[petsc-users] Optimizing MatMatSolve
Barry Smith
bsmith at mcs.anl.gov
Mon Aug 1 16:09:24 CDT 2011
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).
> 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.
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>
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