[petsc-users] Optimizing MatMatSolve
Adam Byrd
adam1.byrd at gmail.com
Mon Aug 1 16:00:58 CDT 2011
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, 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.
---------------------------------------------- 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
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