[petsc-users] Optimizing MatMatSolve
Matthew Knepley
knepley at gmail.com
Mon Aug 1 16:34:30 CDT 2011
On Mon, Aug 1, 2011 at 9:31 PM, Adam Byrd <adam1.byrd at gmail.com> wrote:
> On Mon, Aug 1, 2011 at 5:09 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>>
>> On Aug 1, 2011, at 3:00 PM, Adam Byrd wrote:
>>
>> > Hello,
>> >
>> > I'm looking for help reducing the time and communication of a parallel
>> MatMatSolve using MUMPS. On a single processor I experience decent solve
>> times (~9 seconds each), but when moving to multiple processors I see longer
>> times with more cores. I've run with -log_summary and confirmed
>> (practically) all the time is spent in MatMatSolve. I'm fairly certain it's
>> all communication between nodes and I'm trying to figure out where I can
>> make optimizations, or if it is even feasible for this type of problem. It
>> is a parallel, dense,
>>
>> I hope you mean that the original matrix you use with MUMPS is sparse
>> (you should not use MUMPS to solve dense linear systems).
>>
>
> Oops, yes. The original matrix is sparse. It requires the solution and
> identity matrix to be dense. I was typing faster than thinking.
>
>>
>> > direct solve using MUMPS with an LU preconditioner. I know there are
>> many smaller optimizations that can be done in other areas, but at the
>> moment it is only the solve that concerns me.
>>
>> MUMPS will run slower on 2 processors than 1, this is just a fact of
>> life. You will only gain with parallel for MUMPS for large problems.
>>
>
> I see. It looks like I took off in the wrong direction then. I'm trying to
> solve for the inverse of a sparse matrix in parallel. I'm starting at
> 3600x3600 and will be moving to 30,000x30,000+ in the future. Which solver
> suits this sort of problem?
>
The key to parallel computing (and most other things) is choosing the right
problem.This unfortunately, is not a problem that lends itself to
parallelism.
Matt
>
>> Barry
>>
>>
>>
>> >
>> > ---------------------------------------------- PETSc Performance
>> Summary: ----------------------------------------------
>> >
>> > ./cntor on a complex-c named hpc-1-0.local with 2 processors, by abyrd
>> Mon Aug 1 16:25:51 2011
>> > Using Petsc Release Version 3.1.0, Patch 8, Thu Mar 17 13:37:48 CDT 2011
>> >
>> > Max Max/Min Avg Total
>> > Time (sec): 1.307e+02 1.00000 1.307e+02
>> > Objects: 1.180e+02 1.00000 1.180e+02
>> > Flops: 0.000e+00 0.00000 0.000e+00 0.000e+00
>> > Flops/sec: 0.000e+00 0.00000 0.000e+00 0.000e+00
>> > Memory: 2.091e+08 1.00001 4.181e+08
>> > MPI Messages: 7.229e+03 1.00000 7.229e+03 1.446e+04
>> > MPI Message Lengths: 4.141e+08 1.00000 5.729e+04 8.283e+08
>> > MPI Reductions: 1.464e+04 1.00000
>> >
>> > Flop counting convention: 1 flop = 1 real number operation of type
>> (multiply/divide/add/subtract)
>> > e.g., VecAXPY() for real vectors of length N
>> --> 2N flops
>> > and VecAXPY() for complex vectors of length
>> N --> 8N flops
>> >
>> > Summary of Stages: ----- Time ------ ----- Flops ----- --- Messages
>> --- -- Message Lengths -- -- Reductions --
>> > Avg %Total Avg %Total counts
>> %Total Avg %Total counts %Total
>> > 0: Main Stage: 1.3072e+02 100.0% 0.0000e+00 0.0% 1.446e+04
>> 100.0% 5.729e+04 100.0% 1.730e+02 1.2%
>> >
>> >
>> ------------------------------------------------------------------------------------------------------------------------
>> > See the 'Profiling' chapter of the users' manual for details on
>> interpreting output.
>> > Phase summary info:
>> > Count: number of times phase was executed
>> > Time and Flops: Max - maximum over all processors
>> > Ratio - ratio of maximum to minimum over all
>> processors
>> > Mess: number of messages sent
>> > Avg. len: average message length
>> > Reduct: number of global reductions
>> > Global: entire computation
>> > Stage: stages of a computation. Set stages with PetscLogStagePush()
>> and PetscLogStagePop().
>> > %T - percent time in this phase %F - percent flops in this
>> phase
>> > %M - percent messages in this phase %L - percent message
>> lengths in this phase
>> > %R - percent reductions in this phase
>> > Total Mflop/s: 10e-6 * (sum of flops over all processors)/(max time
>> over all processors)
>> >
>> ------------------------------------------------------------------------------------------------------------------------
>> >
>> >
>> > ##########################################################
>> > # #
>> > # WARNING!!! #
>> > # #
>> > # This code was compiled with a debugging option, #
>> > # To get timing results run config/configure.py #
>> > # using --with-debugging=no, the performance will #
>> > # be generally two or three times faster. #
>> > # #
>> > ##########################################################
>> >
>> >
>> >
>> >
>> > ##########################################################
>> > # #
>> > # WARNING!!! #
>> > # #
>> > # The code for various complex numbers numerical #
>> > # kernels uses C++, which generally is not well #
>> > # optimized. For performance that is about 4-5 times #
>> > # faster, specify --with-fortran-kernels=1 #
>> > # when running config/configure.py. #
>> > # #
>> > ##########################################################
>> >
>> >
>> > Event Count Time (sec) Flops
>> --- Global --- --- Stage --- Total
>> > Max Ratio Max Ratio Max Ratio Mess Avg len
>> Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s
>> >
>> ------------------------------------------------------------------------------------------------------------------------
>> >
>> > --- Event Stage 0: Main Stage
>> >
>> > MatSolve 14400 1.0 1.2364e+02 1.0 0.00e+00 0.0 1.4e+04 5.7e+04
>> 2.0e+01 95 0100100 0 95 0100100 12 0
>> > MatLUFactorSym 4 1.0 2.0027e-05 1.4 0.00e+00 0.0 0.0e+00 0.0e+00
>> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
>> > MatLUFactorNum 4 1.0 3.4223e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
>> 2.4e+01 3 0 0 0 0 3 0 0 0 14 0
>> > MatConvert 1 1.0 2.3644e-01 2.4 0.00e+00 0.0 0.0e+00 0.0e+00
>> 1.1e+01 0 0 0 0 0 0 0 0 0 6 0
>> > MatAssemblyBegin 14 1.0 1.9959e-01 9.3 0.00e+00 0.0 3.0e+01 5.2e+04
>> 1.2e+01 0 0 0 0 0 0 0 0 0 7 0
>> > MatAssemblyEnd 14 1.0 1.9908e-01 1.1 0.00e+00 0.0 4.0e+00 2.8e+01
>> 2.0e+01 0 0 0 0 0 0 0 0 0 12 0
>> > MatGetRow 32 1.0 4.2677e-05 1.2 0.00e+00 0.0 0.0e+00 0.0e+00
>> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
>> > MatGetSubMatrice 4 1.0 7.6661e-03 1.0 0.00e+00 0.0 1.6e+01 1.2e+05
>> 2.4e+01 0 0 0 0 0 0 0 0 0 14 0
>> > MatMatSolve 4 1.0 1.2380e+02 1.0 0.00e+00 0.0 1.4e+04 5.7e+04
>> 2.0e+01 95 0100100 0 95 0100100 12 0
>> > VecSet 4 1.0 1.8590e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
>> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
>> > VecScatterBegin 28800 1.0 2.2810e+00 2.2 0.00e+00 0.0 1.4e+04 5.7e+04
>> 0.0e+00 1 0100100 0 1 0100100 0 0
>> > VecScatterEnd 14400 1.0 4.1534e+00 2.2 0.00e+00 0.0 0.0e+00 0.0e+00
>> 0.0e+00 2 0 0 0 0 2 0 0 0 0 0
>> > KSPSetup 4 1.0 1.1060e-0212.6 0.00e+00 0.0 0.0e+00 0.0e+00
>> 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
>> > PCSetUp 4 1.0 3.4280e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
>> 5.6e+01 3 0 0 0 0 3 0 0 0 32 0
>> >
>> ------------------------------------------------------------------------------------------------------------------------
>> >
>> > Memory usage is given in bytes:
>> >
>> > Object Type Creations Destructions Memory Descendants'
>> Mem.
>> > Reports information only for process 0.
>> >
>> > --- Event Stage 0: Main Stage
>> >
>> > Matrix 27 27 208196712 0
>> > Vec 36 36 1027376 0
>> > Vec Scatter 11 11 7220 0
>> > Index Set 42 42 22644 0
>> > Krylov Solver 1 1 34432 0
>> > Preconditioner 1 1 752 0
>> >
>> ========================================================================================================================
>> > Average time to get PetscTime(): 1.90735e-07
>> > Average time for MPI_Barrier(): 3.8147e-06
>> > Average time for zero size MPI_Send(): 7.51019e-06
>> > #PETSc Option Table entries:
>> > -log_summary
>> > -pc_factor_mat_solver_package mumps
>> > -pc_type lu
>> > #End of PETSc Option Table entries
>> > Compiled without FORTRAN kernels
>> > Compiled with full precision matrices (default)
>> > sizeof(short) 2 sizeof(int) 4 sizeof(long) 8 sizeof(void*) 8
>> sizeof(PetscScalar) 16
>> > Configure run at: Mon Jul 11 15:28:42 2011
>> > Configure options: PETSC_ARCH=complex-cpp-mumps --with-cc=mpicc
>> --with-fc=mpif90 --with-blas-lapack-dir=/usr/lib64 --with-shared
>> --with-clanguage=c++ --with-scalar-type=complex --download-mumps=1
>> --download-blacs=1 --download-scalapack=1 --download-parmetis=1
>> --with-cxx=mpicxx
>> > -----------------------------------------
>> > Libraries compiled on Mon Jul 11 15:39:58 EDT 2011 on sc.local
>> > Machine characteristics: Linux sc.local 2.6.18-194.11.1.el5 #1 SMP Tue
>> Aug 10 19:05:06 EDT 2010 x86_64 x86_64 x86_64 GNU/Linux
>> > Using PETSc directory: /panfs/storage.local/scs/home/abyrd/petsc-3.1-p8
>> > Using PETSc arch: complex-cpp-mumps
>> > -----------------------------------------
>> > Using C compiler: mpicxx -Wall -Wwrite-strings -Wno-strict-aliasing -g
>> -fPIC
>> > Using Fortran compiler: mpif90 -fPIC -Wall -Wno-unused-variable -g
>> > -----------------------------------------
>> > Using include paths:
>> -I/panfs/storage.local/scs/home/abyrd/petsc-3.1-p8/complex-cpp-mumps/include
>> -I/panfs/storage.local/scs/home/abyrd/petsc-3.1-p8/include
>> -I/panfs/storage.local/scs/home/abyrd/petsc-3.1-p8/complex-cpp-mumps/include
>> -I/usr/mpi/gnu/openmpi-1.4.2/include -I/usr/mpi/gnu/openmpi-1.4.2/lib64
>> > ------------------------------------------
>> > Using C linker: mpicxx -Wall -Wwrite-strings -Wno-strict-aliasing -g
>> > Using Fortran linker: mpif90 -fPIC -Wall -Wno-unused-variable -g
>> > Using libraries:
>> -Wl,-rpath,/panfs/storage.local/scs/home/abyrd/petsc-3.1-p8/complex-cpp-mumps/lib
>> -L/panfs/storage.local/scs/home/abyrd/petsc-3.1-p8/complex-cpp-mumps/lib
>> -lpetsc -lX11
>> -Wl,-rpath,/panfs/storage.local/scs/home/abyrd/petsc-3.1-p8/complex-cpp-mumps/lib
>> -L/panfs/storage.local/scs/home/abyrd/petsc-3.1-p8/complex-cpp-mumps/lib
>> -lcmumps -ldmumps -lsmumps -lzmumps -lmumps_common -lpord -lparmetis -lmetis
>> -lscalapack -lblacs -Wl,-rpath,/usr/lib64 -L/usr/lib64 -llapack -lblas -lnsl
>> -lrt -Wl,-rpath,/usr/mpi/gnu/openmpi-1.4.2/lib64
>> -L/usr/mpi/gnu/openmpi-1.4.2/lib64
>> -Wl,-rpath,/usr/lib/gcc/x86_64-redhat-linux/4.1.2
>> -L/usr/lib/gcc/x86_64-redhat-linux/4.1.2 -ldl -lmpi -lopen-rte -lopen-pal
>> -lnsl -lutil -lgcc_s -lpthread -lmpi_f90 -lmpi_f77 -lgfortran -lm -lm -lm
>> -lm -lmpi_cxx -lstdc++ -lmpi_cxx -lstdc++ -ldl -lmpi -lopen-rte -lopen-pal
>> -lnsl -lutil -lgcc_s -lpthread -ldl
>> >
>> > Respectfully,
>> > Adam Byrd
>> > <PETScCntor.zip>
>>
>>
>
--
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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