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<div class="moz-cite-prefix">Hi Matt,<br>
<br>
Thanks for the speedy reply. I tried using the options you
suggested: <br>
<br>
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<br>
<br>
But I still get the warnings:<br>
Option left: name:-st_pc_factor_shift_type value: NONZERO<br>
Option left: name:-st_pc_shift_type_amount value: 1<br>
<br>
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:<br>
<br>
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 <br>
<br>
Generalized eigenproblem stored in file.<br>
<br>
Reading COMPLEX matrices from binary files...<br>
KSP Object:(st_) 1 MPI processes<br>
type: preonly<br>
maximum iterations=10000, initial guess is zero<br>
tolerances: relative=1e-08, absolute=1e-50, divergence=10000<br>
left preconditioning<br>
using NONE norm type for convergence test<br>
PC Object:(st_) 1 MPI processes<br>
type: jacobi<br>
linear system matrix = precond matrix:<br>
Matrix Object: 1 MPI processes<br>
type: seqaij<br>
rows=6000, cols=6000<br>
total: nonzeros=3600, allocated nonzeros=3600<br>
total number of mallocs used during MatSetValues calls =0<br>
using I-node routines: found 4080 nodes, limit used is 5<br>
<br>
...<br>
<br>
Number of iterations of the method: 189<br>
Number of linear iterations of the method: 1520<br>
Number of requested eigenvalues: 1<br>
Stopping condition: tol=1e-08, maxit=750<br>
Number of converged approximate eigenpairs: 2<br>
<br>
k ||Ax-kBx||/||kx||<br>
----------------- ------------------<br>
1388.774454+0.001823 i 0.751726<br>
1388.774441+0.001820 i 0.912665<br>
<br>
<br>
Thanks again,<br>
Toby<br>
<br>
<br>
<br>
<br>
On 25/07/2013 11:26, Matthew Knepley wrote:<br>
</div>
<blockquote
cite="mid:CAMYG4Gm+W6Mw9_LNCafcOM=ZObfkYxRZnyf1=40UNbkOETp_ZA@mail.gmail.com"
type="cite">
<div dir="ltr">On Thu, Jul 25, 2013 at 4:38 AM, Toby <span
dir="ltr"><<a moz-do-not-send="true"
href="mailto:T.W.Searle@sms.ed.ac.uk" target="_blank">T.W.Searle@sms.ed.ac.uk</a>></span>
wrote:<br>
<div class="gmail_extra">
<div class="gmail_quote">
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">Dear
all,<br>
<br>
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.<br>
<br>
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.<br>
<br>
<br>
<br>
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.<br>
<br>
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!<br>
<br>
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.<br>
<br>
The main problem I have is the error: "zero pivot in LU
factorisation!" when I use the default settings.<br>
<br>
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?<br>
<br>
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<br>
</blockquote>
<div><br>
</div>
<div>1) You probably need the correct prefix for this
options, e.g. -st_pc_factor_shift_type NONZERO</div>
<div><br>
</div>
<div>2) We would like to see the output of -st_ksp_view, but
you probably need -st_pc_type jacobi for it to finish</div>
<div><br>
</div>
<div> Matt</div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
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.<br>
<br>
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.<br>
<br>
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.<br>
<br>
I know my matrix problem is not singular, because I can
solve it using scipy.<br>
<br>
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?<br>
<br>
The output from the case with no command line options is
given below.<br>
<br>
Thanks a lot for taking the time to read this!<br>
<br>
Kind Regards,<br>
Toby<br>
<br>
<br>
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<br>
<br>
Generalized eigenproblem stored in file.<br>
<br>
[0]PETSC ERROR: --------------------- Error Message
------------------------------------<br>
[0]PETSC ERROR: Detected zero pivot in LU factorization:<br>
see <a moz-do-not-send="true"
href="http://www.mcs.anl.gov/petsc/documentation/faq.html#ZeroPivot"
target="_blank">http://www.mcs.anl.gov/petsc/documentation/faq.html#ZeroPivot</a>!<br>
[0]PETSC ERROR: Empty row in matrix: row in original
ordering 2395 in permuted ordering 3600!<br>
[0]PETSC ERROR: ------------------------------------------------------------------------<br>
[0]PETSC ERROR: Petsc Release Version 3.3.0, Patch 5, Sat
Dec 1 15:10:41 CST 2012<br>
[0]PETSC ERROR: See docs/changes/index.html for recent
updates.<br>
[0]PETSC ERROR: See docs/faq.html for hints about trouble
shooting.<br>
[0]PETSC ERROR: See docs/index.html for manual pages.<br>
[0]PETSC ERROR: ------------------------------------------------------------------------<br>
[0]PETSC ERROR: ./ex7 on a arch-darw named tobymac by toby
Thu Jul 25 10:20:40 2013<br>
[0]PETSC ERROR: Libraries linked from /opt/local/lib<br>
[0]PETSC ERROR: Configure run at Tue Jul 23 15:11:27 2013<br>
[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"<br>
[0]PETSC ERROR: ------------------------------------------------------------------------<br>
[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<br>
[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<br>
[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<br>
Number of iterations of the method: 0<br>
Number of linear iterations of the method: 0<br>
Number of requested eigenvalues: 1<br>
Stopping condition: tol=1e-08, maxit=750<br>
Number of converged approximate eigenpairs: 0<br>
<br>
[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<br>
[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<br>
[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<br>
[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<br>
[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<br>
[0]PETSC ERROR: STSetUp_Shift() line 94 in
src/st/impls/shift/shift.c<br>
[0]PETSC ERROR: STSetUp() line 280 in
src/st/interface/stsolve.c<br>
[0]PETSC ERROR: EPSSetUp() line 204 in
src/eps/interface/setup.c<br>
[0]PETSC ERROR: EPSSolve() line 109 in
src/eps/interface/solve.c<br>
tobymac:SLEPC toby$<span class="HOEnZb"><font
color="#888888"><br>
<br>
<br>
-- <br>
The University of Edinburgh is a charitable body,
registered in<br>
Scotland, with registration number SC005336.<br>
<br>
</font></span></blockquote>
</div>
<br>
<br clear="all">
<div><br>
</div>
-- <br>
What most experimenters take for granted before they begin
their experiments is infinitely more interesting than any
results to which their experiments lead.<br>
-- Norbert Wiener
</div>
</div>
</blockquote>
<br>
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