[petsc-users] Scalability issue
Barry Smith
bsmith at mcs.anl.gov
Sat Aug 22 16:49:30 CDT 2015
> On Aug 22, 2015, at 4:17 PM, Nelson Filipe Lopes da Silva <nelsonflsilva at ist.utl.pt> wrote:
>
> Hi.
>
>
> I managed to finish the re-implementation. I ran the program with 1,2,3,4,5,6 machines and saved the summary. I send each of them in this email.
> In these executions, the program performs Matrix-Vector (MatMult, MatMultAdd) products and Vector-Vector operations. From what I understand while reading the logs, the program takes most of the time in "VecScatterEnd".
> In this example, the matrix taking part on the Matrix-Vector products is not "much diagonal heavy".
> The following numbers are the percentages of nnz values on the matrix diagonal block for each machine, and each execution time.
> NMachines %NNZ ExecTime
> 1 machine0 100%; 16min08sec
>
> 2 machine0 91.1%; 24min58sec
> machine1 69.2%;
>
> 3 machine0 90.9% 25min42sec
> machine1 82.8%
> machine2 51.6%
>
> 4 machine0 91.9% 26min27sec
> machine1 82.4%
> machine2 73.1%
> machine3 39.9%
>
> 5 machine0 93.2% 39min23sec
> machine1 82.8%
> machine2 74.4%
> machine3 64.6%
> machine4 31.6%
>
> 6 machine0 94.2% 54min54sec
> machine1 82.6%
> machine2 73.1%
> machine3 65.2%
> machine4 55.9%
> machine5 25.4%
Based on this I am guessing the last rows of the matrix have a lot of nonzeros away from the diagonal?
There is a big load imbalance in something: for example with 2 processes you have
VecMax 10509 1.0 2.0602e+02 4.2 0.00e+00 0.0 0.0e+00 0.0e+00 1.1e+04 9 0 0 0 72 9 0 0 0 72 0
VecScatterEnd 18128 1.0 8.9404e+02 1.3 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 53 0 0 0 0 53 0 0 0 0 0
MatMult 10505 1.0 6.5591e+02 1.4 3.16e+10 1.4 2.1e+04 1.2e+06 0.0e+00 37 33 58 38 0 37 33 58 38 0 83
MatMultAdd 7624 1.0 7.0028e+02 2.3 3.26e+10 2.1 1.5e+04 2.8e+06 0.0e+00 34 29 42 62 0 34 29 42 62 0 69
the 5th column has the imbalance between slowest and fastest process. It is 4.2 for max, 1.4 for multi and 2.3 for matmultadd, to get good speed ups these need to be much closer to 1.
How many nonzeros in the matrix are there per process? Is it very different for difference processes? You really need to have each process have similar number of matrix nonzeros. Do you have a picture of the nonzero structure of the matrix? Where does the matrix come from, why does it have this structure?
Also likely there are just to many vector entries that need to be scattered to the last process for the matmults.
>
> In this implementation I'm using MatCreate and VecCreate. I'm also leaving the partition sizes in PETSC_DECIDE.
>
> Finally, to run the application, I'm using mpirun.hydra from mpich, downloaded by PETSc configure script.
> I'm checking the process assignment as suggested on the last email.
>
> Am I missing anything?
Your network is very poor; likely ethernet. It is had to get much speedup with such slow reductions and sends and receives.
Average time to get PetscTime(): 1.19209e-07
Average time for MPI_Barrier(): 0.000215769
Average time for zero size MPI_Send(): 5.94854e-05
I think you are seeing such bad results due to an unkind matrix nonzero structure giving per load balance and too much communication and a very poor computer network that just makes all the needed communication totally dominate.
>
> Regards,
> Nelson
>
> Em 2015-08-20 16:17, Matthew Knepley escreveu:
>
>> On Thu, Aug 20, 2015 at 6:30 AM, Nelson Filipe Lopes da Silva <nelsonflsilva at ist.utl.pt> wrote:
>> Hello.
>>
>> I am sorry for the long time without response. I decided to rewrite my application in a different way and will send the log_summary output when done reimplementing.
>>
>> As for the machine, I am using mpirun to run jobs in a 8 node cluster. I modified the makefile on the steams folder so it would run using my hostfile.
>> The output is attached to this email. It seems reasonable for a cluster with 8 machines. From "lscpu", each machine cpu has 4 cores and 1 socket.
>> 1) You launcher is placing processes haphazardly. I would figure out how to assign them to certain nodes
>> 2) Each node has enough bandwidth for 1 core, so it does not make much sense to use more than 1.
>> Thanks,
>> Matt
>>
>> Cheers,
>> Nelson
>>
>>
>> Em 2015-07-24 16:50, Barry Smith escreveu:
>> It would be very helpful if you ran the code on say 1, 2, 4, 8, 16
>> ... processes with the option -log_summary and send (as attachments)
>> the log summary information.
>>
>> Also on the same machine run the streams benchmark; with recent
>> releases of PETSc you only need to do
>>
>> cd $PETSC_DIR
>> make streams NPMAX=16 (or whatever your largest process count is)
>>
>> and send the output.
>>
>> I suspect that you are doing everything fine and it is more an issue
>> with the configuration of your machine. Also read the information at
>> http://www.mcs.anl.gov/petsc/documentation/faq.html#computers on
>> "binding"
>>
>> Barry
>>
>> On Jul 24, 2015, at 10:41 AM, Nelson Filipe Lopes da Silva <nelsonflsilva at ist.utl.pt> wrote:
>>
>> Hello,
>>
>> I have been using PETSc for a few months now, and it truly is fantastic piece of software.
>>
>> In my particular example I am working with a large, sparse distributed (MPI AIJ) matrix we can refer as 'G'.
>> G is a horizontal - retangular matrix (for example, 1,1 Million rows per 2,1 Million columns). This matrix is commonly very sparse and not diagonal 'heavy' (for example 5,2 Million nnz in which ~50% are on the diagonal block of MPI AIJ representation).
>> To work with this matrix, I also have a few parallel vectors (created using MatCreate Vec), we can refer as 'm' and 'k'.
>> I am trying to parallelize an iterative algorithm in which the most computational heavy operations are:
>>
>> ->Matrix-Vector Multiplication, more precisely G * m + k = b (MatMultAdd). From what I have been reading, to achive a good speedup in this operation, G should be as much diagonal as possible, due to overlapping communication and computation. But even when using a G matrix in which the diagonal block has ~95% of the nnz, I cannot get a decent speedup. Most of the times, the performance even gets worse.
>>
>> ->Matrix-Matrix Multiplication, in this case I need to perform G * G' = A, where A is later used on the linear solver and G' is transpose of G. The speedup in this operation is not worse, although is not very good.
>>
>> ->Linear problem solving. Lastly, In this operation I compute "Ax=b" from the last two operations. I tried to apply a RCM permutation to A to make it more diagonal, for better performance. However, the problem I faced was that, the permutation is performed locally in each processor and thus, the final result is different with different number of processors. I assume this was intended to reduce communication. The solution I found was
>> 1-calculate A
>> 2-calculate, localy to 1 machine, the RCM permutation IS using A
>> 3-apply this permutation to the lines of G.
>> This works well, and A is generated as if RCM permuted. It is fine to do this operation in one machine because it is only done once while reading the input. The nnz of G become more spread and less diagonal, causing problems when calculating G * m + k = b.
>>
>> These 3 operations (except the permutation) are performed in each iteration of my algorithm.
>>
>> So, my questions are.
>> -What are the characteristics of G that lead to a good speedup in the operations I described? Am I missing something and too much obsessed with the diagonal block?
>>
>> -Is there a better way to permute A without permute G and still get the same result using 1 or N machines?
>>
>>
>> I have been avoiding asking for help for a while. I'm very sorry for the long email.
>> Thank you very much for your time.
>> Best Regards,
>> Nelson
>>
>>
>> --
>> 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
>
> <Log01P.txt><Log02P.txt><Log03P.txt><Log04P.txt><Log05P.txt><Log06P.txt>
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