[petsc-users] What is the right way to implement a (block) Diagonal ILU as PC?
Hao DONG
dong-hao at outlook.com
Thu Feb 6 03:43:05 CST 2020
Dear Hong and Barry,
Thanks for the suggestions. So there could be some problems in my PETSc configuration? - but my PETSc lib was indeed compiled without the debug flags (--with-debugging=0). I use GCC/GFortran (Home-brew GCC 9.2.0) for the compiling and building of PETSc and my own fortran code. My Fortran compiling flags are simply like:
-O3 -ffree-line-length-none -fastsse
Which is also used for -FOPTFLAGS in PETSc (I added -openmp for PETSc, but not my fortran code, as I don’t have any OMP optimizations in my program). Note the performance test results I listed yesterday (e.g. 4.08s with 41 bcgs iterations.) are without any CSR-array->PETSc translation overhead (only include the set and solve part).
I have two questions about the performance difference -
1. Is ilu only factorized once for each iteration, or ilu is performed at every outer ksp iteration steps? Sounds unlikely - but if so, this could cause some extra overheads.
2. Some KSP solvers like BCGS or TFQMR has two “half-iterations” for each iteration step. Not sure how it works in PETSc, but is that possible that both the two “half" relative residuals are counted in the output array, doubling the number of iterations (but that cannot explain the extra time consumed)?
Anyway, the output with -log_view from the same 278906 by 278906 matrix with 3-block D-ILU in PETSc is as follows:
---------------------------------------------- PETSc Performance Summary: ----------------------------------------------
MEMsolv.lu on a arch-darwin-c-opt named Haos-MBP with 1 processor, by donghao Thu Feb 6 09:07:35 2020
Using Petsc Release Version 3.12.3, unknown
Max Max/Min Avg Total
Time (sec): 4.443e+00 1.000 4.443e+00
Objects: 1.155e+03 1.000 1.155e+03
Flop: 4.311e+09 1.000 4.311e+09 4.311e+09
Flop/sec: 9.703e+08 1.000 9.703e+08 9.703e+08
MPI Messages: 0.000e+00 0.000 0.000e+00 0.000e+00
MPI Message Lengths: 0.000e+00 0.000 0.000e+00 0.000e+00
MPI Reductions: 0.000e+00 0.000
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 flop
and VecAXPY() for complex vectors of length N --> 8N flop
Summary of Stages: ----- Time ------ ----- Flop ------ --- Messages --- -- Message Lengths -- -- Reductions --
Avg %Total Avg %Total Count %Total Avg %Total Count %Total
0: Main Stage: 4.4435e+00 100.0% 4.3113e+09 100.0% 0.000e+00 0.0% 0.000e+00 0.0% 0.000e+00 0.0%
————————————————————————————————————————————————————————————
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 Flop: Max - maximum over all processors
Ratio - ratio of maximum to minimum over all processors
Mess: number of messages sent
AvgLen: average message length (bytes)
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 flop 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 flop over all processors)/(max time over all processors)
------------------------------------------------------------------------------------------------------------------------
Event Count Time (sec) Flop --- Global --- --- Stage ---- Total
Max Ratio Max Ratio Max Ratio Mess AvgLen Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s
------------------------------------------------------------------------------------------------------------------------
--- Event Stage 0: Main Stage
BuildTwoSidedF 1 1.0 2.3000e-05 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
MatMult 83 1.0 1.7815e+00 1.0 2.08e+09 1.0 0.0e+00 0.0e+00 0.0e+00 40 48 0 0 0 40 48 0 0 0 1168
MatSolve 252 1.0 1.2708e+00 1.0 1.19e+09 1.0 0.0e+00 0.0e+00 0.0e+00 29 28 0 0 0 29 28 0 0 0 939
MatLUFactorNum 3 1.0 7.9725e-02 1.0 2.37e+07 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 298
MatILUFactorSym 3 1.0 2.6998e-02 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
MatAssemblyBegin 5 1.0 3.6000e-05 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
MatAssemblyEnd 5 1.0 3.1619e-02 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
MatGetRowIJ 3 1.0 2.0000e-06 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
MatCreateSubMats 1 1.0 3.9659e-02 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
MatGetOrdering 3 1.0 4.3070e-03 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
MatView 3 1.0 1.3600e-04 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
VecDot 82 1.0 1.8948e-01 1.0 1.83e+08 1.0 0.0e+00 0.0e+00 0.0e+00 4 4 0 0 0 4 4 0 0 0 966
VecDotNorm2 41 1.0 1.6812e-01 1.0 1.83e+08 1.0 0.0e+00 0.0e+00 0.0e+00 4 4 0 0 0 4 4 0 0 0 1088
VecNorm 43 1.0 9.5099e-02 1.0 9.59e+07 1.0 0.0e+00 0.0e+00 0.0e+00 2 2 0 0 0 2 2 0 0 0 1009
VecCopy 2 1.0 1.0120e-03 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
VecSet 271 1.0 3.8922e-02 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
VecAXPY 1 1.0 7.7200e-04 1.0 2.23e+06 1.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 2890
VecAXPBYCZ 82 1.0 2.4370e-01 1.0 3.66e+08 1.0 0.0e+00 0.0e+00 0.0e+00 5 8 0 0 0 5 8 0 0 0 1502
VecWAXPY 82 1.0 1.4148e-01 1.0 1.83e+08 1.0 0.0e+00 0.0e+00 0.0e+00 3 4 0 0 0 3 4 0 0 0 1293
VecAssemblyBegin 2 1.0 0.0000e+00 0.0 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
VecAssemblyEnd 2 1.0 0.0000e+00 0.0 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 84 1.0 5.9300e-04 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
KSPSetUp 4 1.0 1.4167e-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
KSPSolve 1 1.0 4.0250e+00 1.0 4.31e+09 1.0 0.0e+00 0.0e+00 0.0e+00 91100 0 0 0 91100 0 0 0 1071
PCSetUp 4 1.0 1.5207e-01 1.0 2.37e+07 1.0 0.0e+00 0.0e+00 0.0e+00 3 1 0 0 0 3 1 0 0 0 156
PCSetUpOnBlocks 1 1.0 1.1116e-01 1.0 2.37e+07 1.0 0.0e+00 0.0e+00 0.0e+00 3 1 0 0 0 3 1 0 0 0 214
PCApply 84 1.0 1.2912e+00 1.0 1.19e+09 1.0 0.0e+00 0.0e+00 0.0e+00 29 28 0 0 0 29 28 0 0 0 924
PCApplyOnBlocks 252 1.0 1.2909e+00 1.0 1.19e+09 1.0 0.0e+00 0.0e+00 0.0e+00 29 28 0 0 0 29 28 0 0 0 924
------------------------------------------------------------------------------------------------------------------------
# I skipped the memory part - the options (and compiler options) are as follows:
#PETSc Option Table entries:
-ksp_type bcgs
-ksp_view
-log_view
-pc_bjacobi_local_blocks 3
-pc_factor_levels 0
-pc_sub_type ilu
-pc_type bjacobi
#End of PETSc Option Table entries
Compiled with FORTRAN kernels
Compiled with full precision matrices (default)
sizeof(short) 2 sizeof(int) 4 sizeof(long) 8 sizeof(void*) 8 sizeof(PetscScalar) 16 sizeof(PetscInt) 4
Configure options: --with-scalar-type=complex --download-mumps --download-scalapack --with-fortran-kernels=1 -- FOPTFLAGS=“-O3 -fastsse -mp -openmp” --COPTFLAGS=“-O3 -fastsse -mp -openmp” --CXXOPTFLAGS="-O3 -fastsse -mp -openmp" -- with-debugging=0
-----------------------------------------
Libraries compiled on 2020-02-03 10:44:31 on Haos-MBP
Machine characteristics: Darwin-19.2.0-x86_64-i386-64bit
Using PETSc directory: /Users/donghao/src/git/PETSc-current
Using PETSc arch: arch-darwin-c-opt
-----------------------------------------
Using C compiler: mpicc -Wall -Wwrite-strings -Wno-strict-aliasing -Wno-unknown-pragmas -fstack-protector -fno-stack- check -Qunused-arguments -fvisibility=hidden
Using Fortran compiler: mpif90 -Wall -ffree-line-length-0 -Wno-unused-dummy-argument
Using include paths: -I/Users/donghao/src/git/PETSc-current/include -I/Users/donghao/src/git/PETSc-current/arch-darwin-c-opt/include
-----------------------------------------
Using C linker: mpicc
Using Fortran linker: mpif90
Using libraries: -Wl,-rpath,/Users/donghao/src/git/PETSc-current/arch-darwin-c-opt/lib -L/Users/donghao/src/git/PETSc- current/arch-darwin-c-opt/lib -lpetsc -Wl,-rpath,/Users/donghao/src/git/PETSc-current/arch-darwin-c-opt/lib -L/Users/ donghao/src/git/PETSc-current/arch-darwin-c-opt/lib -Wl,-rpath,/usr/local/opt/libevent/lib -L/usr/local/opt/libevent/ lib -Wl,-rpath,/usr/local/Cellar/open-mpi/4.0.2/lib -L/usr/local/Cellar/open-mpi/4.0.2/lib -Wl,-rpath,/usr/local/Cellar/ gcc/9.2.0_3/lib/gcc/9/gcc/x86_64-apple-darwin19/9.2.0 -L/usr/local/Cellar/gcc/9.2.0_3/lib/gcc/9/gcc/x86_64-apple- darwin19/9.2.0 -Wl,-rpath,/usr/local/Cellar/gcc/9.2.0_3/lib/gcc/9 -L/usr/local/Cellar/gcc/9.2.0_3/lib/gcc/9 -lcmumps - ldmumps -lsmumps -lzmumps -lmumps_common -lpord -lscalapack -llapack -lblas -lc++ -ldl -lmpi_usempif08 - lmpi_usempi_ignore_tkr -lmpi_mpifh -lmpi -lgfortran -lquadmath -lm -lc++ -ldl
On the other hand, running PETSc with
-pc_type bjacobi -pc_bjacobi_local_blocks 3 -pc_sub_type lu -ksp_type gmres -ksp_monitor -ksp_view -log_view
For the same problem takes 5.37s and 72 GMRES iterations. Our previous testings show that BiCGstab (bcgs in PETSc) is almost always the most effective KSP solver for our non-symmetrical complex system. Strangely, the system is still using ilu instead of lu for sub blocks. The output is like:
0 KSP Residual norm 2.480412407430e+02
1 KSP Residual norm 8.848059967835e+01
2 KSP Residual norm 3.415272863261e+01
3 KSP Residual norm 1.563045190939e+01
4 KSP Residual norm 6.241296940043e+00
5 KSP Residual norm 2.739710899854e+00
6 KSP Residual norm 1.391304148888e+00
7 KSP Residual norm 7.959262020849e-01
8 KSP Residual norm 4.828323055231e-01
9 KSP Residual norm 2.918529739200e-01
10 KSP Residual norm 1.905508589557e-01
11 KSP Residual norm 1.291541892702e-01
12 KSP Residual norm 8.827145774707e-02
13 KSP Residual norm 6.521331095889e-02
14 KSP Residual norm 5.095787952595e-02
15 KSP Residual norm 4.043060387395e-02
16 KSP Residual norm 3.232590200012e-02
17 KSP Residual norm 2.593944982216e-02
18 KSP Residual norm 2.064639483533e-02
19 KSP Residual norm 1.653916663492e-02
20 KSP Residual norm 1.334946415452e-02
21 KSP Residual norm 1.092886880597e-02
22 KSP Residual norm 8.988004105542e-03
23 KSP Residual norm 7.466501315240e-03
24 KSP Residual norm 6.284389135436e-03
25 KSP Residual norm 5.425231669964e-03
26 KSP Residual norm 4.766338253084e-03
27 KSP Residual norm 4.241238878242e-03
28 KSP Residual norm 3.808113525685e-03
29 KSP Residual norm 3.449383788116e-03
30 KSP Residual norm 3.126025526388e-03
31 KSP Residual norm 2.958328054299e-03
32 KSP Residual norm 2.802344900403e-03
33 KSP Residual norm 2.621993580492e-03
34 KSP Residual norm 2.430066269304e-03
35 KSP Residual norm 2.259043079597e-03
36 KSP Residual norm 2.104287972986e-03
37 KSP Residual norm 1.952916080045e-03
38 KSP Residual norm 1.804988937999e-03
39 KSP Residual norm 1.643302117377e-03
40 KSP Residual norm 1.471661332036e-03
41 KSP Residual norm 1.286445911163e-03
42 KSP Residual norm 1.127543025848e-03
43 KSP Residual norm 9.777148275484e-04
44 KSP Residual norm 8.293314450006e-04
45 KSP Residual norm 6.989331136622e-04
46 KSP Residual norm 5.852307780220e-04
47 KSP Residual norm 4.926715539762e-04
48 KSP Residual norm 4.215941372075e-04
49 KSP Residual norm 3.699489548162e-04
50 KSP Residual norm 3.293897163533e-04
51 KSP Residual norm 2.959954542998e-04
52 KSP Residual norm 2.700193032414e-04
53 KSP Residual norm 2.461789791204e-04
54 KSP Residual norm 2.218839085563e-04
55 KSP Residual norm 1.945154309976e-04
56 KSP Residual norm 1.661128781744e-04
57 KSP Residual norm 1.413198766258e-04
58 KSP Residual norm 1.213984003195e-04
59 KSP Residual norm 1.044317450754e-04
60 KSP Residual norm 8.919957502977e-05
61 KSP Residual norm 8.042584301275e-05
62 KSP Residual norm 7.292784493581e-05
63 KSP Residual norm 6.481935501872e-05
64 KSP Residual norm 5.718564652679e-05
65 KSP Residual norm 5.072589750116e-05
66 KSP Residual norm 4.487930741285e-05
67 KSP Residual norm 3.941040674119e-05
68 KSP Residual norm 3.492873281291e-05
69 KSP Residual norm 3.103798339845e-05
70 KSP Residual norm 2.822943237409e-05
71 KSP Residual norm 2.610615023776e-05
72 KSP Residual norm 2.441692671173e-05
KSP Object: 1 MPI processes
type: gmres
restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
happy breakdown tolerance 1e-30
maximum iterations=150, nonzero initial guess
tolerances: relative=1e-07, absolute=1e-50, divergence=10000.
left preconditioning
using PRECONDITIONED norm type for convergence test
PC Object: 1 MPI processes
type: bjacobi
number of blocks = 3
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object: (sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (sub_) 1 MPI processes
type: ilu
out-of-place factorization
0 levels of fill
tolerance for zero pivot 2.22045e-14
matrix ordering: natural
factor fill ratio given 1., needed 1.
Factored matrix follows:
Mat Object: 1 MPI processes
type: seqaij
rows=92969, cols=92969
package used to perform factorization: petsc
total: nonzeros=638417, allocated nonzeros=638417
total number of mallocs used during MatSetValues calls=0
not using I-node routines
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqaij
rows=92969, cols=92969
total: nonzeros=638417, allocated nonzeros=638417
total number of mallocs used during MatSetValues calls=0
not using I-node routines
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: mpiaij
rows=278906, cols=278906
total: nonzeros=3274027, allocated nonzeros=3274027
total number of mallocs used during MatSetValues calls=0
not using I-node (on process 0) routines
...
------------------------------------------------------------------------------------------------------------------------
Event Count Time (sec) Flop --- Global --- --- Stage ---- Total
Max Ratio Max Ratio Max Ratio Mess AvgLen Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s
------------------------------------------------------------------------------------------------------------------------
--- Event Stage 0: Main Stage
BuildTwoSidedF 1 1.0 2.3000e-05 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
MatMult 75 1.0 1.5812e+00 1.0 1.88e+09 1.0 0.0e+00 0.0e+00 0.0e+00 28 24 0 0 0 28 24 0 0 0 1189
MatSolve 228 1.0 1.1442e+00 1.0 1.08e+09 1.0 0.0e+00 0.0e+00 0.0e+00 20 14 0 0 0 20 14 0 0 0 944
MatLUFactorNum 3 1.0 8.1930e-02 1.0 2.37e+07 1.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 290
MatILUFactorSym 3 1.0 2.7102e-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
MatAssemblyBegin 5 1.0 3.7000e-05 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
MatAssemblyEnd 5 1.0 3.1895e-02 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
MatGetRowIJ 3 1.0 2.0000e-06 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
MatCreateSubMats 1 1.0 4.0904e-02 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
MatGetOrdering 3 1.0 4.2640e-03 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
MatView 3 1.0 1.4400e-04 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 72 1.0 1.1984e+00 1.0 2.25e+09 1.0 0.0e+00 0.0e+00 0.0e+00 21 28 0 0 0 21 28 0 0 0 1877
VecNorm 76 1.0 1.6841e-01 1.0 1.70e+08 1.0 0.0e+00 0.0e+00 0.0e+00 3 2 0 0 0 3 2 0 0 0 1007
VecScale 75 1.0 1.8241e-02 1.0 8.37e+07 1.0 0.0e+00 0.0e+00 0.0e+00 0 1 0 0 0 0 1 0 0 0 4587
VecCopy 3 1.0 1.4970e-03 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
VecSet 276 1.0 9.1970e-02 1.0 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
VecAXPY 6 1.0 3.7450e-03 1.0 1.34e+07 1.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 3575
VecMAXPY 75 1.0 1.0022e+00 1.0 2.41e+09 1.0 0.0e+00 0.0e+00 0.0e+00 18 30 0 0 0 18 30 0 0 0 2405
VecAssemblyBegin 2 1.0 1.0000e-06 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
VecAssemblyEnd 2 1.0 0.0000e+00 0.0 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 76 1.0 5.5100e-04 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
VecNormalize 75 1.0 1.8462e-01 1.0 2.51e+08 1.0 0.0e+00 0.0e+00 0.0e+00 3 3 0 0 0 3 3 0 0 0 1360
KSPSetUp 4 1.0 1.1341e-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
KSPSolve 1 1.0 5.3123e+00 1.0 7.91e+09 1.0 0.0e+00 0.0e+00 0.0e+00 93100 0 0 0 93100 0 0 0 1489
KSPGMRESOrthog 72 1.0 2.1316e+00 1.0 4.50e+09 1.0 0.0e+00 0.0e+00 0.0e+00 37 57 0 0 0 37 57 0 0 0 2110
PCSetUp 4 1.0 1.5531e-01 1.0 2.37e+07 1.0 0.0e+00 0.0e+00 0.0e+00 3 0 0 0 0 3 0 0 0 0 153
PCSetUpOnBlocks 1 1.0 1.1343e-01 1.0 2.37e+07 1.0 0.0e+00 0.0e+00 0.0e+00 2 0 0 0 0 2 0 0 0 0 209
PCApply 76 1.0 1.1671e+00 1.0 1.08e+09 1.0 0.0e+00 0.0e+00 0.0e+00 20 14 0 0 0 20 14 0 0 0 925
PCApplyOnBlocks 228 1.0 1.1668e+00 1.0 1.08e+09 1.0 0.0e+00 0.0e+00 0.0e+00 20 14 0 0 0 20 14 0 0 0 925
————————————————————————————————————————————————————————————
...
#PETSc Option Table entries:
-ksp_monitor
-ksp_type gmres
-ksp_view
-log_view
-pc_bjacobi_local_blocks 3
-pc_sub_type lu
-pc_type bjacobi
#End of PETSc Option Table entries
...
Does any of the setup/output ring a bell?
BTW, out of curiosity - what is a “I-node” routine?
Cheers,
Hao
________________________________
From: Smith, Barry F. <bsmith at mcs.anl.gov>
Sent: Wednesday, February 5, 2020 9:42 PM
To: Hao DONG <dong-hao at outlook.com>
Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] What is the right way to implement a (block) Diagonal ILU as PC?
> On Feb 5, 2020, at 4:36 AM, Hao DONG <dong-hao at outlook.com> wrote:
>
> Thanks a lot for your suggestions, Hong and Barry -
>
> As you suggested, I first tried the LU direct solvers (built-in and MUMPs) out this morning, which work perfectly, albeit slow. As my problem itself is a part of a PDE based optimization, the exact solution in the searching procedure is not necessary (I often set a relative tolerance of 1E-7/1E-8, etc. for Krylov subspace methods). Also tried BJACOBI with exact LU, the KSP just converges in one or two iterations, as expected.
>
> I added -kspview option for the D-ILU test (still with Block Jacobi as preconditioner and bcgs as KSP solver). The KSPview output from one of the examples in a toy model looks like:
>
> KSP Object: 1 MPI processes
> type: bcgs
> maximum iterations=120, nonzero initial guess
> tolerances: relative=1e-07, absolute=1e-50, divergence=10000.
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
> type: bjacobi
> number of blocks = 3
> Local solve is same for all blocks, in the following KSP and PC objects:
> KSP Object: (sub_) 1 MPI processes
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (sub_) 1 MPI processes
> type: ilu
> out-of-place factorization
> 0 levels of fill
> tolerance for zero pivot 2.22045e-14
> matrix ordering: natural
> factor fill ratio given 1., needed 1.
> Factored matrix follows:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=11294, cols=11294
> package used to perform factorization: petsc
> total: nonzeros=76008, allocated nonzeros=76008
> total number of mallocs used during MatSetValues calls=0
> not using I-node routines
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=11294, cols=11294
> total: nonzeros=76008, allocated nonzeros=76008
> total number of mallocs used during MatSetValues calls=0
> not using I-node routines
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: mpiaij
> rows=33880, cols=33880
> total: nonzeros=436968, allocated nonzeros=436968
> total number of mallocs used during MatSetValues calls=0
> not using I-node (on process 0) routines
>
> do you see something wrong with my setup?
>
> I also tried a quick performance test with a small 278906 by 278906 matrix (3850990 nnz) with the following parameters:
>
> -ksp_type bcgs -pc_type bjacobi -pc_bjacobi_local_blocks 3 -pc_sub_type ilu -ksp_view
>
> Reducing the relative residual to 1E-7
>
> Took 4.08s with 41 bcgs iterations.
>
> Merely changing the -pc_bjacobi_local_blocks to 6
>
> Took 7.02s with 73 bcgs iterations. 9 blocks would further take 9.45s with 101 bcgs iterations.
This is normal. more blocks slower convergence
>
> As a reference, my home-brew Fortran code solves the same problem (3-block D-ILU0) in
>
> 1.84s with 24 bcgs iterations (the bcgs code is also a home-brew one)…
>
Run the PETSc code with optimization ./configure --with-debugging=0 an run the code with -log_view this will show where the PETSc code is spending the time (send it to use)
>
>
> Well, by saying “use explicit L/U matrix as preconditioner”, I wonder if a user is allowed to provide his own (separate) L and U Mat for preconditioning (like how it works in Matlab solvers), e.g.
>
> x = qmr(A,b,Tol,MaxIter,L,U,x)
>
> As I already explicitly constructed the L and U matrices in Fortran, it is not hard to convert them to Mat in Petsc to test Petsc and my Fortran code head-to-head. In that case, the A, b, x, and L/U are all identical, it would be easier to see where the problem came from.
>
>
No, we don't provide this kind of support
>
> BTW, there is another thing I wondered - is there a way to output residual in unpreconditioned norm? I tried to
>
> call KSPSetNormType(ksp_local, KSP_NORM_UNPRECONDITIONED, ierr)
>
> But always get an error that current ksp does not support unpreconditioned in LEFT/RIGHT (either way). Is it possible to do that (output unpreconditioned residual) in PETSc at all?
-ksp_monitor_true_residual You can also run GMRES (and some other methods) with right preconditioning, -ksp_pc_side right then the residual computed is by the algorithm the unpreconditioned residual
KSPSetNormType sets the norm used in the algorithm, it generally always has to left or right, only a couple algorithms support unpreconditioned directly.
Barry
>
> Cheers,
> Hao
>
>
> From: Smith, Barry F. <bsmith at mcs.anl.gov>
> Sent: Tuesday, February 4, 2020 8:27 PM
> To: Hao DONG <dong-hao at outlook.com>
> Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> Subject: Re: [petsc-users] What is the right way to implement a (block) Diagonal ILU as PC?
>
>
>
> > On Feb 4, 2020, at 12:41 PM, Hao DONG <dong-hao at outlook.com> wrote:
> >
> > Dear all,
> >
> >
> > I have a few questions about the implementation of diagonal ILU PC in PETSc. I want to solve a very simple system with KSP (in parallel), the nature of the system (finite difference time-harmonic Maxwell) is probably not important to the question itself. Long story short, I just need to solve a set of equations of Ax = b with a block diagonal system matrix, like (not sure if the mono font works):
> >
> > |X |
> > A =| Y |
> > | Z|
> >
> > Note that A is not really block-diagonal, it’s just a multi-diagonal matrix determined by the FD mesh, where most elements are close to diagonal. So instead of a full ILU decomposition, a D-ILU is a good approximation as a preconditioner, and the number of blocks should not matter too much:
> >
> > |Lx | |Ux |
> > L = | Ly | and U = | Uy |
> > | Lz| | Uz|
> >
> > Where [Lx, Ux] = ILU0(X), etc. Indeed, the D-ILU preconditioner (with 3N blocks) is quite efficient with Krylov subspace methods like BiCGstab or QMR in my sequential Fortran/Matlab code.
> >
> > So like most users, I am looking for a parallel implement with this problem in PETSc. After looking through the manual, it seems that the most straightforward way to do it is through PCBJACOBI. Not sure I understand it right, I just setup a 3-block PCJACOBI and give each of the block a KSP with PCILU. Is this supposed to be equivalent to my D-ILU preconditioner? My little block of fortran code would look like:
> > ...
> > call PCBJacobiSetTotalBlocks(pc_local,Ntotal, &
> > & isubs,ierr)
> > call PCBJacobiSetLocalBlocks(pc_local, Nsub, &
> > & isubs(istart:iend),ierr)
> > ! set up the block jacobi structure
> > call KSPSetup(ksp_local,ierr)
> > ! allocate sub ksps
> > allocate(ksp_sub(Nsub))
> > call PCBJacobiGetSubKSP(pc_local,Nsub,istart, &
> > & ksp_sub,ierr)
> > do i=1,Nsub
> > call KSPGetPC(ksp_sub(i),pc_sub,ierr)
> > !ILU preconditioner
> > call PCSetType(pc_sub,ptype,ierr)
> > call PCFactorSetLevels(pc_sub,1,ierr) ! use ILU(1) here
> > call KSPSetType(ksp_sub(i),KSPPREONLY,ierr)]
> > end do
> > call KSPSetTolerances(ksp_local,KSSiter%tol,PETSC_DEFAULT_REAL, &
> > & PETSC_DEFAULT_REAL,KSSiter%maxit,ierr)
> > …
>
> This code looks essentially right. You should call with -ksp_view to see exactly what PETSc is using for a solver.
>
> >
> > I understand that the parallel performance may not be comparable, so I first set up a one-process test (with MPIAij, but all the rows are local since there is only one process). The system is solved without any problem (identical results within error). But the performance is actually a lot worse (code built without debugging flags in performance tests) than my own home-brew implementation in Fortran (I wrote my own ILU0 in CSR sparse matrix format), which is hard to believe. I suspect the difference is from the PC as the PETSc version took much more BiCGstab iterations (60-ish vs 100-ish) to converge to the same relative tol.
>
> PETSc uses GMRES by default with a restart of 30 and left preconditioning. It could be different exact choices in the solver (which is why -ksp_view is so useful) can explain the differences in the runs between your code and PETSc's
> >
> > This is further confirmed when I change the setup of D-ILU (using 6 or 9 blocks instead of 3). While my Fortran/Matlab codes see minimal performance difference (<5%) when I play with the D-ILU setup, increasing the number of D-ILU blocks from 3 to 9 caused the ksp setup with PCBJACOBI to suffer a performance decrease of more than 50% in sequential test.
>
> This is odd, the more blocks the smaller each block so the quicker the ILU set up should be. You can run various cases with -log_view and send us the output to see what is happening at each part of the computation in time.
>
> > So my implementation IS somewhat different in PETSc. Do I miss something in the PCBJACOBI setup? Or do I have some fundamental misunderstanding of how PCBJACOBI works in PETSc?
>
> Probably not.
> >
> > If this is not the right way to implement a block diagonal ILU as (parallel) PC, please kindly point me to the right direction. I searched through the mail list to find some answers, only to find a couple of similar questions... An example would be nice.
>
> You approach seems fundamentally right but I cannot be sure of possible bugs.
> >
> > On the other hand, does PETSc support a simple way to use explicit L/U matrix as a preconditioner? I can import the D-ILU matrix (I already converted my A matrix into Mat) constructed in my Fortran code to make a better comparison. Or do I have to construct my own PC using PCshell? If so, is there a good tutorial/example to learn about how to use PCSHELL (in a more advanced sense, like how to setup pc side and transpose)?
>
> Not sure what you mean by explicit L/U matrix as a preconditioner. As Hong said, yes you can use a parallel LU from MUMPS or SuperLU_DIST or Pastix as the solver. You do not need any shell code. You simply need to set the PCType to lu
>
> You can also set all this options from the command line and don't need to write the code specifically. So call KSPSetFromOptions() and then for example
>
> -pc_type bjacobi -pc_bjacobi_local_blocks 3 -pc_sub_type ilu (this last one is applied to each block so you could use -pc_type lu and it would use lu on each block.)
>
> -ksp_type_none -pc_type lu -pc_factor_mat_solver_type mumps (do parallel LU with mumps)
>
> By not hardwiring in the code and just using options you can test out different cases much quicker
>
> Use -ksp_view to make sure that is using the solver the way you expect.
>
> Barry
>
>
>
> Barry
>
> >
> > Thanks in advance,
> >
> > Hao
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