[petsc-users] petsc4py: parallel matrix-vector multiplication
Dave May
dave.mayhem23 at gmail.com
Sun May 6 11:14:14 CDT 2018
On Sun, 6 May 2018 at 17:52, Robert Speck <r.speck at fz-juelich.de> wrote:
> OK, thanks, I see. This is basically what happens in the poisson2d.py
> example, too, right?
>
> I tried it with the shell matrix (?) used in the poisson2d example and
> it works right away, but then I fail to see how to make use of the
> preconditioners for KSP (see my original message)..
If you want assemble something within the operator created by
DMCreateMatrix(), take a look at this function
http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetValuesStencil.html
Study some of the examples listed at the bottom of the page.
(But you will have to concern yourself with the spatial decomposition, just
like in the poisson2d and Bratu example.)
Thanks,
Dave
>
> Thanks again!
> -Robert-
>
>
> On 06.05.18 16:52, Jed Brown wrote:
> > Robert Speck <r.speck at fz-juelich.de> writes:
> >
> >> Thanks for your reply and help. Yes, this is going to be a PDE solver
> >> for structured grids. The first goal would be IDC (or Crank-Nicholson)
> >> for the heat equation, which would require both solving a linear system
> >> and application of the matrix.
> >>
> >> The code I wrote for testing parallel matrix-vector multiplication can
> >> be found here:
> >>
> https://github.com/Parallel-in-Time/pySDC/blob/petsc/pySDC/playgrounds/PETSc/playground_matmult.py
> >>
> >> Both vectors and matrix come from the DMDA, but I guess filling them is
> >> done in a wrong way? Or do I need to convert global/natural vectors to
> >> local ones somewhere?
> >
> > Global and Natural are not the same (see user's manual for details).
> > The matrix acts on a Global vector. See
> > petsc4py/demo/bratu3d/bratu3d.py for examples of efficiently setting
> > values (and computing residuals) using Global vectors. It should be
> > simpler/cleaner code than you currently have.
> >
> >>
> >> Best
> >> -Robert-
> >>
> >>
> >>
> >> On 06.05.18 14:44, Dave May wrote:
> >>> On Sun, 6 May 2018 at 10:40, Robert Speck <r.speck at fz-juelich.de
> >>> <mailto:r.speck at fz-juelich.de>> wrote:
> >>>
> >>> Hi!
> >>>
> >>> I would like to do a matrix-vector multiplication (besides using
> linear
> >>> solvers and so on) with petsc4py. I took the matrix from this
> example
> >>>
> >>> (
> https://bitbucket.org/petsc/petsc4py/src/master/demo/kspsolve/petsc-mat.py
> )
> >>>
> >>>
> >>> This example only produces a matrix. And from the code the matrix
> >>> produced is identical in serial or parallel.
> >>>
> >>>
> >>>
> >>> and applied it to a PETSc Vector. All works well in serial, but in
> >>> parallel (in particular if ordering becomes relevant) the resulting
> >>> vector looks very different.
> >>>
> >>>
> >>> Given this, the way you defined the x vector in y = A x must be
> >>> different when run on 1 versus N mpi ranks.
> >>>
> >>>
> >>> Using the shell matrix of this example
> >>> (
> https://bitbucket.org/petsc/petsc4py/src/master/demo/poisson2d/poisson2d.py
> )
> >>> helps, but then I cannot use matrix-based preconditioners for KSP
> >>> directly (right?). I also tried using DMDA for creating vectors and
> >>> matrix and for taking care of their ordering (which seems to be my
> >>> problem here), but that did not help either.
> >>>
> >>> So, my question is this: How do I do easy parallel matrix-vector
> >>> multiplication with petsc4py in a way that allows me to use
> parallel
> >>> linear solvers etc. later on? I want to deal with spatial
> decomposition
> >>> as little as possible.
> >>>
> >>>
> >>> What's the context - are you solving a PDE?
> >>>
> >>> Assuming you are using your own grid object (e.g. as you might have if
> >>> solving a PDE), and assuming you are not solving a 1D problem, you
> >>> actually have to "deal" with the spatial decomposition otherwise
> >>> performance could be quite terrible - even for something simple like a
> 5
> >>> point Laplacian on a structured grid in 2D
> >>>
> >>> What data structures should I use? DMDA or
> >>> PETSc.Vec() and PETSc.Mat() or something else?
> >>>
> >>>
> >>> The mat vec product is not causing you a problem. Your issue appears to
> >>> be that you do not have a way to label entries in a vector in a
> >>> consistent manner.
> >>>
> >>> What's the objective? Are you solving a PDE? If yes, structured grid?
> If
> >>> yes again, use the DMDA. It takes care of all the local-to-global and
> >>> global-to-local mapping you need.
> >>>
> >>> Thanks,
> >>> Dave
> >>>
> >>>
> >>>
> >>> Thanks!
> >>> -Robert-
> >>>
> >>> --
> >>> Dr. Robert Speck
> >>> Juelich Supercomputing Centre
> >>> Institute for Advanced Simulation
> >>> Forschungszentrum Juelich GmbH
> >>> 52425 Juelich, Germany
> >>>
> >>> Tel: +49 2461 61 1644
> >>> Fax: +49 2461 61 6656
> >>>
> >>> Email: r.speck at fz-juelich.de <mailto:r.speck at fz-juelich.de>
> >>> Website: http://www.fz-juelich.de/ias/jsc/speck_r
> >>> PinT: http://www.fz-juelich.de/ias/jsc/pint
> >>>
> >>>
> >>>
> >>>
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> >>>
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> >>> 52425 Juelich
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> >>> Vorsitzender des Aufsichtsrats: MinDir Dr. Karl Eugen Huthmacher
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> (Vorsitzender),
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> >>>
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> >>>
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> >>>
> >>
> >> --
> >> Dr. Robert Speck
> >> Juelich Supercomputing Centre
> >> Institute for Advanced Simulation
> >> Forschungszentrum Juelich GmbH
> >> 52425 Juelich, Germany
> >>
> >> Tel: +49 2461 61 1644
> >> Fax: +49 2461 61 6656
> >>
> >> Email: r.speck at fz-juelich.de
> >> Website: http://www.fz-juelich.de/ias/jsc/speck_r
> >> PinT: http://www.fz-juelich.de/ias/jsc/pint
>
> --
> Dr. Robert Speck
> Juelich Supercomputing Centre
> Institute for Advanced Simulation
> Forschungszentrum Juelich GmbH
> 52425 Juelich, Germany
>
> Tel: +49 2461 61 1644
> Fax: +49 2461 61 6656
>
> Email: r.speck at fz-juelich.de
> Website: http://www.fz-juelich.de/ias/jsc/speck_r
> PinT: http://www.fz-juelich.de/ias/jsc/pint
>
>
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