[petsc-users] Using MATAIJ and MATSBAIJ

[Jed Brown]

Chih-Chuen Lin via petsc-users <petsc-users at mcs.anl.gov> writes:

> Dear PETSc users,
>
> I am Ian. I trying to implement a solver which involves a sparse symmetric matrix A multiplied by a dense matrix X. And because of the nature of the problem, the bandwidth of the matrix A would be kind of large.For A*X, I am thinking using reverse Cuthill-Mckee algorithm to reduce the bandwidth.
>
> Are the following approach reasonable, or do you have a better advice?
>
> 1. Use MatGetOrdering to get a MATORDERINGRCM ordering, and MatPermute to create a new with it.

You can do this.  It may not make much difference.  Note that if you
permute columns of A, you'll also need to permute rows of X.

> 2. What’s the difference by using MATAIJ and MATBAIJ in terms of the entry insertion and computation and MPI efficiency for a sparse-dense matrix multiplication? Would it be better to use MATSBAIJ in terms of the computational efficiency?

The sparse-dense variant isn't implemented for all cases and may not
provide benefit anyway.  Using a parallel symmetric format for SpMV
requires more communication of the "vector", which in your case is a
dense matrix.