[petsc-dev] [petsc-users] Poor weak scaling when solving successive linearsystems
Mark Adams
mfadams at lbl.gov
Mon Jun 11 08:09:18 CDT 2018
On Mon, Jun 11, 2018 at 12:46 AM, Junchao Zhang <jczhang at mcs.anl.gov> wrote:
> I used an LCRC machine named Bebop. I tested on its Intel Broadwell nodes.
> Each nodes has 2 CPUs and 36 cores in total. I collected data using 36
> cores in a node or 18 cores in a node. As you can see, 18 cores/node gave
> much better performance, which is reasonable as routines like MatSOR,
> MatMult, MatMultAdd are all bandwidth bound.
>
> The code uses a DMDA 3D grid, 7-point stencil, and defines nodes(vertices)
> at the surface or second to the surface as boundary nodes. Boundary nodes
> only have a diagonal one in their row in the matrix. Interior nodes have 7
> nonzeros in their row. Boundary processors in the processor grid has less
> nonzero. This is one source of load-imbalance. Will load-imbalance get
> severer at coarser grids of an MG level?
>
Yes.
You can use a simple Jacobi solver to see the basic performance of your
operator and machine. Do you see as much time spent in Vec Scatters?
VecAXPY? etc.
>
> I attach a trace view figure that show activity of each ranks along the
> time axis in one KSPSove. White color means MPI wait. You can see white
> takes a large space.
>
> I don't have a good explanation why at large scale (1728 cores),
> processors wait longer time, as the communication pattern is still 7-point
> stencil in a cubic processor gird.
>
> --Junchao Zhang
>
> On Sat, Jun 9, 2018 at 11:32 AM, Smith, Barry F. <bsmith at mcs.anl.gov>
> wrote:
>
>>
>> Junchao,
>>
>> Thanks, the load balance of matrix entries is remarkably similar
>> for the two runs so it can't be a matter of worse work load imbalance for
>> SOR for the larger case explaining why the SOR takes more time.
>>
>> Here is my guess (and I know no way to confirm it). In the smaller
>> case the overlap of different processes on the same node running SOR at the
>> same time is lower than the larger case hence the larger case is slower
>> because there are more SOR processes fighting over the same memory
>> bandwidth at the same time than in the smaller case. Ahh, here is
>> something you can try, lets undersubscribe the memory bandwidth needs, run
>> on say 16 processes per node with 8 nodes and 16 processes per node with 64
>> nodes and send the two -log_view output files. I assume this is an LCRC
>> machine and NOT a KNL system?
>>
>> Thanks
>>
>>
>> Barry
>>
>>
>> > On Jun 9, 2018, at 8:29 AM, Mark Adams <mfadams at lbl.gov> wrote:
>> >
>> > -pc_gamg_type classical
>> >
>> > FYI, we only support smoothed aggregation "agg" (the default). (This
>> thread started by saying you were using GAMG.)
>> >
>> > It is not clear how much this will make a difference for you, but you
>> don't want to use classical because we do not support it. It is meant as a
>> reference implementation for developers.
>> >
>> > First, how did you get the idea to use classical? If the documentation
>> lead you to believe this was a good thing to do then we need to fix that!
>> >
>> > Anyway, here is a generic input for GAMG:
>> >
>> > -pc_type gamg
>> > -pc_gamg_type agg
>> > -pc_gamg_agg_nsmooths 1
>> > -pc_gamg_coarse_eq_limit 1000
>> > -pc_gamg_reuse_interpolation true
>> > -pc_gamg_square_graph 1
>> > -pc_gamg_threshold 0.05
>> > -pc_gamg_threshold_scale .0
>> >
>> >
>> >
>> >
>> > On Thu, Jun 7, 2018 at 6:52 PM, Junchao Zhang <jczhang at mcs.anl.gov>
>> wrote:
>> > OK, I have thought that space was a typo. btw, this option does not
>> show up in -h.
>> > I changed number of ranks to use all cores on each node to avoid
>> misleading ratio in -log_view. Since one node has 36 cores, I ran with
>> 6^3=216 ranks, and 12^3=1728 ranks. I also found call counts of MatSOR etc
>> in the two tests were different. So they are not strict weak scaling tests.
>> I tried to add -ksp_max_it 6 -pc_mg_levels 6, but still could not make the
>> two have the same MatSOR count. Anyway, I attached the load balance output.
>> >
>> > I find PCApply_MG calls PCMGMCycle_Private, which is recursive and
>> indirectly calls MatSOR_MPIAIJ. I believe the following code in
>> MatSOR_MPIAIJ practically syncs {MatSOR, MatMultAdd}_SeqAIJ between
>> processors through VecScatter at each MG level. If SOR and MatMultAdd are
>> imbalanced, the cost is accumulated along MG levels and shows up as large
>> VecScatter cost.
>> > 1460: while
>> > (its--) {
>> >
>> > 1461: VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCA
>> TTER_FORWARD
>> > );
>> >
>> > 1462: VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER
>> _FORWARD
>> > );
>> >
>> >
>> > 1464: /* update rhs: bb1 = bb - B*x */
>> > 1465: VecScale
>> > (mat->lvec,-1.0);
>> >
>> > 1466: (*mat->B->ops->multadd)(mat->
>> > B,mat->lvec,bb,bb1);
>> >
>> >
>> > 1468: /* local sweep */
>> > 1469: (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,
>> > fshift,lits,1,xx);
>> >
>> > 1470: }
>> >
>> >
>> >
>> > --Junchao Zhang
>> >
>> > On Thu, Jun 7, 2018 at 3:11 PM, Smith, Barry F. <bsmith at mcs.anl.gov>
>> wrote:
>> >
>> >
>> > > On Jun 7, 2018, at 12:27 PM, Zhang, Junchao <jczhang at mcs.anl.gov>
>> wrote:
>> > >
>> > > Searched but could not find this option, -mat_view::load_balance
>> >
>> > There is a space between the view and the : load_balance is a
>> particular viewer format that causes the printing of load balance
>> information about number of nonzeros in the matrix.
>> >
>> > Barry
>> >
>> > >
>> > > --Junchao Zhang
>> > >
>> > > On Thu, Jun 7, 2018 at 10:46 AM, Smith, Barry F. <bsmith at mcs.anl.gov>
>> wrote:
>> > > So the only surprise in the results is the SOR. It is embarrassingly
>> parallel and normally one would not see a jump.
>> > >
>> > > The load balance for SOR time 1.5 is better at 1000 processes than
>> for 125 processes of 2.1 not worse so this number doesn't easily explain
>> it.
>> > >
>> > > Could you run the 125 and 1000 with -mat_view ::load_balance and see
>> what you get out?
>> > >
>> > > Thanks
>> > >
>> > > Barry
>> > >
>> > > Notice that the MatSOR time jumps a lot about 5 secs when the
>> -log_sync is on. My only guess is that the MatSOR is sharing memory
>> bandwidth (or some other resource? cores?) with the VecScatter and for some
>> reason this is worse for 1000 cores but I don't know why.
>> > >
>> > > > On Jun 6, 2018, at 9:13 PM, Junchao Zhang <jczhang at mcs.anl.gov>
>> wrote:
>> > > >
>> > > > Hi, PETSc developers,
>> > > > I tested Michael Becker's code. The code calls the same KSPSolve
>> 1000 times in the second stage and needs cubic number of processors to run.
>> I ran with 125 ranks and 1000 ranks, with or without -log_sync option. I
>> attach the log view output files and a scaling loss excel file.
>> > > > I profiled the code with 125 processors. It looks {MatSOR,
>> MatMult, MatMultAdd, MatMultTranspose, MatMultTransposeAdd}_SeqAIJ in aij.c
>> took ~50% of the time, The other half time was spent on waiting in MPI.
>> MatSOR_SeqAIJ took 30%, mostly in PetscSparseDenseMinusDot().
>> > > > I tested it on a 36 cores/node machine. I found 32 ranks/node gave
>> better performance (about 10%) than 36 ranks/node in the 125 ranks
>> testing. I guess it is because processors in the former had more balanced
>> memory bandwidth. I collected PAPI_DP_OPS (double precision operations) and
>> PAPI_TOT_CYC (total cycles) of the 125 ranks case (see the attached files).
>> It looks ranks at the two ends have less DP_OPS and TOT_CYC.
>> > > > Does anyone familiar with the algorithm have quick explanations?
>> > > >
>> > > > --Junchao Zhang
>> > > >
>> > > > On Mon, Jun 4, 2018 at 11:59 AM, Michael Becker <
>> Michael.Becker at physik.uni-giessen.de> wrote:
>> > > > Hello again,
>> > > >
>> > > > this took me longer than I anticipated, but here we go.
>> > > > I did reruns of the cases where only half the processes per node
>> were used (without -log_sync):
>> > > >
>> > > > 125 procs,1st 125 procs,2nd
>> 1000 procs,1st 1000 procs,2nd
>> > > > Max Ratio Max Ratio
>> Max Ratio Max Ratio
>> > > > KSPSolve 1.203E+02 1.0 1.210E+02 1.0
>> 1.399E+02 1.1 1.365E+02 1.0
>> > > > VecTDot 6.376E+00 3.7 6.551E+00 4.0
>> 7.885E+00 2.9 7.175E+00 3.4
>> > > > VecNorm 4.579E+00 7.1 5.803E+00 10.2
>> 8.534E+00 6.9 6.026E+00 4.9
>> > > > VecScale 1.070E-01 2.1 1.129E-01 2.2
>> 1.301E-01 2.5 1.270E-01 2.4
>> > > > VecCopy 1.123E-01 1.3 1.149E-01 1.3
>> 1.301E-01 1.6 1.359E-01 1.6
>> > > > VecSet 7.063E-01 1.7 6.968E-01 1.7
>> 7.432E-01 1.8 7.425E-01 1.8
>> > > > VecAXPY 1.166E+00 1.4 1.167E+00 1.4
>> 1.221E+00 1.5 1.279E+00 1.6
>> > > > VecAYPX 1.317E+00 1.6 1.290E+00 1.6
>> 1.536E+00 1.9 1.499E+00 2.0
>> > > > VecScatterBegin 6.142E+00 3.2 5.974E+00 2.8
>> 6.448E+00 3.0 6.472E+00 2.9
>> > > > VecScatterEnd 3.606E+01 4.2 3.551E+01 4.0
>> 5.244E+01 2.7 4.995E+01 2.7
>> > > > MatMult 3.561E+01 1.6 3.403E+01 1.5
>> 3.435E+01 1.4 3.332E+01 1.4
>> > > > MatMultAdd 1.124E+01 2.0 1.130E+01 2.1
>> 2.093E+01 2.9 1.995E+01 2.7
>> > > > MatMultTranspose 1.372E+01 2.5 1.388E+01 2.6
>> 1.477E+01 2.2 1.381E+01 2.1
>> > > > MatSolve 1.949E-02 0.0 1.653E-02 0.0
>> 4.789E-02 0.0 4.466E-02 0.0
>> > > > MatSOR 6.610E+01 1.3 6.673E+01 1.3
>> 7.111E+01 1.3 7.105E+01 1.3
>> > > > MatResidual 2.647E+01 1.7 2.667E+01 1.7
>> 2.446E+01 1.4 2.467E+01 1.5
>> > > > PCSetUpOnBlocks 5.266E-03 1.4 5.295E-03 1.4
>> 5.427E-03 1.5 5.289E-03 1.4
>> > > > PCApply 1.031E+02 1.0 1.035E+02 1.0
>> 1.180E+02 1.0 1.164E+02 1.0
>> > > >
>> > > > I also slimmed down my code and basically wrote a simple weak
>> scaling test (source files attached) so you can profile it yourself. I
>> appreciate the offer Junchao, thank you.
>> > > > You can adjust the system size per processor at runtime via
>> "-nodes_per_proc 30" and the number of repeated calls to the function
>> containing KSPsolve() via "-iterations 1000". The physical problem is
>> simply calculating the electric potential from a homogeneous charge
>> distribution, done multiple times to accumulate time in KSPsolve().
>> > > > A job would be started using something like
>> > > > mpirun -n 125 ~/petsc_ws/ws_test -nodes_per_proc 30 -mesh_size 1E-4
>> -iterations 1000 \\
>> > > > -ksp_rtol 1E-6 \
>> > > > -log_view -log_sync\
>> > > > -pc_type gamg -pc_gamg_type classical\
>> > > > -ksp_type cg \
>> > > > -ksp_norm_type unpreconditioned \
>> > > > -mg_levels_ksp_type richardson \
>> > > > -mg_levels_ksp_norm_type none \
>> > > > -mg_levels_pc_type sor \
>> > > > -mg_levels_ksp_max_it 1 \
>> > > > -mg_levels_pc_sor_its 1 \
>> > > > -mg_levels_esteig_ksp_type cg \
>> > > > -mg_levels_esteig_ksp_max_it 10 \
>> > > > -gamg_est_ksp_type cg
>> > > > , ideally started on a cube number of processes for a cubical
>> process grid.
>> > > > Using 125 processes and 10.000 iterations I get the output in
>> "log_view_125_new.txt", which shows the same imbalance for me.
>> > > > Michael
>> > > >
>> > > >
>> > > > Am 02.06.2018 um 13:40 schrieb Mark Adams:
>> > > >>
>> > > >>
>> > > >> On Fri, Jun 1, 2018 at 11:20 PM, Junchao Zhang <
>> jczhang at mcs.anl.gov> wrote:
>> > > >> Hi,Michael,
>> > > >> You can add -log_sync besides -log_view, which adds barriers to
>> certain events but measures barrier time separately from the events. I find
>> this option makes it easier to interpret log_view output.
>> > > >>
>> > > >> That is great (good to know).
>> > > >>
>> > > >> This should give us a better idea if your large VecScatter costs
>> are from slow communication or if it catching some sort of load imbalance.
>> > > >>
>> > > >>
>> > > >> --Junchao Zhang
>> > > >>
>> > > >> On Wed, May 30, 2018 at 3:27 AM, Michael Becker <
>> Michael.Becker at physik.uni-giessen.de> wrote:
>> > > >> Barry: On its way. Could take a couple days again.
>> > > >>
>> > > >> Junchao: I unfortunately don't have access to a cluster with a
>> faster network. This one has a mixed 4X QDR-FDR InfiniBand 2:1 blocking
>> fat-tree network, which I realize causes parallel slowdown if the nodes are
>> not connected to the same switch. Each node has 24 processors (2x12/socket)
>> and four NUMA domains (two for each socket).
>> > > >> The ranks are usually not distributed perfectly even, i.e. for 125
>> processes, of the six required nodes, five would use 21 cores and one 20.
>> > > >> Would using another CPU type make a difference communication-wise?
>> I could switch to faster ones (on the same network), but I always assumed
>> this would only improve performance of the stuff that is unrelated to
>> communication.
>> > > >>
>> > > >> Michael
>> > > >>
>> > > >>
>> > > >>
>> > > >>> The log files have something like "Average time for zero size
>> MPI_Send(): 1.84231e-05". It looks you ran on a cluster with a very slow
>> network. A typical machine should give less than 1/10 of the latency you
>> have. An easy way to try is just running the code on a machine with a
>> faster network and see what happens.
>> > > >>>
>> > > >>> Also, how many cores & numa domains does a compute node have? I
>> could not figure out how you distributed the 125 MPI ranks evenly.
>> > > >>>
>> > > >>> --Junchao Zhang
>> > > >>>
>> > > >>> On Tue, May 29, 2018 at 6:18 AM, Michael Becker <
>> Michael.Becker at physik.uni-giessen.de> wrote:
>> > > >>> Hello again,
>> > > >>>
>> > > >>> here are the updated log_view files for 125 and 1000 processors.
>> I ran both problems twice, the first time with all processors per node
>> allocated ("-1.txt"), the second with only half on twice the number of
>> nodes ("-2.txt").
>> > > >>>
>> > > >>>>> On May 24, 2018, at 12:24 AM, Michael Becker <
>> Michael.Becker at physik.uni-giessen.de>
>> > > >>>>> wrote:
>> > > >>>>>
>> > > >>>>> I noticed that for every individual KSP iteration, six vector
>> objects are created and destroyed (with CG, more with e.g. GMRES).
>> > > >>>>>
>> > > >>>> Hmm, it is certainly not intended at vectors be created and
>> destroyed within each KSPSolve() could you please point us to the code that
>> makes you think they are being created and destroyed? We create all the
>> work vectors at KSPSetUp() and destroy them in KSPReset() not during the
>> solve. Not that this would be a measurable distance.
>> > > >>>>
>> > > >>>
>> > > >>> I mean this, right in the log_view output:
>> > > >>>
>> > > >>>> Memory usage is given in bytes:
>> > > >>>>
>> > > >>>> Object Type Creations Destructions Memory Descendants' Mem.
>> > > >>>> Reports information only for process 0.
>> > > >>>>
>> > > >>>> --- Event Stage 0: Main Stage
>> > > >>>>
>> > > >>>> ...
>> > > >>>>
>> > > >>>> --- Event Stage 1: First Solve
>> > > >>>>
>> > > >>>> ...
>> > > >>>>
>> > > >>>> --- Event Stage 2: Remaining Solves
>> > > >>>>
>> > > >>>> Vector 23904 23904 1295501184 0.
>> > > >>> I logged the exact number of KSP iterations over the 999
>> timesteps and its exactly 23904/6 = 3984.
>> > > >>> Michael
>> > > >>>
>> > > >>>
>> > > >>> Am 24.05.2018 um 19:50 schrieb Smith, Barry F.:
>> > > >>>>
>> > > >>>> Please send the log file for 1000 with cg as the solver.
>> > > >>>>
>> > > >>>> You should make a bar chart of each event for the two cases to
>> see which ones are taking more time and which are taking less (we cannot
>> tell with the two logs you sent us since they are for different solvers.)
>> > > >>>>
>> > > >>>>
>> > > >>>>
>> > > >>>>
>> > > >>>>> On May 24, 2018, at 12:24 AM, Michael Becker <
>> Michael.Becker at physik.uni-giessen.de>
>> > > >>>>> wrote:
>> > > >>>>>
>> > > >>>>> I noticed that for every individual KSP iteration, six vector
>> objects are created and destroyed (with CG, more with e.g. GMRES).
>> > > >>>>>
>> > > >>>> Hmm, it is certainly not intended at vectors be created and
>> destroyed within each KSPSolve() could you please point us to the code that
>> makes you think they are being created and destroyed? We create all the
>> work vectors at KSPSetUp() and destroy them in KSPReset() not during the
>> solve. Not that this would be a measurable distance.
>> > > >>>>
>> > > >>>>
>> > > >>>>
>> > > >>>>
>> > > >>>>> This seems kind of wasteful, is this supposed to be like this?
>> Is this even the reason for my problems? Apart from that, everything seems
>> quite normal to me (but I'm not the expert here).
>> > > >>>>>
>> > > >>>>>
>> > > >>>>> Thanks in advance.
>> > > >>>>>
>> > > >>>>> Michael
>> > > >>>>>
>> > > >>>>>
>> > > >>>>>
>> > > >>>>> <log_view_125procs.txt><log_vi
>> > > >>>>> ew_1000procs.txt>
>> > > >>>>>
>> > > >>>
>> > > >>>
>> > > >>
>> > > >>
>> > > >>
>> > > >
>> > > >
>> > > > <o-wstest-125.txt><Scaling-loss.png><o-wstest-1000.txt><o-
>> wstest-sync-125.txt><o-wstest-sync-1000.txt><MatSOR_SeqAIJ.
>> png><PAPI_TOT_CYC.png><PAPI_DP_OPS.png>
>> > >
>> > >
>> >
>> >
>> >
>>
>>
>
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