most efficient way to use local CSR matrix?

[Barry Smith]

On Oct 20, 2009, at 10:13 PM, Chris Kees wrote:

> Thanks. Just to make sure I'm following, when I create the matrix I  
> do:
>
>      MatCreate(PETSC_COMM_WORLD,&self->m);
>      MatSetSizes(self->m,n,n,N,N);
>      MatSetType(self->m,MATMPIAIJ);
>      MatSetFromOptions(self->m);
>      MatSeqAIJSetPreallocationCSR(self->m,SMP(L)->A.rowptr,SMP(L)- 
> >A.colind,(double*)(SMP(L)->A.nzval));
>      MatMPIAIJSetPreallocationCSR(self->m,SMP(L)->A.rowptr,SMP(L)- 
> >A.colind,(double*)(SMP(L)->A.nzval));
>
> and then I copy the matrix at each Newton iteration using the code  
> in the first message below.  You said "...PreallocationCSR() does  
> the copy very efficiently", but I don't think I'm supposed to  
> repeatedly call it, right?  Looking at the output some more it does  
> seem like building the preconditioner initially is taking much more  
> time than the initial pass through MatSetValues.

    If the matrix nonzero structure stays the same then yes you need  
call MatMPIAIJSetPreallocationCSR() only once and use the  
MatSetValues() calls each Newton step to update the nonzeros.

    Barry

>
> Chris
>
> On Oct 20, 2009, at 8:32 PM, Barry Smith wrote:
>
>>
>>  Here's the deal. In parallel PETSc does not use a single CSR  
>> matrix on each process to hold the MPIAIJ matrix. Hence if you  
>> store the matrix on a process as a single CSR matrix then it has to  
>> be copied into the PETSc datastructure.  
>> MatMPIAIJSetPreallocationCSR() does the copy very efficiently. But  
>> you are right, until you free YOUR rowpt[], colind[] and a[] there  
>> are two copies of the matrix.
>> One could argue that this is ok, because anyways any preconditioner  
>> worth anything will take up at least that much memory later  
>> anyways.  For example, if you use the PETSc default preconditioner,  
>> block Jacobi with ILU(0) on each block it will take pretty much the  
>> same amount of memory.
>>
>>  For people who use SOR or some other preconditioner that requires  
>> very little memory this is not satisfactory because they feel they  
>> could run larger problems without the copy.
>>
>>  I strongly recommend you use MatMPIAIJSetPreallocationCSR() and  
>> live with any memory limitation. The reason is that doing more than  
>> that has orders of magnitude more pain with generally little payoff.
>> If you like pain then you can
>> 1) change your code to not build directly into CSR, instead call  
>> MatSetValuesLocal() as you compute the entries. With this you need  
>> to figure out the preallocation which can be painful code.
>> 2) write an entire matrix class that stores the matrix like you  
>> store it, not like you store it. This is a huge project, since you  
>> have to write your own matrix-vector, ILU factorization etc.
>>
>>  Barry
>>
>>
>>
>> On Oct 20, 2009, at 8:04 PM, Chris Kees wrote:
>>
>>> Hi,
>>>
>>> Our unstructured finite element code does a fairly standard  
>>> overlapping decomposition that allows it to calculate all the non- 
>>> zero column entries for the rows owned by the processor (rows  
>>> 0...ldim-1 in the local numbering).  We assemble them into a local  
>>> CSR matrix and then copy them into a PETSc matrix like this:
>>>
>>> for (int i=0;i<ldim;i++)
>>> {
>>> irow[0] = i;
>>> MatSetValuesLocal(PETSCMAT(par_L),1,irow,rowptr[i+1]- 
>>> rowptr[i],&colind[rowptr[i]],&a[rowptr[i]],INSERT_VALUES);
>>> }
>>>
>>> where rowptr and colind are the CSR indexing arrays in the local  
>>> numbering.
>>>
>>> I would like to eliminate the duplicate memory (and the copy  
>>> above). Is there a recommended way to let PETSc reference array  
>>> 'a' directly or a way to get rid of 'a' and translate our CSR  
>>> assembly routines to use low level PETSc data structures?
>>>
>>> So far I've added MatMPIAIJSetPreallocationCSR to try to speed up  
>>> the first solve, but the documentation is clear that 'a' is not a  
>>> pointer to the AIJ storage so I still need the copy. I tried using  
>>> MatCreateMPIAIJWithSplitArrays with the 'o' arrays set to zero but  
>>> I got indexing errors, and the documentation really seems to imply  
>>> that the local matrix is really not a standard CSR anyway. If  
>>> that's true then it seems like the options I have are to write a  
>>> shell matrix for parallel CSR storage or write some new assembly  
>>> routines that use MatSetValuesLocal. I'm more concerned about the  
>>> memory than the overhead of MatSetValuesLocal, but it would  
>>> certainly be easier on me to use the CSR-based assembly routines  
>>> we already have.
>>>
>>> Thanks,
>>> Chris
>>>
>>>
>>>
>>
>