# [petsc-users] MatMatMul inefficient

Guido Margherita margherita.guido at epfl.ch
Mon Feb 13 08:38:40 CST 2023

```A is a sparse MATSEQAIJ, Q is dense.

Thanks,
Margherita

> Il giorno 13 feb 2023, alle ore 3:27 PM, knepley at gmail.com ha scritto:
>
> On Mon, Feb 13, 2023 at 9:21 AM Guido Margherita via petsc-users <petsc-users at mcs.anl.gov> wrote:
> Hi all,
>
> I realised that performing a matrix-matrix multiplication using the function MatMatMult it is not at all computationally efficient with respect to performing N times a matrix-vector multiplication with MatMul, being N the number of columns of the second matrix in the product.
> When I multiply I matrix A  46816 x 46816 to a matrix Q  46816 x 6, the MatMatMul function is indeed 6 times more expensive than 6 times a call to MatMul, when performed sequentially (0.04056  s vs 0.0062 s ). When the same code is run in parallel the gap grows even more, being10 times more expensive.
>   Is there an explanation for it?
>
> So we can reproduce this, what kind of matrix is A? I am assuming that Q is dense.
>
>   Thanks,
>
>      Matt
>
>
> t1 = MPI_Wtime()
> call MatMatMult(A,Q,MAT_INITIAL_MATRIX, PETSC_DEFAULT_REAL, AQ, ierr )
> t2 = MPI_Wtime()
> t_MatMatMul = t2-t1
>
> t_MatMul=0.0
> do j = 0, m-1
>         call MatGetColumnVector(Q, q_vec, j,ierr)
>
>         t1 = MPI_Wtime()
>         call MatMult(A, q_vec, aq_vec, ierr)
>         t2 = MPI_Wtime()
>
>         t_MatMul = t_MatMul + t2-t1
> end do
>
> Thank you,
> Margherita Guido
>
>
>
> --
> 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/

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