[petsc-users] Zero pivot in LU factorisation
Matthew Knepley
knepley at gmail.com
Thu Jul 25 06:51:24 CDT 2013
On Thu, Jul 25, 2013 at 6:46 AM, Toby <T.W.Searle at sms.ed.ac.uk> wrote:
>
> Ok, it looks like the -st_pc_factor_shift_type option is now being used,
> thanks. Unfortunately it hasn't fixed the problem.
>
> if I use the NONZERO type and a shift amount, the shift amount option is
> not recognised and I still get the zero pivot error. If I use the
> POSITIVE_DEFINITE type I also get the pivot error. Output is below
>
> Thanks,
> 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 -st_pc_type lu
> -st_pc_factor_shift_type NONZERO -st_pc_shift_type_amount 1
>
> Generalized eigenproblem stored in file.
>
> Reading COMPLEX matrices from binary files...
> [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!
>
1) You misspelled the option: -st_pc_factor_shift_amount 1
2) It was used, and fixed you problem on row 0, now you have a problem on
row 2395, namely that it is missing. No
LU factorization routine will succeed here. You must at least put a
diagonal 0.0 on all rows.
3) Same goes for the run below.
4) A completely empty row means your matrix is indeed rank deficient. I
have no idea what results are coming out of
scipy, but they are not using factorization.
Matt
> [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
> 12:41:57 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
> [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
> 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
>
> WARNING! There are options you set that were not used!
> WARNING! could be spelling mistake, etc!
> Option left: name:-st_pc_shift_type_amount value: 1
>
> 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 -st_pc_type lu
> -st_pc_factor_shift_type POSITIVE_DEFINITE
>
> Generalized eigenproblem stored in file.
>
> Reading COMPLEX matrices from binary files...
> [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
> 12:40:20 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
> [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
> 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
>
>
>
>
> On 25/07/2013 12:34, Jose E. Roman wrote:
>
>> El 25/07/2013, a las 13:30, Toby escribió:
>>
>> Hi Matt,
>>>
>>> Thanks for the speedy reply. I tried using the options you suggested:
>>>
>>> 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 -st_pc_factor_shift_type
>>> NONZERO -st_pc_shift_type_amount 1
>>>
>>> But I still get the warnings:
>>> Option left: name:-st_pc_factor_shift_type value: NONZERO
>>> Option left: name:-st_pc_shift_type_amount value: 1
>>>
>> By default, ST is using PCREDUNDANT. In order to use the above options
>> you must change it to e.g. PCLU.
>> That is, add -st_pc_type lu
>>
>> Jose
>>
>>
>> I have tried it with just the -st_pc_type jacobi and -st_ksp_view. This
>>> gives me some eigenvalues, but I don't believe them (they do not appear on
>>> the spectrum which I solve using LAPACK where all eigenvalues have a real
>>> part less than 0). The output was very large, but consists of repetitions
>>> of this:
>>>
>>> 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 -st_pc_type jacobi
>>> -st_ksp_view
>>>
>>> Generalized eigenproblem stored in file.
>>>
>>> Reading COMPLEX matrices from binary files...
>>> 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: jacobi
>>> linear system matrix = precond matrix:
>>> Matrix Object: 1 MPI processes
>>> type: seqaij
>>> rows=6000, cols=6000
>>> total: nonzeros=3600, allocated nonzeros=3600
>>> total number of mallocs used during MatSetValues calls =0
>>> using I-node routines: found 4080 nodes, limit used is 5
>>>
>>> ...
>>>
>>> Number of iterations of the method: 189
>>> Number of linear iterations of the method: 1520
>>> Number of requested eigenvalues: 1
>>> Stopping condition: tol=1e-08, maxit=750
>>> Number of converged approximate eigenpairs: 2
>>>
>>> k ||Ax-kBx||/||kx||
>>> ----------------- ------------------
>>> 1388.774454+0.001823 i 0.751726
>>> 1388.774441+0.001820 i 0.912665
>>>
>>>
>>> Thanks again,
>>> Toby
>>>
>>
>>
>
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>
--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
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