[petsc-users] The multiplication of the transpose of a dense matrix(A^T) and a large sparse matrix(X1)

[Hong Zhang]

Joon,
We have implemented MatTransposeMatMult() for aij and dense matrices in the
master branch of petsc-dev
https://bitbucket.org/petsc/petsc/commits/cf22a14bc6cad51fdcbb947b8ac26f3ebf0d4d04?at=master
based on Jed's suggestion.

You may give it a try and let us know if there is a problem.
Hong



On Tue, Jun 4, 2013 at 6:15 PM, Joon hee Choi <choi240 at purdue.edu> wrote:

> I am trying to compress the matrix. I think it is the best way, because it
> may be not storable by MPI aij.
> If you get better solution in your lab meeting, then please let me know. :)
> Anyhow, thank you very much.
>
> Joon
>
> ----- Original Message -----
> From: "Jed Brown" <jedbrown at mcs.anl.gov>
> To: "Joon hee Choi" <choi240 at purdue.edu>
> Cc: petsc-users at mcs.anl.gov
> Sent: Tuesday, June 4, 2013 2:35:15 PM
> Subject: Re: [petsc-users] The multiplication of the transpose of a dense
> matrix(A^T) and a large sparse matrix(X1)
>
> Joon hee Choi <choi240 at purdue.edu> writes:
>
> > Thank you for your fast reply.
> > I got the out-of-memory error from MatTranspose(X1, MAT_INITIAL_MATRIX,
> &tempX1).
> > Also, it may take so much time to create X1 as X1^T because nnz for X1
> cannot have 1200Tril elements because of memory.
>
> Yes, that is also the dimension of the result matrix, which would be
> dense with the normal rules about products of sparse and dense matrices.
>
> Instead, you should compress the column space, perhaps by just removing
> all the columns that have no nonzeros.
>
> > Is there a fast way to create X1^T?
> >
> > Thank you,
> > Joon
> >
> >
> > ----- Original Message -----
> > From: "Jed Brown" <jedbrown at mcs.anl.gov>
> > To: "Joon hee Choi" <choi240 at purdue.edu>, petsc-users at mcs.anl.gov
> > Sent: Tuesday, June 4, 2013 7:55:31 AM
> > Subject: Re: [petsc-users] The multiplication of the transpose of a
> dense matrix(A^T) and a large sparse matrix(X1)
> >
> > Joon hee Choi <choi240 at purdue.edu> writes:
> >
> >> Hello,
> >>
> >> I am trying to multiply the transpose of a dense matrix(A) and a large
> sparse matrix(X1). That is, A^T x X1.
> >>
> >> X1 is a 26Mil x 1200Tril, 144Mil non-zeros sparse matrix and A is a
> 26Mil x 10 dense matrix.
> >>
> >> I know that sparse x dense is faster than dense x sparse when using
> MatMatMult.  Thus, I tried to implement the following code:
> >>
> >>         ierr = MatTranspose(X1, MAT_INITIAL_MATRIX, &tempX1);
> CHKERRQ(ierr);
> >>         ierr = MatMatMult(tempX1, A, MAT_INITIAL_MATRIX, 1.0, &MT);
> >>         ierr = MatDestroy(&tempX1); CHKERRQ(ierr);
> >>         ierr = MatTranspose(MT, MAT_INITIAL_MATRIX, &M); CHKERRQ(ierr);
> >>         ierr = MatDestroy(&MT); CHKERRQ(ierr);
> >>
> >> However, I got the "out-of-memory" error when implementing
> >> MatTranspose().
> >
> > Which MatTranspose?
> >
> >> I think this is because the number of columns of X1 is much larger
> >> than that of rows of X1.  If there is a fast way to calculate M = A^T
> >> x X1,
> >
> > Hong, do you have time to implement MatTransposeMatMult_MPIAIJ_MPIDense?
> >
> > Can you create X1 as X1^T instead?
> >
> > If you want to keep storing X1 is you do now, you can either store it as
> > ten vectors and use MatMultTranspose or you can pack it into one vector
> and use
> >
> >   MatCreateMAIJ(X1,10,&X1m);
> >   MatMultTranspose(X1m,Apacked,Bpacked);
> >
> > This is actually a better ordering for memory bandwidth.  The MAIJ
> > matrix does not need extra storage.
>
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