[petsc-users] Using edge-weights for partitioning

[Barry Smith]

> On Aug 29, 2020, at 2:23 PM, Eda Oktay <eda.oktay at metu.edu.tr> wrote:
> 
> Hi all,
> 
> I am trying to partition a sparse matrix by using ParMETIS. I am converting my matrix to adjacency type and then applying partitioning.

 You don't need to do this. Just pass your original matrix directly into MatPartitioningSetAdjacency() it will handle any conversions needed.

 Edge weights need to be positive, since they represent how much communication is to take place over that link. You may need to force your matrix to have all positive values before giving it to MatPartitioningSetAdjacency and using edge weights. 

  I this doesn't work than our code is broken, please send us a simple test case

  Question: Why are you partitioning a matrix? Is it for load balancing of solves or matrix vector products with the matrix? To reduce interprocess communication during solves or matrix vector products with the matrix? If so the numerical values in the matrix don't affect load balance or interprocess communication for these operations. 


  Barry




> Default, I understood that partitioning doesn't use edge-weights. However, when I used the following codes I saw from ex15 and used "-test_use_edge_weights 1", I am getting the same results as when I don't consider edge weights.
> 
> PetscBool use_edge_weights=PETSC_FALSE;
>   PetscOptionsGetBool(NULL,NULL,"-test_use_edge_weights",&use_edge_weights,NULL);
>   if (use_edge_weights) {
>       MatPartitioningSetUseEdgeWeights(part,use_edge_weights);
> 
>       MatPartitioningGetUseEdgeWeights(part,&use_edge_weights);
>       if (!use_edge_weights) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP, "use_edge_weights flag does not setup correctly \n");
>     }
> 
> My matrix does not consist of 1s and 0s, so I want partitioning to consider all the nonzero elements in the matrix as edge weights. Don't MatPartitioningSetUseEdgeWeights and MatPartitioningGetUseEdgeWeights do that? Should I add something more? In the page of MatPartitioningSetUseEdgeWeights, it is written that "If set use_edge_weights to TRUE, users need to make sure legal edge weights are stored in an ADJ matrix.". How can I make sure of this? 
> 
> I am trying to compare the use of ParMETIS with the spectral partitioning algorithm when I used a weighted Laplacian.
> 
> Thanks!
> 
> Eda
>