://www.math.ttu.edu/~eaulisa/ > phone: (806) 834-6684 > fax: (806) 742-1112 > > > > > From: Jose E. Roman <jro...@dsic.upv.es> > Sent: Wednesday, July 8, 2020 10:01 AM > To: Aulisa, Eugenio <eugenio.aul...@ttu.edu> > Cc: petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov>; Kara, Erdi > <erdi.k...@ttu.edu> > Subject: Re: [petsc-users] Help with generalized eigenvalue problem > > In a standard symmetric eigenproblem, a small perturbation of the matrix > results in a small perturbation of the eigenvalues. In generalized > eigenproblems, especially with singular matrices, I don't think perturbation > theory guarantees this in all cases. > > What do you mean by small problems? Do you have millions of problems of size > 6? In that case you should use EPSLAPACK. It will not factor the matrix (if > solved as a non-symmetric problem). > > Jose > > > > El 8 jul 2020, a las 15:55, Aulisa, Eugenio <eugenio.aul...@ttu.edu> > > escribió: > > > > Dear Jose, > > > > Thank you for your answer. > > > > I tried MLU but it did not help. > > > > I also tried to eliminate the null space of B, but I do not know it > > apriori, > > and at least to my knowledge of PETSC-SLEPC there is not an explicit way to > > find it > > but to find all the 0 eigenvectors of B, which again it requires the > > inverse of B. > > > > I am solving similar small problems millions of times, and this works fine > > most of the time, > > but once in a while it fails with the same LU zero pivot exception. > > > > One thing I tried yesterday, and it seams to work all the times, > > is perturbing the diagonal of B of a small factor, += 1.0e-10 ||B||, > > but I do not know how theoretically it sounds with all these indeterminate > > eigenvalues, > > maybe you have a clue on this. > > > > Thanks, > > Eugenio > > > > > > > > Eugenio Aulisa > > > > Department of Mathematics and Statistics, > > Texas Tech University > > Lubbock TX, 79409-1042 > > room: 226 > > http://www.math.ttu.edu/~eaulisa/ > > phone: (806) 834-6684 > > fax: (806) 742-1112 > > > > > > > > > > From: Jose E. Roman <jro...@dsic.upv.es> > > Sent: Tuesday, July 7, 2020 11:01 AM > > To: Aulisa, Eugenio <eugenio.aul...@ttu.edu> > > Cc: petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov>; Kara, Erdi > > <erdi.k...@ttu.edu> > > Subject: Re: [petsc-users] Help with generalized eigenvalue problem > > > > I don't know what options you are using, shift-and-invert or not, which, > > target. Anyway, if A and B have a common null space, then A-sigma*B will > > always be singular, so the KSP solver will have to deal with a singular > > system. > > > > If you pass the nullspace vectors to the EPS solver via > > https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fslepc.upv.es%2Fdocumentation%2Fcurrent%2Fdocs%2Fmanualpages%2FEPS%2FEPSSetDeflationSpace.html&data=02%7C01%7CEugenio.Aulisa%40ttu.edu%7C018ff09384674480f2e808d8234fce62%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298172963555933&sdata=iPBn%2FYR7mw2Q8EEjTQ%2BhDphUftUctK2lLj1KjnPgUZw%3D&reserved=0 > > then these vectors will also be attached to the KSP solver. > > > > Also, since you have MUMPS, try adding > > -st_pc_factor_mat_solver_type mumps > > (see section 3.4.1 of the SLEPc users manual). MUMPS should be quite robust > > with respect to singular linear systems. > > > > Jose > > > > > > > El 7 jul 2020, a las 17:40, Aulisa, Eugenio <eugenio.aul...@ttu.edu> > > > escribió: > > > > > > Can somebody help me figure it out the solver options for the attached > > > generalized eigenvalue problem? > > > > > > A x = lambda B x > > > > > > where A and B have the same null space, with 5 zero eigenvalues. > > > > > > The only non indefinite eigenvalue should be 41.1892 > > > > > > The problem is Hermite semi-positive so automatically slepc should purify > > > it, but to be sure I added > > > > > > EPSSetPurify(eps, PETSC_TRUE); > > > > > > I guess with my non-solver-options slepc is still trying to do the > > > inverse of the full > > > B matrix with an LU decomposition and gets zero pivot. > > > > > > This is what I get as a PETSC error Message > > > > > > [0]PETSC ERROR: --------------------- Error Message > > > -------------------------------------------------------------- > > > [0]PETSC ERROR: Zero pivot in LU factorization: > > > https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.mcs.anl.gov%2Fpetsc%2Fdocumentation%2Ffaq.html%23zeropivot&data=02%7C01%7CEugenio.Aulisa%40ttu.edu%7C018ff09384674480f2e808d8234fce62%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298172963555933&sdata=4ZYkCiAdAjVgNZeQBJXyFmL%2BaICquqkJvc7gQ%2BNs0QQ%3D&reserved=0 > > > [0]PETSC ERROR: Bad LU factorization > > > [0]PETSC ERROR: See > > > https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.mcs.anl.gov%2Fpetsc%2Fdocumentation%2Ffaq.html&data=02%7C01%7CEugenio.Aulisa%40ttu.edu%7C018ff09384674480f2e808d8234fce62%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298172963555933&sdata=SV%2F7S0Se8T4ftzroH%2FAYJKB6GDmnrZVlwfCsKI4M1bo%3D&reserved=0 > > > for trouble shooting. > > > [0]PETSC ERROR: Petsc Development GIT revision: > > > v3.11.3-2263-gce77f2ed1a GIT Date: 2019-09-26 13:31:14 -0500 > > > [0]PETSC ERROR: Nitsche_ex4a on a arch-linux2-c-opt named linux-8biu > > > by eaulisa Tue Jul 7 10:17:55 2020 > > > [0]PETSC ERROR: Configure options --with-debugging=0 --with-x=1 > > > COPTFLAGS="-O3 -march=native -mtune=native" CXXOPTFLAGS="-O3 > > > -march=native -mtune=native" FOPTFLAGS="-O3 -march=native -mtune=native" > > > --download-openmpi=1 --download-fblaslapack=1 --download-hdf5=1 > > > --download-metis=1 --download-parmetis=1 --with-shared-libraries=1 > > > --download-blacs=1 --download-scalapack=1 --download-mumps=1 > > > --download-suitesparse > > > [0]PETSC ERROR: #1 MatLUFactor_SeqDense() line 633 in > > > /home/eaulisa/software/petsc/src/mat/impls/dense/seq/dense.c > > > [0]PETSC ERROR: #2 MatLUFactorNumeric_SeqDense() line 432 in > > > /home/eaulisa/software/petsc/src/mat/impls/dense/seq/dense.c > > > [0]PETSC ERROR: #3 MatLUFactorNumeric() line 3056 in > > > /home/eaulisa/software/petsc/src/mat/interface/matrix.c > > > [0]PETSC ERROR: #4 PCSetUp_LU() line 126 in > > > /home/eaulisa/software/petsc/src/ksp/pc/impls/factor/lu/lu.c > > > [0]PETSC ERROR: #5 PCSetUp() line 894 in > > > /home/eaulisa/software/petsc/src/ksp/pc/interface/precon.c > > > [0]PETSC ERROR: #6 KSPSetUp() line 377 in > > > /home/eaulisa/software/petsc/src/ksp/ksp/interface/itfunc.c > > > [0]PETSC ERROR: #7 STSetUp_Shift() line 119 in > > > /home/eaulisa/software/slepc/src/sys/classes/st/impls/shift/shift.c > > > [0]PETSC ERROR: #8 STSetUp() line 271 in > > > /home/eaulisa/software/slepc/src/sys/classes/st/interface/stsolve.c > > > [0]PETSC ERROR: #9 EPSSetUp() line 273 in > > > /home/eaulisa/software/slepc/src/eps/interface/epssetup.c > > > [0]PETSC ERROR: #10 EPSSolve() line 136 in > > > /home/eaulisa/software/slepc/src/eps/interface/epssolve.c > > > > > > > > > > > > Thanks > > > Eugenio > > > > > > > > > > > > > > > Eugenio Aulisa > > > > > > Department of Mathematics and Statistics, > > > Texas Tech University > > > Lubbock TX, 79409-1042 > > > room: 226 > > > http://www.math.ttu.edu/~eaulisa/ > > > phone: (806) 834-6684 > > > fax: (806) 742-1112 > > > > > > > > > > > > <genEigen.cpp> > > >
