<div class="gmail_quote">On Mon, Aug 1, 2011 at 5:09 PM, Barry Smith <span dir="ltr"><<a href="mailto:bsmith@mcs.anl.gov">bsmith@mcs.anl.gov</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div class="im"><br>
On Aug 1, 2011, at 3:00 PM, Adam Byrd wrote:<br>
<br>
> Hello,<br>
><br>
> 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,<br>
<br>
</div> I hope you mean that the original matrix you use with MUMPS is sparse (you should not use MUMPS to solve dense linear systems).<br></blockquote><div><br>Oops, yes. The original matrix is sparse. It requires the solution and identity matrix to be dense. I was typing faster than thinking. <br>
</div><blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
<div class="im"><br>
> 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.<br>
<br>
</div> 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.<br></blockquote><div><br>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?<br>
</div><blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
<br>
Barry<br>
<div><div></div><div class="h5"><br>
<br>
<br>
><br>
> ---------------------------------------------- PETSc Performance Summary: ----------------------------------------------<br>
><br>
> ./cntor on a complex-c named hpc-1-0.local with 2 processors, by abyrd Mon Aug 1 16:25:51 2011<br>
> Using Petsc Release Version 3.1.0, Patch 8, Thu Mar 17 13:37:48 CDT 2011<br>
><br>
> Max Max/Min Avg Total<br>
> Time (sec): 1.307e+02 1.00000 1.307e+02<br>
> Objects: 1.180e+02 1.00000 1.180e+02<br>
> Flops: 0.000e+00 0.00000 0.000e+00 0.000e+00<br>
> Flops/sec: 0.000e+00 0.00000 0.000e+00 0.000e+00<br>
> Memory: 2.091e+08 1.00001 4.181e+08<br>
> MPI Messages: 7.229e+03 1.00000 7.229e+03 1.446e+04<br>
> MPI Message Lengths: 4.141e+08 1.00000 5.729e+04 8.283e+08<br>
> MPI Reductions: 1.464e+04 1.00000<br>
><br>
> Flop counting convention: 1 flop = 1 real number operation of type (multiply/divide/add/subtract)<br>
> e.g., VecAXPY() for real vectors of length N --> 2N flops<br>
> and VecAXPY() for complex vectors of length N --> 8N flops<br>
><br>
> Summary of Stages: ----- Time ------ ----- Flops ----- --- Messages --- -- Message Lengths -- -- Reductions --<br>
> Avg %Total Avg %Total counts %Total Avg %Total counts %Total<br>
> 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%<br>
><br>
> ------------------------------------------------------------------------------------------------------------------------<br>
> See the 'Profiling' chapter of the users' manual for details on interpreting output.<br>
> Phase summary info:<br>
> Count: number of times phase was executed<br>
> Time and Flops: Max - maximum over all processors<br>
> Ratio - ratio of maximum to minimum over all processors<br>
> Mess: number of messages sent<br>
> Avg. len: average message length<br>
> Reduct: number of global reductions<br>
> Global: entire computation<br>
> Stage: stages of a computation. Set stages with PetscLogStagePush() and PetscLogStagePop().<br>
> %T - percent time in this phase %F - percent flops in this phase<br>
> %M - percent messages in this phase %L - percent message lengths in this phase<br>
> %R - percent reductions in this phase<br>
> Total Mflop/s: 10e-6 * (sum of flops over all processors)/(max time over all processors)<br>
> ------------------------------------------------------------------------------------------------------------------------<br>
><br>
><br>
> ##########################################################<br>
> # #<br>
> # WARNING!!! #<br>
> # #<br>
> # This code was compiled with a debugging option, #<br>
> # To get timing results run config/configure.py #<br>
> # using --with-debugging=no, the performance will #<br>
> # be generally two or three times faster. #<br>
> # #<br>
> ##########################################################<br>
><br>
><br>
><br>
><br>
> ##########################################################<br>
> # #<br>
> # WARNING!!! #<br>
> # #<br>
> # The code for various complex numbers numerical #<br>
> # kernels uses C++, which generally is not well #<br>
> # optimized. For performance that is about 4-5 times #<br>
> # faster, specify --with-fortran-kernels=1 #<br>
> # when running config/configure.py. #<br>
> # #<br>
> ##########################################################<br>
><br>
><br>
> Event Count Time (sec) Flops --- Global --- --- Stage --- Total<br>
> Max Ratio Max Ratio Max Ratio Mess Avg len Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s<br>
> ------------------------------------------------------------------------------------------------------------------------<br>
><br>
> --- Event Stage 0: Main Stage<br>
><br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> 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<br>
> ------------------------------------------------------------------------------------------------------------------------<br>
><br>
> Memory usage is given in bytes:<br>
><br>
> Object Type Creations Destructions Memory Descendants' Mem.<br>
> Reports information only for process 0.<br>
><br>
> --- Event Stage 0: Main Stage<br>
><br>
> Matrix 27 27 208196712 0<br>
> Vec 36 36 1027376 0<br>
> Vec Scatter 11 11 7220 0<br>
> Index Set 42 42 22644 0<br>
> Krylov Solver 1 1 34432 0<br>
> Preconditioner 1 1 752 0<br>
> ========================================================================================================================<br>
> Average time to get PetscTime(): 1.90735e-07<br>
> Average time for MPI_Barrier(): 3.8147e-06<br>
> Average time for zero size MPI_Send(): 7.51019e-06<br>
> #PETSc Option Table entries:<br>
> -log_summary<br>
> -pc_factor_mat_solver_package mumps<br>
> -pc_type lu<br>
> #End of PETSc Option Table entries<br>
> Compiled without FORTRAN kernels<br>
> Compiled with full precision matrices (default)<br>
> sizeof(short) 2 sizeof(int) 4 sizeof(long) 8 sizeof(void*) 8 sizeof(PetscScalar) 16<br>
> Configure run at: Mon Jul 11 15:28:42 2011<br>
> 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<br>
> -----------------------------------------<br>
> Libraries compiled on Mon Jul 11 15:39:58 EDT 2011 on sc.local<br>
> 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<br>
> Using PETSc directory: /panfs/storage.local/scs/home/abyrd/petsc-3.1-p8<br>
> Using PETSc arch: complex-cpp-mumps<br>
> -----------------------------------------<br>
> Using C compiler: mpicxx -Wall -Wwrite-strings -Wno-strict-aliasing -g -fPIC<br>
> Using Fortran compiler: mpif90 -fPIC -Wall -Wno-unused-variable -g<br>
> -----------------------------------------<br>
> 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<br>
> ------------------------------------------<br>
> Using C linker: mpicxx -Wall -Wwrite-strings -Wno-strict-aliasing -g<br>
> Using Fortran linker: mpif90 -fPIC -Wall -Wno-unused-variable -g<br>
> 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<br>
><br>
> Respectfully,<br>
> Adam Byrd<br>
</div></div>> <PETScCntor.zip><br>
<br>
</blockquote></div><br>