[petsc-users] Kronecker Product

[Matthew Knepley]

On Mon, Jan 30, 2023 at 3:08 PM Guglielmo, Tyler Hardy via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> I would need the Kronecker product to be explicitly available to perform
> matrix exponentials.  A and B are of order 5000, so not too large.  I will
> give storing them on all ranks a shot.  Thanks for the tips!
>

Were you going to do exponentials by explicit factorization? For large
matrices, I thought it was common to
use matrix-free methods (
https://slepc.upv.es/documentation/current/docs/manualpages/MFN/index.html)

  Thanks,

    Matt


>
>
> Best,
>
> Tyler
>
>
>
> *From: *Barry Smith <bsmith at petsc.dev>
> *Date: *Monday, January 30, 2023 at 12:01 PM
> *To: *Guglielmo, Tyler Hardy <guglielmo2 at llnl.gov>
> *Cc: *petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> *Subject: *Re: [petsc-users] Kronecker Product
>
>
>
>   What is large? If A and B have dimensions of 1000, then the Kronecker
> product is of size 1,000,000. Do you want the Kronecker product to be
> explicitly formed or just available as matrix vector products?  If just
> explicitly available then I think you can just store sparse A (for example)
> completely on all ranks, 10,000 by 10,000 sparse matrix is small for
> sequential) while B is distributed.
>
>
>
> Barry
>
>
>
>
>
> On Jan 30, 2023, at 2:48 PM, Guglielmo, Tyler Hardy <guglielmo2 at llnl.gov>
> wrote:
>
>
>
> Both matrices (A and B) would be approximately the same size and large.
> The use case (for me at least) is to create several large sparse matrices
> which will be combined in various ways through Kronecker products.  The
> combination happens at every time step in an evolution, so it really needs
> to be fast as well.  I’m thinking mpi/petsc is probably not the most
> optimal way for dealing with this, and might just have to work with single
> node multi-threading.
>
>
>
> Best,
>
> Tyler
>
>
>
> *From: *Matthew Knepley <knepley at gmail.com>
> *Date: *Monday, January 30, 2023 at 11:31 AM
> *To: *Guglielmo, Tyler Hardy <guglielmo2 at llnl.gov>
> *Cc: *Barry Smith <bsmith at petsc.dev>, petsc-users at mcs.anl.gov <
> petsc-users at mcs.anl.gov>
> *Subject: *Re: [petsc-users] Kronecker Product
>
> On Mon, Jan 30, 2023 at 2:24 PM Guglielmo, Tyler Hardy via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
> Thanks Barry,
>
>
>
> I saw that function, but wasn’t sure how to apply it since the
> documentation says that S and T are dense matrices, but in my case all
> matrices involved are sparse.  Is there a way to work around the dense
> requirement?
>
>
>
> We don't have parallel sparse-sparse. It would not be too hard to write,
> but it would be some work.
>
>
>
> It is hard to understand the use case. Is one matrix much smaller? If not,
> and you inherit the distribution from A, it seems
>
> like it might be very suboptimal, and otherwise you would have to
> redistribute on the fly and it would get very complicated.
>
>
>
>   Thanks,
>
>
>
>      Matt
>
>
>
> Best,
>
> Tyler
>
>
>
> *From: *Barry Smith <bsmith at petsc.dev>
> *Date: *Monday, January 30, 2023 at 11:12 AM
> *To: *Guglielmo, Tyler Hardy <guglielmo2 at llnl.gov>
> *Cc: *petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> *Subject: *Re: [petsc-users] Kronecker Product
>
>
>
>    Do you need the explicit sparse representation of the Kronecker
> product? Or do you want to apply it as an operator or solve systems with
> it? If the latter you can use
> https://petsc.org/release/docs/manualpages/Mat/MatCreateKAIJ/#matcreatekaij
> <https://urldefense.us/v3/__https:/petsc.org/release/docs/manualpages/Mat/MatCreateKAIJ/*matcreatekaij__;Iw!!G2kpM7uM-TzIFchu!lSQ9WFlYi6PMdfs3WAfEq4ydgCLZtfDgyFy9PjdLNTisCsHtwmVuukcpIv1J0i1EtiQ$>
>
>
>
>   Barry
>
>
>
>
>
>
>
> On Jan 30, 2023, at 12:53 PM, Guglielmo, Tyler Hardy via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
>
>
> Hi all,
>
>
>
> I am wondering if there is any functionality for taking Kronecker products
> of large sparse matrices that are parallel?  MatSeqAIJKron is as close as I
> have found, but it seems like this does not work for parallel matrices.
> Any ideas here?
>
>
>
> An option could be to make A and B sequential, compute the Kronecker
> product, C, then scatter C into a parallel matrix?  This seems like a
> horribly inefficient procedure.  I’m still fairly new to petsc, so thanks
> for patience :)!
>
>
>
> Best,
>
> Tyler
>
>
>
> +++++++++++++++++++++++++++++
>
> Tyler Guglielmo
>
> Postdoctoral Researcher
>
> Lawrence Livermore National Lab
>
> Office: 925-423-6186
>
> Cell: 210-480-8000
>
> +++++++++++++++++++++++++++++
>
>
>
>
>
>
> --
>
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
>
>
> https://www.cse.buffalo.edu/~knepley/
> <https://urldefense.us/v3/__http:/www.cse.buffalo.edu/*knepley/__;fg!!G2kpM7uM-TzIFchu!nK03nUENfNtHoOs8RWmJWJQYJH2IlC_lYQPNn7kV9FsBv2CQKR_VSqbLGRLFShVpKmY$>
>
>
>


-- 
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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