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<span>I tried with <span>-esp_type lapack</span>, but it still tries to do LU<br>
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<span>I attached the code without perturbation of B, <br>
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<span>probably something is missing in my way of setting up the problem.<br>
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<span>I also attached the eps_view with perturbation</span></div>
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<span>Thanks<br>
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<span>Eugenio<br>
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<span> Nitsche_genEigen -esp_type lapack<br>
</span>
<div>[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------<br>
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<div>[0]PETSC ERROR: Zero pivot in LU factorization: https://www.mcs.anl.gov/petsc/documentation/faq.html#zeropivot<br>
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<div>[0]PETSC ERROR: Zero pivot row 1 value 0. tolerance 2.22045e-14<br>
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<div>[0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html for trouble shooting.<br>
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<div>[0]PETSC ERROR: Petsc Development GIT revision: v3.11.3-2263-gce77f2ed1a GIT Date: 2019-09-26 13:31:14 -0500<br>
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<div>[0]PETSC ERROR: Nitsche_genEigen on a arch-linux2-c-opt named linux-8biu by eaulisa Wed Jul 8 10:09:31 2020<br>
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<div>[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<br>
</div>
<div>[0]PETSC ERROR: #1 MatPivotCheck_none() line 731 in /home/eaulisa/software/petsc/include/petsc/private/matimpl.h<br>
</div>
<div>[0]PETSC ERROR: #2 MatPivotCheck() line 748 in /home/eaulisa/software/petsc/include/petsc/private/matimpl.h<br>
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<div>[0]PETSC ERROR: #3 MatLUFactorNumeric_SeqAIJ_Inode() line 1676 in /home/eaulisa/software/petsc/src/mat/impls/aij/seq/inode.c<br>
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<div>[0]PETSC ERROR: #4 MatLUFactorNumeric() line 3056 in /home/eaulisa/software/petsc/src/mat/interface/matrix.c<br>
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<div>[0]PETSC ERROR: #5 PCSetUp_LU() line 126 in /home/eaulisa/software/petsc/src/ksp/pc/impls/factor/lu/lu.c<br>
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<div>[0]PETSC ERROR: #6 PCSetUp() line 894 in /home/eaulisa/software/petsc/src/ksp/pc/interface/precon.c<br>
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<div>[0]PETSC ERROR: #7 KSPSetUp() line 377 in /home/eaulisa/software/petsc/src/ksp/ksp/interface/itfunc.c<br>
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<div>[0]PETSC ERROR: #8 STSetUp_Shift() line 119 in /home/eaulisa/software/slepc/src/sys/classes/st/impls/shift/shift.c<br>
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<div>[0]PETSC ERROR: #9 STSetUp() line 271 in /home/eaulisa/software/slepc/src/sys/classes/st/interface/stsolve.c<br>
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<div>[0]PETSC ERROR: #10 EPSSetUp() line 273 in /home/eaulisa/software/slepc/src/eps/interface/epssetup.c<br>
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<div>[0]PETSC ERROR: #11 EPSSolve() line 136 in /home/eaulisa/software/slepc/src/eps/interface/epssolve.c<br>
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<div>[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------<br>
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<div>[0]PETSC ERROR: Argument out of range<br>
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<div>[0]PETSC ERROR: Argument 2 out of range<br>
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<div>[0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html for trouble shooting.<br>
</div>
<div>[0]PETSC ERROR: Petsc Development GIT revision: v3.11.3-2263-gce77f2ed1a GIT Date: 2019-09-26 13:31:14 -0500<br>
</div>
<div>[0]PETSC ERROR: Nitsche_genEigen on a arch-linux2-c-opt named linux-8biu by eaulisa Wed Jul 8 10:09:31 2020<br>
</div>
<div>[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<br>
</div>
<div>[0]PETSC ERROR: #12 EPSGetEigenpair() line 399 in /home/eaulisa/software/slepc/src/eps/interface/epssolve.c<br>
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<span>2.96439e-323 </span><br>
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<div align="left"><font size="2">Eugenio Aulisa<br>
<br>
Department of Mathematics and Statistics,<br>
Texas Tech University<br>
Lubbock TX, 79409-1042 <br>
room: 226<br>
http://www.math.ttu.edu/~eaulisa/<br>
phone: (806) 834-6684<br>
fax: (806) 742-1112 <br>
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<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Jose E. Roman <jroman@dsic.upv.es><br>
<b>Sent:</b> Wednesday, July 8, 2020 10:07 AM<br>
<b>To:</b> Aulisa, Eugenio <Eugenio.Aulisa@ttu.edu><br>
<b>Cc:</b> petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov>; Kara, Erdi <Erdi.Kara@ttu.edu><br>
<b>Subject:</b> Re: [petsc-users] Help with generalized eigenvalue problem</font>
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<div class="PlainText">Run with -eps_type lapack<br>
<br>
Eigen is not interfaced from SLEPc.<br>
<br>
Jose<br>
<br>
<br>
> El 8 jul 2020, a las 17:06, Aulisa, Eugenio <Eugenio.Aulisa@ttu.edu> escribió:<br>
> <br>
> yes the size varies from 6 to 100,<br>
> <br>
> I will try EPSLAPACK or EIGEN to see how it works<br>
> <br>
> Thanks again<br>
> Eugenio<br>
> <br>
> <br>
> <br>
> <br>
> <br>
> Eugenio Aulisa<br>
> <br>
> Department of Mathematics and Statistics,<br>
> Texas Tech University<br>
> Lubbock TX, 79409-1042 <br>
> room: 226<br>
> <a href="http://www.math.ttu.edu/~eaulisa/">http://www.math.ttu.edu/~eaulisa/</a><br>
> phone: (806) 834-6684<br>
> fax: (806) 742-1112 <br>
> <br>
> <br>
> <br>
> <br>
> From: Jose E. Roman <jroman@dsic.upv.es><br>
> Sent: Wednesday, July 8, 2020 10:01 AM<br>
> To: Aulisa, Eugenio <Eugenio.Aulisa@ttu.edu><br>
> Cc: petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov>; Kara, Erdi <Erdi.Kara@ttu.edu><br>
> Subject: Re: [petsc-users] Help with generalized eigenvalue problem<br>
> <br>
> 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.<br>
> <br>
> 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).<br>
> <br>
> Jose<br>
> <br>
> <br>
> > El 8 jul 2020, a las 15:55, Aulisa, Eugenio <Eugenio.Aulisa@ttu.edu> escribió:<br>
> > <br>
> > Dear Jose,<br>
> > <br>
> > Thank you for your answer.<br>
> > <br>
> > I tried MLU but it did not help. <br>
> > <br>
> > I also tried to eliminate the null space of B, but I do not know it apriori, <br>
> > and at least to my knowledge of PETSC-SLEPC there is not an explicit way to find it<br>
> > but to find all the 0 eigenvectors of B, which again it requires the inverse of B.
<br>
> > <br>
> > I am solving similar small problems millions of times, and this works fine most of the time,<br>
> > but once in a while it fails with the same LU zero pivot exception.<br>
> > <br>
> > One thing I tried yesterday, and it seams to work all the times, <br>
> > is perturbing the diagonal of B of a small factor, += 1.0e-10 ||B||,<br>
> > but I do not know how theoretically it sounds with all these indeterminate eigenvalues,
<br>
> > maybe you have a clue on this.<br>
> > <br>
> > Thanks,<br>
> > Eugenio<br>
> > <br>
> > <br>
> > <br>
> > Eugenio Aulisa<br>
> > <br>
> > Department of Mathematics and Statistics,<br>
> > Texas Tech University<br>
> > Lubbock TX, 79409-1042 <br>
> > room: 226<br>
> > <a href="http://www.math.ttu.edu/~eaulisa/">http://www.math.ttu.edu/~eaulisa/</a><br>
> > phone: (806) 834-6684<br>
> > fax: (806) 742-1112 <br>
> > <br>
> > <br>
> > <br>
> > <br>
> > From: Jose E. Roman <jroman@dsic.upv.es><br>
> > Sent: Tuesday, July 7, 2020 11:01 AM<br>
> > To: Aulisa, Eugenio <Eugenio.Aulisa@ttu.edu><br>
> > Cc: petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov>; Kara, Erdi <Erdi.Kara@ttu.edu><br>
> > Subject: Re: [petsc-users] Help with generalized eigenvalue problem<br>
> > <br>
> > 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.<br>
> > <br>
> > If you pass the nullspace vectors to the EPS solver via <a href="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%7C48eb040474e44a2af2f208d82350b5a7%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298176878634547&sdata=lL%2B5GTRzFgeviU%2BedhKieyXDO%2Fgyko2CLYGU%2BxtilB0%3D&reserved=0">
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%7C48eb040474e44a2af2f208d82350b5a7%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298176878634547&sdata=lL%2B5GTRzFgeviU%2BedhKieyXDO%2Fgyko2CLYGU%2BxtilB0%3D&reserved=0</a>
then these vectors will also be attached to the KSP solver. <br>
> > <br>
> > Also, since you have MUMPS, try adding<br>
> > -st_pc_factor_mat_solver_type mumps <br>
> > (see section 3.4.1 of the SLEPc users manual). MUMPS should be quite robust with respect to singular linear systems.<br>
> > <br>
> > Jose<br>
> > <br>
> > <br>
> > > El 7 jul 2020, a las 17:40, Aulisa, Eugenio <Eugenio.Aulisa@ttu.edu> escribió:<br>
> > > <br>
> > > Can somebody help me figure it out the solver options for the attached generalized eigenvalue problem?<br>
> > > <br>
> > > A x = lambda B x <br>
> > > <br>
> > > where A and B have the same null space, with 5 zero eigenvalues.<br>
> > > <br>
> > > The only non indefinite eigenvalue should be 41.1892<br>
> > > <br>
> > > The problem is Hermite semi-positive so automatically slepc should purify it, but to be sure I added<br>
> > > <br>
> > > EPSSetPurify(eps, PETSC_TRUE);<br>
> > > <br>
> > > I guess with my non-solver-options slepc is still trying to do the inverse of the full<br>
> > > B matrix with an LU decomposition and gets zero pivot.<br>
> > > <br>
> > > This is what I get as a PETSC error Message<br>
> > > <br>
> > > [0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------<br>
> > > [0]PETSC ERROR: Zero pivot in LU factorization: <a href="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%7C48eb040474e44a2af2f208d82350b5a7%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298176878634547&sdata=MfAJt1HSEK5wvhRzx0BM9OEEGxWjnlI%2FwTlzhN4BDeE%3D&reserved=0">
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%7C48eb040474e44a2af2f208d82350b5a7%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298176878634547&sdata=MfAJt1HSEK5wvhRzx0BM9OEEGxWjnlI%2FwTlzhN4BDeE%3D&reserved=0</a><br>
> > > [0]PETSC ERROR: Bad LU factorization<br>
> > > [0]PETSC ERROR: See <a href="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%7C48eb040474e44a2af2f208d82350b5a7%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298176878634547&sdata=NTc7lCzIo1Vj2sYmAehiE5b8ToXDTvN0wzDyh7JC30w%3D&reserved=0">
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%7C48eb040474e44a2af2f208d82350b5a7%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637298176878634547&sdata=NTc7lCzIo1Vj2sYmAehiE5b8ToXDTvN0wzDyh7JC30w%3D&reserved=0</a>
for trouble shooting.<br>
> > > [0]PETSC ERROR: Petsc Development GIT revision: v3.11.3-2263-gce77f2ed1a GIT Date: 2019-09-26 13:31:14 -0500<br>
> > > [0]PETSC ERROR: Nitsche_ex4a on a arch-linux2-c-opt named linux-8biu by eaulisa Tue Jul 7 10:17:55 2020<br>
> > > [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<br>
> > > [0]PETSC ERROR: #1 MatLUFactor_SeqDense() line 633 in /home/eaulisa/software/petsc/src/mat/impls/dense/seq/dense.c<br>
> > > [0]PETSC ERROR: #2 MatLUFactorNumeric_SeqDense() line 432 in /home/eaulisa/software/petsc/src/mat/impls/dense/seq/dense.c<br>
> > > [0]PETSC ERROR: #3 MatLUFactorNumeric() line 3056 in /home/eaulisa/software/petsc/src/mat/interface/matrix.c<br>
> > > [0]PETSC ERROR: #4 PCSetUp_LU() line 126 in /home/eaulisa/software/petsc/src/ksp/pc/impls/factor/lu/lu.c<br>
> > > [0]PETSC ERROR: #5 PCSetUp() line 894 in /home/eaulisa/software/petsc/src/ksp/pc/interface/precon.c<br>
> > > [0]PETSC ERROR: #6 KSPSetUp() line 377 in /home/eaulisa/software/petsc/src/ksp/ksp/interface/itfunc.c<br>
> > > [0]PETSC ERROR: #7 STSetUp_Shift() line 119 in /home/eaulisa/software/slepc/src/sys/classes/st/impls/shift/shift.c<br>
> > > [0]PETSC ERROR: #8 STSetUp() line 271 in /home/eaulisa/software/slepc/src/sys/classes/st/interface/stsolve.c<br>
> > > [0]PETSC ERROR: #9 EPSSetUp() line 273 in /home/eaulisa/software/slepc/src/eps/interface/epssetup.c<br>
> > > [0]PETSC ERROR: #10 EPSSolve() line 136 in /home/eaulisa/software/slepc/src/eps/interface/epssolve.c<br>
> > > <br>
> > > <br>
> > > <br>
> > > Thanks<br>
> > > Eugenio<br>
> > > <br>
> > > <br>
> > > <br>
> > > <br>
> > > Eugenio Aulisa<br>
> > > <br>
> > > Department of Mathematics and Statistics,<br>
> > > Texas Tech University<br>
> > > Lubbock TX, 79409-1042 <br>
> > > room: 226<br>
> > > <a href="http://www.math.ttu.edu/~eaulisa/">http://www.math.ttu.edu/~eaulisa/</a><br>
> > > phone: (806) 834-6684<br>
> > > fax: (806) 742-1112 <br>
> > > <br>
> > > <br>
> > > <br>
> > > <genEigen.cpp><br>
> > <br>
> <br>
<br>
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