Am Dienstag, 4. November 2014, 10:08:27 schrieb Barry Smith: > > There are a lot of questions here.
Yes, thanks for replying! > > On Nov 4, 2014, at 328 AM, Florian Lindner <mailingli...@xgm.de> wrote: > > > > Hello, > > > > I have a fulll matrix of size e.g. 603x603 of which I'm very disappointed > > with the runtime, compared to a naive LU / forward / backward solution. My > > petsc solution takes about 14s, while the old one takes just 0.5s. (when > > you're looking at sparse matrices the figures are almost inversed). I try > > to investigate what's the problem. > > For small problems like this direct dense LU could easily be faster than > iterative schemes. Especially if you have many right hand sides with the same > matrix since the factorization only needs to be done one. > > > > > Most of the time is spent in the KSPSolve. > > > > 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 > > > > MatMult 10334 1.0 6.3801e+00 1.0 7.51e+09 1.0 0.0e+00 0.0e+00 > > 0.0e+00 45 49 0 0 0 45 49 0 0 0 1177 > > MatSolve 10334 1.0 6.9187e+00 1.0 7.51e+09 1.0 0.0e+00 0.0e+00 > > 0.0e+00 49 49 0 0 0 49 49 0 0 0 1085 > > If this is for a single solver for a 603 by 603 matrix then this is > absurd. 10000 plus iterations But that's the output I got. When I run with -info I get a lot of messages: [0] PCSetUp(): Leaving PC with identical preconditioner since operator is unchanged though doing just on KSPSolve / KSPSetOperators. Is that ok? > > MatCholFctrNum 1 1.0 1.8968e-01 1.0 6.03e+02 1.0 0.0e+00 0.0e+00 > > 0.0e+00 1 0 0 0 0 1 0 0 0 0 0 > > KSPGMRESOrthog 10000 1.0 2.1417e-01 1.0 3.73e+08 1.0 0.0e+00 0.0e+00 > > 0.0e+00 2 2 0 0 0 2 2 0 0 0 1744 > > KSPSolve 1 1.0 1.3763e+01 1.0 1.54e+10 1.0 0.0e+00 0.0e+00 > > 0.0e+00 97100 0 0 0 97100 0 0 0 1120 > > Prealloc Matrix C 1 1.0 5.7458e-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 > > Filling Matrix C 1 1.0 6.7984e-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 > > VecMDot 10000 1.0 8.8615e-02 1.0 1.87e+08 1.0 0.0e+00 0.0e+00 > > 0.0e+00 1 1 0 0 0 1 1 0 0 0 2106 > > VecMAXPY 10334 1.0 1.2585e-01 1.0 1.99e+08 1.0 0.0e+00 0.0e+00 > > 0.0e+00 1 1 0 0 0 1 1 0 0 0 1580 > > Prealloc Matrix A 1 1.0 1.1071e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 > > 0.0e+00 1 0 0 0 0 1 0 0 0 0 0 > > Filling Matrix A 1 1.0 1.2574e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 > > 0.0e+00 1 0 0 0 0 1 0 0 0 0 0 > > PCSetUp 1 1.0 1.9073e-01 1.0 6.03e+02 1.0 0.0e+00 0.0e+00 > > 0.0e+00 1 0 0 0 0 1 0 0 0 0 0 > > PCApply 10334 1.0 6.9233e+00 1.0 7.51e+09 1.0 0.0e+00 0.0e+00 > > 0.0e+00 49 49 0 0 0 49 49 0 0 0 1085 > > ------------------------------------------------------------------------------------------------------------------------ > > > > Removed all events with global %T == 0, but my own ones. > > > > Matrix type is sequential MATSBAIJ on PETSC_COMM_SELF. > > > > KSP is initalized once: > > > > KSPSetOperators(_solver, _matrixC.matrix, _matrixC.matrix); > > KSPSetTolerances(_solver, _solverRtol, PETSC_DEFAULT, PETSC_DEFAULT, > > PETSC_DEFAULT); > > KSPSetFromOptions(_solver); > > > > KSPSolve: > > > > ierr = KSPSolve(_solver, in.vector, p.vector); CHKERRV(ierr) > > > > KSPSolve may be executed multiple times with the same SetOperators acording > > to dimensionality of the data. Here it's just one. > > > > -ksp_view says: > > > > KSP Object: 1 MPI processes > > type: gmres > > GMRES: restart=30, using Classical (unmodified) Gram-Schmidt > > Orthogonalization with no iterative refinement > > GMRES: happy breakdown tolerance 1e-30 > > maximum iterations=10000, initial guess is zero > > tolerances: relative=1e-09, absolute=1e-50, divergence=10000 > > left preconditioning > > using PRECONDITIONED norm type for convergence test > > PC Object: 1 MPI processes > > type: icc > > 0 levels of fill > > tolerance for zero pivot 2.22045e-14 > > using Manteuffel shift [POSITIVE_DEFINITE] > > matrix ordering: natural > > factor fill ratio given 1, needed 1 > > Factored matrix follows: > > Mat Object: 1 MPI processes > > type: seqsbaij > > rows=603, cols=603 > > package used to perform factorization: petsc > > total: nonzeros=182103, allocated nonzeros=182103 > > total number of mallocs used during MatSetValues calls =0 > > block size is 1 > > linear system matrix = precond matrix: > > Mat Object: C 1 MPI processes > > type: seqsbaij > > rows=603, cols=603 > > total: nonzeros=182103, allocated nonzeros=182103 > > total number of mallocs used during MatSetValues calls =0 > > block size is 1 > > > > > > I've tried to use a direct solver like suggested on pp 72, but: > > > > ./petBench 600 1 -ksp_type preonly -pc_type lu > > You cannot use LU with SBAIJ format. Only Cholesky. So use -pc_type cholesky I tried that too, it gives me an error message: % ./petBench 100 1 -pc_type cholesky Mesh of size: 100 Do mappings: 1 KSP Init Do KSPSolve consistent [0]PETSC ERROR: --------------------- Error Message -------------------------------------------------------------- [0]PETSC ERROR: Zero pivot in LU factorization: http://www.mcs.anl.gov/petsc/documentation/faq.html#ZeroPivot [0]PETSC ERROR: Zero pivot row 0 value 0 tolerance 2.22045e-14 [0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html for trouble shooting. [0]PETSC ERROR: Petsc Release Version 3.5.2, unknown [0]PETSC ERROR: ./petBench on a arch-linux2-c-debug named helium by lindnefn Wed Nov 5 10:22:07 2014 [0]PETSC ERROR: Configure options --with-debugging=1 [0]PETSC ERROR: #1 MatPivotCheck_none() line 622 in /data2/scratch/lindner/petsc/include/petsc-private/matimpl.h [0]PETSC ERROR: #2 MatPivotCheck() line 641 in /data2/scratch/lindner/petsc/include/petsc-private/matimpl.h [0]PETSC ERROR: #3 MatCholeskyFactorNumeric_SeqSBAIJ_1_NaturalOrdering() line 1435 in /data2/scratch/lindner/petsc/src/mat/impls/sbaij/seq/sbaijfact.c [0]PETSC ERROR: #4 MatCholeskyFactorNumeric() line 3063 in /data2/scratch/lindner/petsc/src/mat/interface/matrix.c [0]PETSC ERROR: #5 PCSetUp_Cholesky() line 150 in /data2/scratch/lindner/petsc/src/ksp/pc/impls/factor/cholesky/cholesky.c [0]PETSC ERROR: #6 PCSetUp() line 902 in /data2/scratch/lindner/petsc/src/ksp/pc/interface/precon.c [0]PETSC ERROR: #7 KSPSetUp() line 305 in /data2/scratch/lindner/petsc/src/ksp/ksp/interface/itfunc.c [0]PETSC ERROR: #8 KSPSolve() line 417 in /data2/scratch/lindner/petsc/src/ksp/ksp/interface/itfunc.c [0]PETSC ERROR: #9 map() line 401 in /data2/scratch/lindner/precice/src/mapping/PetRadialBasisFctMapping.hpp FAQ says I likely have an error in my matrix generation when it occurs in the zeroth row. But for RBF the main diagonal is always BasisFunction( | x_n - x_n | ). Since I test with ThinPlateSplines as basis function here it's TPS(0) == 0. > > Mesh of size: 600 > > Do mappings: 1 > > [0]PETSC ERROR: --------------------- Error Message > > -------------------------------------------------------------- > > [0]PETSC ERROR: No support for this operation for this object type > > [0]PETSC ERROR: Factor type not supported > > [0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html for > > trouble shooting. > > [0]PETSC ERROR: Petsc Release Version 3.5.2, unknown > > [0]PETSC ERROR: ./petBench on a arch-linux2-c-opt named helium by lindnefn > > Tue Nov 4 10:19:28 2014 > > [0]PETSC ERROR: Configure options --with-debugging=0 > > [0]PETSC ERROR: #1 MatGetFactor_seqsbaij_petsc() line 1833 in > > /data2/scratch/lindner/petsc/src/mat/impls/sbaij/seq/sbaij.c > > [0]PETSC ERROR: #2 MatGetFactor() line 3963 in > > /data2/scratch/lindner/petsc/src/mat/interface/matrix.c > > [0]PETSC ERROR: #3 PCSetUp_LU() line 125 in > > /data2/scratch/lindner/petsc/src/ksp/pc/impls/factor/lu/lu.c > > [0]PETSC ERROR: #4 PCSetUp() line 902 in > > /data2/scratch/lindner/petsc/src/ksp/pc/interface/precon.c > > [0]PETSC ERROR: #5 KSPSetUp() line 305 in > > /data2/scratch/lindner/petsc/src/ksp/ksp/interface/itfunc.c > > [0]PETSC ERROR: #6 KSPSolve() line 417 in > > /data2/scratch/lindner/petsc/src/ksp/ksp/interface/itfunc.c > > [0]PETSC ERROR: #7 map() line 391 in > > /data2/scratch/lindner/precice/src/mapping/PetRadialBasisFctMapping.hpp Thanks, Florian
