[petsc-users] block ILU(K) is slower than the point-wise version?

[Barry Smith]

   It is too big for email you can post it somewhere so we can download it.


> On Mar 7, 2017, at 12:01 PM, Kong, Fande <fande.kong at inl.gov> wrote:
> 
> 
> 
> On Tue, Mar 7, 2017 at 10:23 AM, Hong <hzhang at mcs.anl.gov> wrote:
> I checked 
> MatILUFactorSymbolic_SeqBAIJ() and MatILUFactorSymbolic_SeqAIJ(),
> they are virtually same. Why the version for BAIJ is so much slower?
> I'll investigate it. 
> 
> Fande,
> How large is your matrix? Is it possible to send us your matrix so I can test it?
> 
> Thanks, Hong,
> 
> It is a 3020875x3020875 matrix, and it is large. I can make a small one if you like, but not sure it will reproduce this issue or not.
> 
> Fande,
> 
>  
> 
> Hong
> 
> 
> On Mon, Mar 6, 2017 at 9:08 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> 
>   Thanks. Even the symbolic is slower for BAIJ. I don't like that, it definitely should not be since it is (at least should be) doing a symbolic factorization on a symbolic matrix 1/11th the size!
> 
>    Keep us informed.
> 
> 
> 
> > On Mar 6, 2017, at 5:44 PM, Kong, Fande <fande.kong at inl.gov> wrote:
> >
> > Thanks, Barry,
> >
> > Log info:
> >
> > AIJ:
> >
> > MatSolve             850 1.0 8.6543e+00 4.2 3.04e+09 1.8 0.0e+00 0.0e+00 0.0e+00  0 41  0  0  0   0 41  0  0  0 49594
> > MatLUFactorNum        25 1.0 1.7622e+00 2.0 2.04e+09 2.1 0.0e+00 0.0e+00 0.0e+00  0 26  0  0  0   0 26  0  0  0 153394
> > MatILUFactorSym       13 1.0 2.8002e-01 2.9 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
> >
> > BAIJ:
> >
> > MatSolve             826 1.0 1.3016e+01 1.7 1.42e+10 1.8 0.0e+00 0.0e+00 0.0e+00  1 29  0  0  0   1 29  0  0  0 154617
> > MatLUFactorNum        25 1.0 1.5503e+01 2.0 3.55e+10 2.1 0.0e+00 0.0e+00 0.0e+00  1 67  0  0  0   1 67  0  0  0 303190
> > MatILUFactorSym       13 1.0 5.7561e-01 1.8 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
> >
> > It looks like both MatSolve and MatLUFactorNum are slower.
> >
> > I will try your suggestions.
> >
> > Fande
> >
> > On Mon, Mar 6, 2017 at 4:14 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >
> >   Note also that if the 11 by 11 blocks are actually sparse (and you don't store all the zeros in the blocks in the AIJ format) then then AIJ non-block factorization involves less floating point operations and less memory access so can be faster than the BAIJ format, depending on "how sparse" the blocks are. If you actually "fill in" the 11 by 11 blocks with AIJ (with zeros maybe in certain locations) then the above is not true.
> >
> >
> > > On Mar 6, 2017, at 5:10 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> > >
> > >
> > >   This is because for block size 11 it is using calls to LAPACK/BLAS for the block operations instead of custom routines for that block size.
> > >
> > >   Here is what you need to do. For a good sized case run both with -log_view and check the time spent in
> > > MatLUFactorNumeric, MatLUFactorSymbolic and in MatSolve for AIJ and BAIJ. If they have a different number of function calls then divide by the function call count to determine the time per function call.
> > >
> > >   This will tell you which routine needs to be optimized first either MatLUFactorNumeric or MatSolve. My guess is MatSolve.
> > >
> > >   So edit src/mat/impls/baij/seq/baijsolvnat.c and copy the function MatSolve_SeqBAIJ_15_NaturalOrdering_ver1() to a new function MatSolve_SeqBAIJ_11_NaturalOrdering_ver1. Edit the new function for the block size of 11.
> > >
> > >   Now edit MatLUFactorNumeric_SeqBAIJ_N() so that if block size is 11 it uses the new routine something like.
> > >
> > > if (both_identity) {
> > >   if (b->bs == 11)
> > >    C->ops->solve = MatSolve_SeqBAIJ_11_NaturalOrdering_ver1;
> > >   } else {
> > >    C->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
> > >   }
> > >
> > >   Rerun and look at the new -log_view. Send all three -log_view to use at this point.  If this optimization helps and now
> > > MatLUFactorNumeric is the time sink you can do the process to MatLUFactorNumeric_SeqBAIJ_15_NaturalOrdering() to make an 11 size block custom version.
> > >
> > >  Barry
> > >
> > >> On Mar 6, 2017, at 4:32 PM, Kong, Fande <fande.kong at inl.gov> wrote:
> > >>
> > >>
> > >>
> > >> On Mon, Mar 6, 2017 at 3:27 PM, Patrick Sanan <patrick.sanan at gmail.com> wrote:
> > >> On Mon, Mar 6, 2017 at 1:48 PM, Kong, Fande <fande.kong at inl.gov> wrote:
> > >>> Hi All,
> > >>>
> > >>> I am solving a nonlinear system whose Jacobian matrix has a block structure.
> > >>> More precisely, there is a mesh, and for each vertex there are 11 variables
> > >>> associated with it. I am using BAIJ.
> > >>>
> > >>> I thought block ILU(k) should be more efficient than the point-wise ILU(k).
> > >>> After some numerical experiments, I found that the block ILU(K) is much
> > >>> slower than the point-wise version.
> > >> Do you mean that it takes more iterations to converge, or that the
> > >> time per iteration is greater, or both?
> > >>
> > >> The number of iterations is very similar, but the timer per iteration is greater.
> > >>
> > >>
> > >>>
> > >>> Any thoughts?
> > >>>
> > >>> Fande,
> > >>
> > >
> >
> >
> 
> 
>