[petsc-users] Computing part of the inverse of a large matrix

[Jan Grießer]

Hey Matt,
Can you elaborate a little bit on your idea for calculating the inverse
matrix ?
Greetings Jan

Am Mo., 30. Sept. 2019 um 17:50 Uhr schrieb Matthew Knepley <
knepley at gmail.com>:

> I think the easier way to do it is to use a KSP which is configured to do
> preonly and LU. That will do the right thing in parallel.
>
>    Matt
>
> On Mon, Sep 30, 2019 at 11:47 AM Smith, Barry F. via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
>>
>>    The Python wrapper for PETSc may be missing some functionality; there
>> is a manual process involved in creating new ones. You could poke around
>> the petsc4py source and see how easy it would be to add more functionality
>> that you need.
>>
>>
>>
>> > On Sep 30, 2019, at 10:13 AM, Jan Grießer <griesser.jan at googlemail.com>
>> wrote:
>> >
>> > I configured PETSc with MUMPS and tested it already for the spectrum
>> slicing method in Slepc4py but i have problems in setting up the LU
>> factorization in the PETSc4py. Since i do not find the corresponding
>> methods and commands in the source code. Thats why is was wondering if this
>> is even possible in the python version.
>> >
>> > Am Mo., 30. Sept. 2019 um 16:57 Uhr schrieb Smith, Barry F. <
>> bsmith at mcs.anl.gov>:
>> >
>> >   If you want a parallal LU (and hence the ability to build the inverse
>> in parallel) you need to configure PETSc with --download-mumps
>> --download-scalapack
>> >
>> >   Barry
>> >
>> >
>> > > On Sep 30, 2019, at 9:44 AM, Jan Grießer <griesser.jan at googlemail.com>
>> wrote:
>> > >
>> > > Is the MatMumpsGetInverse also wrapped to the python version in
>> PETSc4py ? If yes is there any example for using it ?
>> > > My other question is related to the LU factoriation (
>> https://www.mcs.anl.gov/petsc/documentation/faq.html#invertmatrix).
>> > > Is the LU factorization only possible for sequential Aij matrices ? I
>> read in the docs that this is the case for ordering.
>> > > After setting up my matrix A, B and x i tried:
>> > >  r, c = dynamical_matrix_nn.getOrdering("nd")
>> > >  fac_dyn_matrix = dynamical_matrix_nn.factorLU(r,c)
>> > >
>> > > resulting in an error:
>> > > [0] No support for this operation for this object type
>> > > [0] Mat type mpiaij
>> > >
>> > > Am Fr., 27. Sept. 2019 um 16:26 Uhr schrieb Zhang, Hong <
>> hzhang at mcs.anl.gov>:
>> > > See ~petsc/src/mat/examples/tests/ex214.c on how to compute selected
>> entries of inv(A) using mumps.
>> > > Hong
>> > >
>> > > On Fri, Sep 27, 2019 at 8:04 AM Smith, Barry F. via petsc-users <
>> petsc-users at mcs.anl.gov> wrote:
>> > >
>> > > MatMumpsGetInverse() maybe useful. Also simply using MatMatSolve()
>> with the first 1000 columns of the identity and "throwing away" the part
>> you don't need may be most effective.
>> > >
>> > >    Barry
>> > >
>> > >
>> > >
>> > > > On Sep 27, 2019, at 3:34 AM, Jan Grießer via petsc-users <
>> petsc-users at mcs.anl.gov> wrote:
>> > > >
>> > > > Hi all,
>> > > > i am using petsc4py. I am dealing with rather large sparse matrices
>> up to 600kx600k and i am interested in calculating a part of the inverse of
>> the matrix(I know it will be a dense matrix). Due to the nature of my
>> problem, I am only interested in approximately the first 1000 rows and 1000
>> columns (i.e. a large block in the upper left ofthe matrix).  Before I
>> start to play around now, I wanted to ask if there is a clever way to
>> tackle this kind of problem in PETSc in principle. For any input I would be
>> very grateful!
>> > > > Greetings Jan
>> > >
>> >
>>
>>
>
> --
> 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
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
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