[petsc-users] Get LU decomposition of a rectangular matrix

[Natacha BEREUX]

Thanks for your answer
In between I tried to call directly MatLUFactorSymbolic then
MatLUFactorNumeric to avoid MatGetOrdering, and the code fails later (in
the call to SuperLu routine pdgssvx).

I would prefer to use PETSc for the computation of the nullbasis: the input
matrix is a PETSc "Mat" (MPIAIJ) and the ouput basis will be used to
project a linear system (also a PETSc "Mat" and Vec) on a reduced space.
Parallel format conversion is quite tricky and error prone. Using Petsc
"Mat" is much easier and safe than maintaining my own SuperLU interface.

Here are some details on what I plan to do :
get a LU decomposition of a rectangular constraints matrix :
P C Q = ( L1 )
             ( L2 )
then obtain L1^{-1} L2
II hoped to get the factors after LU decomposition (possible with SuperLu
and SuperLU_dist, but ot with MUMPS) and call MatMatSolve afterwards (which
is only possible if L2 is a dense matrix - if my understanding of the
documentation is correct)
then the basis Z is used to project a rigidity matrix K ( ie compute or
define as a MatShell  Z^T K Z )

Do you confirm that it is not a good option to use PETSc for this ?
Thanks a lot again for your advice and help
Natacha

On Tue, Mar 13, 2018 at 10:14 PM, Smith, Barry F. <bsmith at mcs.anl.gov>
wrote:

>    For your purposes you should just use superlu or superlu_dist directly
> in your code not through PETSc.
>
>    Barry
>
> There is nothing to be gained by doing it through PETSc.
>
> This is not relevant for your use case but I have noted that the unneeded
> use of MatGetOrdering() should be eliminated https://bitbucket.org/petsc/
> petsc/issues/211/matgetordering-should-not-be-called-for
>
> > On Mar 13, 2018, at 7:04 AM, Natacha BEREUX <natacha.bereux at gmail.com>
> wrote:
> >
> > Hi Barry
> > Thanks for your answer,
> > I followed your suggestion (matrix type = MPIAIJ and superlu_dist on a
> single processor)   but I still get the same problem.
> >
> >
> > Rectangular matrices seem to be forbidden in MatGetOrdering(), whatever
> package is used for the LU decomposition
> >
> > Here is the output :
> >  ./ex12f -f data/constraints.bin -pc_factor_mat_solver_package
> superlu_dist -pc_type lu
> >
> >    9   33    9   33  1.     0.3E+02 0.3E+02  0.     0.7E+04  1.      0.
> > [0]PETSC ERROR: --------------------- Error Message
> --------------------------------------------------------------
> > [0]PETSC ERROR: Invalid argument
> > [0]PETSC ERROR: Must be square matrix, rows 33 columns 9
> >
> >
> > Should I call directly a factorization routine ?  Instead of trying to
> build a preconditionner ?
> >
> >
> > Best regards,
> > Natacha
> >
> >
> > On Mon, Mar 12, 2018 at 3:46 PM, Smith, Barry F. <bsmith at mcs.anl.gov>
> wrote:
> >
> >    Create the matrix on one process but make it a MPIAIJ matrix (not
> SeqAIJ or AIJ) then you should be able to do the factorization with
> SuperLU_Dist
> >
> >     Please let us know how it goes,
> >
> >     Barry
> >
> >
> > > On Mar 12, 2018, at 4:35 AM, Natacha BEREUX <natacha.bereux at gmail.com>
> wrote:
> > >
> > > Dear Petsc user's
> > >
> > > I am trying to use SuperLU_dist to compute LU decomposition of a
> non-square matrix.
> > >
> > > My purpose is to build a basis of the nullspace of a matrix C . This
> matrix stores constraints (i.e. linear relationships between degrees of
> freedom): it is thus rectangular (size 9 x 33) and not square
> > > I need to get the L U factors of C^T which is a tall skinny matrix.
> > > It is possible when using directly SuperLu or SuperLU_dist
> > > But when I use Petsc interface to SuperLU I get the following error :
> > >
> > > [0]PETSC ERROR: Invalid argument
> > > [0]PETSC ERROR: Must be square matrix, rows 9 columns 33
> > > [0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/
> documentation/faq.html for trouble shooting.
> > > [0]PETSC ERROR: Petsc Release Version 3.8.3, Dec, 09, 2017
> > > [0]PETSC ERROR: #1 MatGetOrdering() line 243 in
> /home/H03755/Librairies/petsc-3.8.3/src/mat/order/sorder.c
> > > [0]PETSC ERROR: #2 PCSetUp_LU() line 84 in
> /home/H03755/Librairies/petsc-3.8.3/src/ksp/pc/impls/factor/lu/lu.c
> > > [0]PETSC ERROR: #3 PCSetUp() line 924 in /home/H03755/Librairies/petsc-
> 3.8.3/src/ksp/pc/interface/precon.c
> > > [0]PETSC ERROR: #4 KSPSetUp() line 381 in
> /home/H03755/Librairies/petsc-3.8.3/src/ksp/ksp/interface/itfunc.c
> > > [0]PETSC ERROR: #5 KSPSolve() line 612 in
> /home/H03755/Librairies/petsc-3.8.3/src/ksp/ksp/interface/itfunc.c
> > > [0]PETSC ERROR: #6 User provided function() line 0 in User file
> > >
> > > The use of non-square matrices is forbidden.
> > >
> > > Is there a way to specify that I want to use a rectangular matrix ?
> How can I proceed to call SuperLU through PETSc with a rectangular matrix ?
> > >
> > > Thanks a lot for your help
> > > Best regards,
> > >
> > > Natacha
> >
> >
>
>
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