most efficient way to use local CSR matrix?
Chris Kees
christopher.e.kees at usace.army.mil
Thu Oct 29 22:18:37 CDT 2009
On Oct 29, 2009, at 8:43 PM, Hong Zhang wrote:
>
> On Oct 29, 2009, at 5:02 PM, Chris Kees wrote:
>
>> I think I added the correct test code and got a difference of 0,
>> but spooles is still not returning the correct result, at least not
>> until the 2nd iteration. I'm attaching some of the code and output.
>
> We have not been actively updating spooles interface since
> Spooles has been out of support by its developers for 10+ years.
> For direct parallel solvers, mumps and superlu_dist have been
> constantly supported and
> outperform spooles in general.
>
> Why do you use spooles?
>
Inertia mainly. It doesn't require a fortran compiler, which comes in
handy on some systems, and it has been a reliable way to make sure
everything else in the code is working before trying to loosen the
linear solver tolerances on larger parallel runs. There were also some
problems about 10 years ago when superlu_dist was not giving reliable
results on Jacobians from degenerate nonlinear pde's. If you guys
aren't going to support the spooles wrapper, it would be nice to
provide some kind of robust C version of a sparse direct solver in
it's place for building a minimal petsc for debugging/development/
porting.
Chris
> Hong
>>
>> Chris
>>
>> code for mat creates
>> ---------------------------
>> MatCreateMPIAIJ(Py_PETSC_COMM_WORLD,n,n,N,N,
>> 1,PETSC_NULL,max_nNeighbors,PETSC_NULL,&self->m2);
>>
>> MatCreate(Py_PETSC_COMM_WORLD,&self->m);
>> MatSetSizes(self->m,n,n,N,N);
>> 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));
>>
>>
>> code for difference in mats
>> -----------------------------------
>>
>> MatAXPY
>> (PETSCMAT2(par_L),-1.0,PETSCMAT(par_L),DIFFERENT_NONZERO_PATTERN);
>> PetscReal norm=-1.0;
>> MatNorm(PETSCMAT2(par_L),NORM_INFINITY,&norm);
>> std::cout<<"inf norm of L - L2 = "<<norm<<std::endl;
>>
>> results for -pc_type lu -pc_factor_mat_solver_package spooles -
>> ksp_monitor_true_residual -mat_type mpiaij
>> -----------------------------------
>>
>> inf norm of L - L2 = 0
>> 0 KSP preconditioned resid norm 2.284405915285e+01 true resid norm
>> 1.062801511746e+01 ||Ae||/||Ax|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 3.936838941525e-01 true resid norm
>> 1.050257318153e+01 ||Ae||/||Ax|| 9.881970495395e-01
>> 2 KSP preconditioned resid norm 7.332823321496e-14 true resid norm
>> 2.408053447453e-13 ||Ae||/||Ax|| 2.265760276816e-14
>> On Oct 29, 2009, at 3:56 PM, Barry Smith wrote:
>>
>>>
>>> Hmm, this should not happen. The matrix should be identical in
>>> both cases (note the initial residual is the same in both cases so
>>> they may be identical).
>>>
>>> Here's one more thing you can try. In the same routine create TWO
>>> matrices; one each way, then use MatAXPY() to take the difference
>>> between them.
>>> Is it zero? If not, that will help lead to where the problem might
>>> be.
>>>
>>> If that does not help the situation, can you send the code the
>>> demonstrates this problem to petsc-maint at mcs.anl.gov
>>>
>>>
>>> Barry
>>>
>>> On Oct 29, 2009, at 3:34 PM, Chris Kees wrote:
>>>
>>>> I pulled the most recent version of petsc-dev and added
>>>> superlu_dist. The only case that fails is spooles on 1 processor
>>>> with an mpiaij matrix created with the Create/SetSizes/...
>>>> paradigm. I would suspect something in spooles wrapper code.
>>>>
>>>> code allocating mat:
>>>> MatCreate(Py_PETSC_COMM_WORLD,&self->m);
>>>> MatSetSizes(self->m,n,n,N,N);
>>>> MatSetType(self->m,MATMPIAIJ);
>>>>
>>>> results:
>>>> -pc_type lu -pc_factor_mat_solver_packages spooles -
>>>> ksp_monitor_true_residual (spooles on 1 proc)
>>>> 0 KSP preconditioned resid norm 2.284405915285e+01 true resid
>>>> norm 1.062801511746e+01 ||Ae||/||Ax|| 1.000000000000e+00
>>>> 1 KSP preconditioned resid norm 3.936838941525e-01 true resid
>>>> norm 1.050257318153e+01 ||Ae||/||Ax|| 9.881970495395e-01
>>>> 2 KSP preconditioned resid norm 7.332823321496e-14 true resid
>>>> norm 2.408053447453e-13 ||Ae||/||Ax|| 2.265760276816e-14
>>>>
>>>> -pc_type lu -pc_factor_mat_solver_packages spooles -
>>>> ksp_monitor_true_residual (spooleson 8 procs)
>>>> 0 KSP preconditioned resid norm 2.284405915285e+01 true resid
>>>> norm 1.062801511746e+01 ||Ae||/||Ax|| 1.000000000000e+00
>>>> 1 KSP preconditioned resid norm 2.898588418444e-14 true resid
>>>> norm 1.045214942604e-13 ||Ae||/||Ax|| 9.834526306678e-15
>>>>
>>>> -pc_type lu -pc_factor_mat_solver_packages superlu_dist -
>>>> ksp_monitor_true_residual
>>>> 0 KSP preconditioned resid norm 2.284405915285e+01 true resid
>>>> norm 1.062801511746e+01 ||Ae||/||Ax|| 1.000000000000e+00
>>>> 1 KSP preconditioned resid norm 2.917052183641e-14 true resid
>>>> norm 1.299023464819e-13 ||Ae||/||Ax|| 1.222263471084e-14
>>>>
>>>> code allocating mat:
>>>>
>>>> MatCreateMPIAIJ(Py_PETSC_COMM_WORLD,n,n,N,N,
>>>> 1,PETSC_NULL,max_nNeighbors,PETSC_NULL,&self->m);
>>>>
>>>> results:
>>>> -pc_type lu -pc_factor_mat_solver_packages spooles -
>>>> ksp_monitor_true_residual (spooles on 1 proc)
>>>> 0 KSP preconditioned resid norm 2.284405915285e+01 true resid
>>>> norm 1.062801511746e+01 ||Ae||/||Ax|| 1.000000000000e+00
>>>> 1 KSP preconditioned resid norm 3.093811333624e-14 true resid
>>>> norm 1.046870732638e-13 ||Ae||/||Ax|| 9.850105791801e-15
>>>>
>>>> On Oct 29, 2009, at 1:50 PM, Matthew Knepley wrote:
>>>>
>>>>> On Thu, Oct 29, 2009 at 1:46 PM, Chris Kees <christopher.e.kees at usace.army.mil
>>>>> > wrote:
>>>>> Mark, Barry,
>>>>>
>>>>> Thanks for the help. For now I'm sticking with the approach of
>>>>> copying the csr matrix and using the csr data structures to do
>>>>> the preallocations. I'll eventually get around to writing the
>>>>> code for assembling directly into the petsc matrix. I have two
>>>>> more questions.
>>>>>
>>>>> 1) On 1 processor, the linear solver is not converging in 1
>>>>> iteration using -pc_type lu -pc_factor_mat_solver_package
>>>>> spooles. It converges in one iteration in parallel or on a
>>>>> single processor if I set -mat_type seqaij. Also, if I go back
>>>>> to the old way of constructing the matrix it DOES converge in 1
>>>>> iteration on 1 processor. That is, if I replace the MatCreate/
>>>>> MatSetSizes/... calls from the earlier email, with what I had
>>>>> originally:
>>>>>
>>>>> MatCreateMPIAIJ(Py_PETSC_COMM_WORLD,n,n,N,N,
>>>>> 1,PETSC_NULL,max_nNeighbors,PETSC_NULL,&self->m);
>>>>>
>>>>> then the solver converges in 1 iteration as expected. This
>>>>> wouldn't be a big deal except that we're trying to verify that
>>>>> our quadratic finite elements are working, and the behavior for
>>>>> p1 and p2 elements is different. The above observations are for
>>>>> p2, while all the cases work as expected for p1. Should we just
>>>>> not be using mpiaij at all on 1 processor?
>>>>>
>>>>> No, you have a problem.
>>>>>
>>>>> 2) In the code snippet I took from the petsc example there are
>>>>> two preallocation calls (see below). Is that correct, or should
>>>>> I be checking the matrix type and calling only the preallocation
>>>>> function for the actual matrix type? i.e. something like
>>>>>
>>>>> MatCreate(...
>>>>> MatSetSizes(...
>>>>> MatSetFromOptions(...
>>>>> MatGetType(...
>>>>> if type==mpiaij: MatMPIAIJSetPreallocationCSR(...
>>>>>
>>>>> It does not hurt to call them all.
>>>>>
>>>>> Matt
>>>>>
>>>>> Chris
>>>>>
>>>>> On Oct 21, 2009, at 11:50 AM, Mark F. Adams wrote:
>>>>>
>>>>> Chris, just a note,
>>>>>
>>>>> Perhaps I missed something here but do something similar to you,
>>>>> eg overlapping partitions, and PETSc is setup very well to be
>>>>> intrusive in your code (I sometimes write a little 'addvalue'
>>>>> wrapper) and assemble your FE matrices directly into a global
>>>>> matrix. You use the (global) MatSetValues(...) and set the
>>>>> matrix option MAT_IGNORE_OFF_PROC_ENTRIES (or something like
>>>>> that) so that these off processor matrix entries, which are
>>>>> computed redundantly, are thrown away and you get the correct
>>>>> matrix.
>>>>>
>>>>> As Barry said you don't need exact non-zero counts to allocate
>>>>> storage in PETSC matrices, just don't underestimate.
>>>>>
>>>>> Mark
>>>>>
>>>>> On Oct 21, 2009, at 9:16 AM, Barry Smith wrote:
>>>>>
>>>>>
>>>>> 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
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> 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
>>>>
>>>
>>
>
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