[petsc-users] The product of two MPIDENSE matrices

[Jed Brown]

S V N Vishwanathan <vishy at stat.purdue.edu> writes:

> Hi
>
>> > I am wondering whether I can multiply MATELEMENTAL and MATAIJ
>> > matrices. If I cannot multiply those, could you build the
>> > multiplication?
>> 
>> What are the dimensions of the matrices?
>> 
>> Jack, does Clique support multiplication of sparse matrices with
>> [MC,MR] dense matrices?
>
> The dense matrix is very flat and long (e.g. 10 x few 1000s) and the
> sparse matrix is also flat and very very long (e.g. few 1000s x few
> millions). I saw the code which is used to multiply a MPIAIJ matrix with
> a dense matrix. We need something very similar, but which uses elemental
> matrices. 

In practice, you'll probably get the (sparse) * (dense) version instead.
These aren't implemented yet for Elemental matrices, but you can
MatConvert to MPIDENSE and then do the sparse-dense product.  Why is the
original (few 1000s)x10 matrix in Elemental format?

PETSc does not currently support the [VC,*] distributions.  We can do
it, and maybe should, but it's not what the first users were asking for
and it's basically the same as MATDENSE except in its ability to
interact with [MC,MR].

> There seems to be some inconsistency right now in PETSc. I can multiple
> a MPIAIJ matrix with MPIDENSE, but I cannot multiply MPIDENSE with
> MPIDENSE since there is no PLAPACK support anymore. 

MPIDENSE was a bad distribution for squarish matrices.

> On other hand, I can multiply a MATELEMENTAL with MATELEMENTAL but I
> cannot multiply a MPIDENSE with MATELEMENTAL. Is the eventual plan to
> remove MPIDENSE completely and replace it with MATELEMENTAL?

Yes, at least partially.  Elemental is sort of a heavy dependency for
the large faction that only need Sparse x [VC,*].  For more general
distributions and some other algorithms (in the realm that PLAPACK was
used in the past), Elemental is the right way to go.
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