[petsc-users] Zero pivot in LU factorisation

Thu Jul 25 05:26:03 CDT 2013

On Thu, Jul 25, 2013 at 4:38 AM, Toby <T.W.Searle at sms.ed.ac.uk> wrote:

> Dear all,
>
> I have a generalised matrix problem: A x = lambda B x. My matrix B is
> diagonal and positive semi-definite. My matrix A is a non-hermitian complex
> matrix.
>
> My problem is essentially that when using the SLEPc generalised eigenvalue
> solver I get the error "zero pivot in LU factorisation". The rest of the
> below is details about the problem and things I have tried so far.
>
>
>
> The matrix will be at its largest about 48000 by 48000, and I want to find
> the eigenvalues. The eigenvalues I am interested in are ones with the
> largest real part near 0+0i. Ideally, I want to be able to find them even
> if they are internal (i.e when there are other eigenvalues with larger
> positive real part in the spectrum). However, I would be happy if I could
> get it to work for problems where all eigenvalues have real parts < 0 apart
> from the eigenvalue of interest.
>
> At the moment I have used the scipy linalg.eig and sparse.eigs functions.
> As far as I know, these use LAPACK and ARPACK respectively to do the heavy
> lifting. I have decided to see if I can achieve better performance through
> using the SLEPc library. If this is a bad decision, let me know!
>
> I want to move onto using PETSc with the SLEPc eigenvalue solvers. I have
> been trying out SLEPc using the examples provided as part of the tutorial.
> Exercise 7 reads matricies A and B from a file and outputs the solutions. I
> got this to work fine using the matrices provided. However, if I substitute
> a smaller sized test version of my problem (6000x6000), I get a variety of
> errors depending on the command line arguments I supply.
>
> The main problem I have is the error: "zero pivot in LU factorisation!"
> when I use the default settings.
>
> I think this might be related to the fact that B contains rows of zeros,
> although my understanding of linear algebra is somewhat basic. Is this true?
>
> I have tried setting the options suggested on the petsc website,
> -pc_factor_shift_type NONZERO etc but all I get is an additional warning
> that these options were not used
>

1) You probably need the correct prefix for this options, e.g.
-st_pc_factor_shift_type NONZERO

2) We would like to see the output of -st_ksp_view, but you probably need
-st_pc_type jacobi for it to finish

   Matt

> I assumed that this was a problem with the preconditioner, so I tried
> setting -eps_target to 0.1 and both with and without specifying -st_type
> sinvert and shift. Still I get the same error.
>
> Then I tried -st_pc_type jacobi and st_pc_type bjacobi. jacobi runs, but
> does not produce any eigenvalues. Block jacobi does an LU factorisation and
> gives me the same error again.
>
> The default method is krylov-schur, so I have experimented with the
> -eps_type gd and -eps_type jd options. Unfortunately these seem to produce
> nonsense eigenvalues, which do not appear on the spectrum at all when I
> solve using LAPACK in scipy.
>
> I know my matrix problem is not singular, because I can solve it using
> scipy.
>
> Do you know of any books/guides I might need to read besides the PETSC and
> SLEPC manuals to understand the behaviour of all these different solvers?
>
> The output from the case with no command line options is given below.
>
> Thanks a lot for taking the time to read this!
>
> Kind Regards,
> Toby
>
>
> tobymac:SLEPC toby$ mpiexec ./ex7 -f1 LHS-N7-M40-Re0.0-b0.1-Wi5.0-**amp0.02.petsc
>  -f2 RHS-N7-M40-Re0.0-b0.1-Wi5.0-**amp0.02.petsc -eps_view
>
> Generalized eigenproblem stored in file.
>
> [0]PETSC ERROR: --------------------- Error Message
> ------------------------------**------
> [0]PETSC ERROR: Detected zero pivot in LU factorization:
> see http://www.mcs.anl.gov/petsc/**documentation/faq.html#**ZeroPivot<http://www.mcs.anl.gov/petsc/documentation/faq.html#ZeroPivot>
> !
> [0]PETSC ERROR: Empty row in matrix: row in original ordering 2395 in
> permuted ordering 3600!
> [0]PETSC ERROR: ------------------------------**
> ------------------------------**------------
> [0]PETSC ERROR: Petsc Release Version 3.3.0, Patch 5, Sat Dec  1 15:10:41
> CST 2012
> [0]PETSC ERROR: See docs/changes/index.html for recent updates.
> [0]PETSC ERROR: See docs/faq.html for hints about trouble shooting.
> [0]PETSC ERROR: See docs/index.html for manual pages.
> [0]PETSC ERROR: ------------------------------**
> ------------------------------**------------
> [0]PETSC ERROR: ./ex7 on a arch-darw named tobymac by toby Thu Jul 25
> 10:20:40 2013
> [0]PETSC ERROR: Libraries linked from /opt/local/lib
> [0]PETSC ERROR: Configure run at Tue Jul 23 15:11:27 2013
> [0]PETSC ERROR: Configure options --prefix=/opt/local
> --with-valgrind-dir=/opt/local --with-shared-libraries
> --with-scalar-type=complex --with-clanguage=C++
> --with-superlu-dir=/opt/local --with-blacs-dir=/opt/local
> --with-scalapack-dir=/opt/**local --with-mumps-dir=/opt/local
> --with-metis-dir=/opt/local --with-parmetis-dir=/opt/local --COPTFLAGS=-O2
> --CXXOPTFLAGS=-O2 --FOPTFLAGS=-O2 --LDFLAGS=-L/opt/local/lib --CFLAGS="-O2
> -mtune=native" --CXXFLAGS="-O2 -mtune=native"
> [0]PETSC ERROR: ------------------------------**
> ------------------------------**------------
> [0]PETSC ERROR: MatLUFactorSymbolic_SeqAIJ() line 334 in
> /opt/local/var/macports/build/**_Users_toby_MyPorts_**
> scienceports_math_petsc/petsc/**work/petsc-3.3-p5/src/mat/**
> impls/aij/seq/aijfact.c
> [0]PETSC ERROR: MatLUFactorSymbolic() line 2750 in
> /opt/local/var/macports/build/**_Users_toby_MyPorts_**
> scienceports_math_petsc/petsc/**work/petsc-3.3-p5/src/mat/**
> interface/matrix.c
> [0]PETSC ERROR: PCSetUp_LU() line 135 in /opt/local/var/macports/build/**
> _Users_toby_MyPorts_**scienceports_math_petsc/petsc/**
> work/petsc-3.3-p5/src/ksp/pc/**impls/factor/lu/lu.c
>  Number of iterations of the method: 0
>  Number of linear iterations of the method: 0
>  Number of requested eigenvalues: 1
>  Stopping condition: tol=1e-08, maxit=750
>  Number of converged approximate eigenpairs: 0
>
> [0]PETSC ERROR: PCSetUp() line 832 in /opt/local/var/macports/build/**
> _Users_toby_MyPorts_**scienceports_math_petsc/petsc/**
> work/petsc-3.3-p5/src/ksp/pc/**interface/precon.c
> [0]PETSC ERROR: KSPSetUp() line 278 in /opt/local/var/macports/build/**
> _Users_toby_MyPorts_**scienceports_math_petsc/petsc/**
> work/petsc-3.3-p5/src/ksp/ksp/**interface/itfunc.c
> [0]PETSC ERROR: PCSetUp_Redundant() line 176 in
> /opt/local/var/macports/build/**_Users_toby_MyPorts_**
> scienceports_math_petsc/petsc/**work/petsc-3.3-p5/src/ksp/pc/**
> impls/redundant/redundant.c
> [0]PETSC ERROR: PCSetUp() line 832 in /opt/local/var/macports/build/**
> _Users_toby_MyPorts_**scienceports_math_petsc/petsc/**
> work/petsc-3.3-p5/src/ksp/pc/**interface/precon.c
> [0]PETSC ERROR: KSPSetUp() line 278 in /opt/local/var/macports/build/**
> _Users_toby_MyPorts_**scienceports_math_petsc/petsc/**
> work/petsc-3.3-p5/src/ksp/ksp/**interface/itfunc.c
> [0]PETSC ERROR: STSetUp_Shift() line 94 in src/st/impls/shift/shift.c
> [0]PETSC ERROR: STSetUp() line 280 in src/st/interface/stsolve.c
> [0]PETSC ERROR: EPSSetUp() line 204 in src/eps/interface/setup.c
> [0]PETSC ERROR: EPSSolve() line 109 in src/eps/interface/solve.c
> tobymac:SLEPC toby$
>
>
> --
> The University of Edinburgh is a charitable body, registered in
> Scotland, with registration number SC005336.
>
>

-- 
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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