[petsc-users] Efficiently build a matrix from two asymmetric diagonal block matrices

[Emile Soutter]

Thanks a lot for the reply. The context is that the matrix itself will be
used as a matrix projection in the context of multigrid algorithm. So the
final matrix,P, will be used as the interpolation matrix in PCMG routine (
https://www.mcs.anl.gov/petsc/petsc-3.6/docs/manualpages/PC/PCMGSetInterpolation.html
), and then it will be used in matrix multiplication ( operation of the
kind A'=PAP^T, A is a matrix on a fine MG level, A' the matrix on a coarser
level, P is the final matrix that I want to build by blocks and P^T its
transpose).

As I am using petsc4py, I will try the first option (that exists in
petsc4py) and if it is not sufficient, I will look into
https://petsc.org/main/docs/manualpages/Mat/MatCreateLocalRef/.

Thanks a lot,

Emile

On Thu, Jul 21, 2022 at 2:03 PM Matthew Knepley <knepley at gmail.com> wrote:

> On Thu, Jul 21, 2022 at 6:28 AM Emile Soutter <emile.soutter at corintis.com>
> wrote:
>
>> Dear all,
>>
>> I am struggling with the simple following problem : Having a first matrix
>> B1 of size n1xm1, a second matrix B2 of size n2 x m2, build a matrix M of
>> size (n1+n2)x(m1+m2) where the blocks B1 and B2 are the "diagonal" of M
>> (M[0:n1,0:m1]=B1, M[n1:(n1+n2),m1:(m1+m2)]=B2). In my case, the blocks B1
>> and B2 are obtained from another routine, directly in the petsc matrix form
>> (or pyop2.Sparsity form). However the blocks are not squared (n1,n2,m1,m2
>> are all different integers). The operation is easy to do with the SetValues
>> option. However, it takes a large amount of time (too much) when the system
>> becomes large. I struggle to do it efficiently and in parallel. What method
>> do you recommend to use to do this as fast as possible?
>>
>> Thanks you for any tips,
>>
>
> I think it depends on what you want to do with the final matrix. If you
> only want MatMult, then I think you can just use MatNest
>
>   https://petsc.org/main/docs/manualpages/Mat/MatCreateNest/
>
> which will wrap up the submatrices. However, if you want to manipulate the
> values (factorization, relaxation, etc) then you need
> to assemble a monolithic matrix. For this you could create the global
> matrix, and then use
>
>   https://petsc.org/main/docs/manualpages/Mat/MatCreateLocalRef/
>
> to get a submatrix to assemble directly into, which you pass to your
> assembly routine. Clearly this is more complicated, but
> sometimes necessary.
>
>   Thanks,
>
>       Matt
>
>
>> Emile
>>
>
>
> --
> 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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