Sorry you are right. Now it does not crash, but without perturbation it gives max eigenvalue
-1.79769e+308 i.e. -infinity while with perturbation I get max eigenvalue 41.1892 which is the same I get with Mathematica (without perturbation) With this last statement I mean that -1.79769e+308 is not the real one. Also matrices A and B are semipositive definite. 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 10:34 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 eps_view shows it is using Krylov-Schur, it seems you mistyped the option: -eps_type lapack instead of -esp_type lapack > El 8 jul 2020, a las 17:29, Aulisa, Eugenio <eugenio.aul...@ttu.edu> escribió: > > I tried with -esp_type lapack, but it still tries to do LU > > I attached the code without perturbation of B, > probably something is missing in my way of setting up the problem. > > I also attached the eps_view with perturbation > > Thanks > Eugenio > > Nitsche_genEigen -esp_type lapack > [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%7Cffdfdcc73b2d45bd055508d823547501%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298192933095536&sdata=MB9cEbQo8PHWvVmap6Mk%2FRVKO7cID9qypNShiySTEK8%3D&reserved=0 > [0]PETSC ERROR: Zero pivot row 1 value 0. tolerance 2.22045e-14 > > [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%7Cffdfdcc73b2d45bd055508d823547501%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298192933095536&sdata=q2HkYMvL%2FjZ5c03sTALoJ8pky%2BbSPJCHTsK6N70%2Fqbs%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_genEigen on a arch-linux2-c-opt named linux-8biu by > eaulisa Wed Jul 8 10:09:31 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 MatPivotCheck_none() line 731 in > /home/eaulisa/software/petsc/include/petsc/private/matimpl.h > [0]PETSC ERROR: #2 MatPivotCheck() line 748 in > /home/eaulisa/software/petsc/include/petsc/private/matimpl.h > [0]PETSC ERROR: #3 MatLUFactorNumeric_SeqAIJ_Inode() line 1676 in > /home/eaulisa/software/petsc/src/mat/impls/aij/seq/inode.c > [0]PETSC ERROR: #4 MatLUFactorNumeric() line 3056 in > /home/eaulisa/software/petsc/src/mat/interface/matrix.c > [0]PETSC ERROR: #5 PCSetUp_LU() line 126 in > /home/eaulisa/software/petsc/src/ksp/pc/impls/factor/lu/lu.c > [0]PETSC ERROR: #6 PCSetUp() line 894 in > /home/eaulisa/software/petsc/src/ksp/pc/interface/precon.c > [0]PETSC ERROR: #7 KSPSetUp() line 377 in > /home/eaulisa/software/petsc/src/ksp/ksp/interface/itfunc.c > [0]PETSC ERROR: #8 STSetUp_Shift() line 119 in > /home/eaulisa/software/slepc/src/sys/classes/st/impls/shift/shift.c > [0]PETSC ERROR: #9 STSetUp() line 271 in > /home/eaulisa/software/slepc/src/sys/classes/st/interface/stsolve.c > [0]PETSC ERROR: #10 EPSSetUp() line 273 in > /home/eaulisa/software/slepc/src/eps/interface/epssetup.c > [0]PETSC ERROR: #11 EPSSolve() line 136 in > /home/eaulisa/software/slepc/src/eps/interface/epssolve.c > [0]PETSC ERROR: --------------------- Error Message > -------------------------------------------------------------- > [0]PETSC ERROR: Argument out of range > [0]PETSC ERROR: Argument 2 out of range > [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%7Cffdfdcc73b2d45bd055508d823547501%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298192933095536&sdata=q2HkYMvL%2FjZ5c03sTALoJ8pky%2BbSPJCHTsK6N70%2Fqbs%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_genEigen on a arch-linux2-c-opt named linux-8biu by > eaulisa Wed Jul 8 10:09:31 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: #12 EPSGetEigenpair() line 399 in > /home/eaulisa/software/slepc/src/eps/interface/epssolve.c > 2.96439e-323 > > 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 10:07 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 > > 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%7Cffdfdcc73b2d45bd055508d823547501%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298192933095536&sdata=UMcNl4UZYOg7sytYEAsyQRDmptm6XG%2B6C0Ylh%2F1dj8Q%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%7Cffdfdcc73b2d45bd055508d823547501%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298192933095536&sdata=MB9cEbQo8PHWvVmap6Mk%2FRVKO7cID9qypNShiySTEK8%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%7Cffdfdcc73b2d45bd055508d823547501%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298192933095536&sdata=q2HkYMvL%2FjZ5c03sTALoJ8pky%2BbSPJCHTsK6N70%2Fqbs%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> > > > > > > > <genEigen.cpp><eps_view.txt>
genEigen.nb
Description: genEigen.nb
EPS Object: 1 MPI processes
type: lapack
problem type: generalized non-symmetric eigenvalue problem
selected portion of the spectrum: largest eigenvalues in magnitude
number of eigenvalues (nev): 1
number of column vectors (ncv): 6
maximum dimension of projected problem (mpd): 0
maximum number of iterations: 0
tolerance: 1e-08
convergence test: relative to the eigenvalue
BV Object: 1 MPI processes
type: svec
6 columns of global length 6
vector orthogonalization method: classical Gram-Schmidt
orthogonalization refinement: if needed (eta: 0.7071)
block orthogonalization method: GS
doing matmult as a single matrix-matrix product
DS Object: 1 MPI processes
type: gnhep
ST Object: 1 MPI processes
type: shift
shift: 0.
number of matrices: 2
all matrices have different nonzero pattern
KSP Object: (st_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-08, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (st_) 1 MPI processes
type: none
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqaij
rows=6, cols=6
total: nonzeros=36, allocated nonzeros=36
total number of mallocs used during MatSetValues calls =0
using I-node routines: found 2 nodes, limit used is 5
41.1892
genEigen.nb.pdf
Description: genEigen.nb.pdf
