[petsc-users] GAMG scaling

Sat Dec 22 09:53:59 CST 2018

Wow, this is an old thread.

Sorry if I sound like an old fart talking about the good old days but I
originally did RAP. in Prometheus, in a non work optimal way that might be
of interest. Not hard to implement. I bring this up because we continue to
struggle with this damn thing. I think this approach is perfectly scalable
and pretty low overhead, and simple.

Note, I talked to the hypre people about this in like 97 when they were
implementing RAP and perhaps they are doing it this way ... the 4x slower
way.

Anyway, my data for this is in my SC 2004 paper (MakeNextMat_private in
attached, NB, this is code that I wrote in grad school). It is memory
efficient and simple, just four nested loops i,j,I,J: C(I,J) =
P(i,I)*A(i,j)*P(j,J). In eyeballing the numbers and from new data that I am
getting from my bone modeling colleagues, that use this old code on
Stampede now, the times look reasonable compared to GAMG. This is optimized
for elasticity, where I unroll loops (so it is really six nested loops).

In thinking about this now, I think you want to make a local copy of P with
rows (j) for every column in A that you have locally, then transpose this
local thing for the P(j,J) term. A sparse AXPY on j. (My code uses a
special tree data structure but a matrix is simpler.)

On Sat, Dec 22, 2018 at 3:39 AM Mark Adams <mfadams at lbl.gov> wrote:

> OK, so this thread has drifted, see title :)
>
> On Fri, Dec 21, 2018 at 10:01 PM Fande Kong <fdkong.jd at gmail.com> wrote:
>
>> Sorry, hit the wrong button.
>>
>>
>>
>> On Fri, Dec 21, 2018 at 7:56 PM Fande Kong <fdkong.jd at gmail.com> wrote:
>>
>>>
>>>
>>> On Fri, Dec 21, 2018 at 9:44 AM Mark Adams <mfadams at lbl.gov> wrote:
>>>
>>>> Also, you mentioned that you are using 10 levels. This is very strange
>>>> with GAMG. You can run with -info and grep on GAMG to see the sizes and the
>>>> number of non-zeros per level. You should coarsen at a rate of about 2^D to
>>>> 3^D with GAMG (with 10 levels this would imply a very large fine grid
>>>> problem so I suspect there is something strange going on with coarsening).
>>>> Mark
>>>>
>>>
>>> Hi Mark,
>>>
>>>
>> Thanks for your email. We did not try GAMG much for our problems since we
>> still have troubles to figure out how to effectively use GAMG so far.
>> Instead, we are building our own customized  AMG  that needs to use PtAP to
>> construct coarse matrices.  The customized AMG works pretty well for our
>> specific simulations. The bottleneck right now is that PtAP might
>> take too much memory, and the code crashes within the function "PtAP". I
>> defiantly need a memory profiler to confirm my statement here.
>>
>> Thanks,
>>
>> Fande Kong,
>>
>>
>>
>>>
>>>
>>>
>>>>
>>>> On Fri, Dec 21, 2018 at 11:36 AM Zhang, Hong via petsc-users <
>>>> petsc-users at mcs.anl.gov> wrote:
>>>>
>>>>> Fande:
>>>>> I will explore it and get back to you.
>>>>> Does anyone know how to profile memory usage?
>>>>> Hong
>>>>>
>>>>> Thanks, Hong,
>>>>>>
>>>>>> I just briefly went through the code. I was wondering if it is
>>>>>> possible to destroy "c->ptap" (that caches a lot of intermediate data) to
>>>>>> release the memory after the coarse matrix is assembled. I understand you
>>>>>> may still want to reuse these data structures by default but for my
>>>>>> simulation, the preconditioner is fixed and there is no reason to keep the
>>>>>> "c->ptap".
>>>>>>
>>>>>
>>>>>> It would be great, if we could have this optional functionality.
>>>>>>
>>>>>> Fande Kong,
>>>>>>
>>>>>> On Thu, Dec 20, 2018 at 9:45 PM Zhang, Hong <hzhang at mcs.anl.gov>
>>>>>> wrote:
>>>>>>
>>>>>>> We use nonscalable implementation as default, and switch to scalable
>>>>>>> for matrices over finer grids. You may use option '-matptap_via scalable'
>>>>>>> to force scalable PtAP  implementation for all PtAP. Let me know if it
>>>>>>> works.
>>>>>>> Hong
>>>>>>>
>>>>>>> On Thu, Dec 20, 2018 at 8:16 PM Smith, Barry F. <bsmith at mcs.anl.gov>
>>>>>>> wrote:
>>>>>>>
>>>>>>>>
>>>>>>>>   See MatPtAP_MPIAIJ_MPIAIJ(). It switches to scalable
>>>>>>>> automatically for "large" problems, which is determined by some heuristic.
>>>>>>>>
>>>>>>>>    Barry
>>>>>>>>
>>>>>>>>
>>>>>>>> > On Dec 20, 2018, at 6:46 PM, Fande Kong via petsc-users <
>>>>>>>> petsc-users at mcs.anl.gov> wrote:
>>>>>>>> >
>>>>>>>> >
>>>>>>>> >
>>>>>>>> > On Thu, Dec 20, 2018 at 4:43 PM Zhang, Hong <hzhang at mcs.anl.gov>
>>>>>>>> wrote:
>>>>>>>> > Fande:
>>>>>>>> > Hong,
>>>>>>>> > Thanks for your improvements on PtAP that is critical for MG-type
>>>>>>>> algorithms.
>>>>>>>> >
>>>>>>>> > On Wed, May 3, 2017 at 10:17 AM Hong <hzhang at mcs.anl.gov> wrote:
>>>>>>>> > Mark,
>>>>>>>> > Below is the copy of my email sent to you on Feb 27:
>>>>>>>> >
>>>>>>>> > I implemented scalable MatPtAP and did comparisons of three
>>>>>>>> implementations using ex56.c on alcf cetus machine (this machine has small
>>>>>>>> memory, 1GB/core):
>>>>>>>> > - nonscalable PtAP: use an array of length PN to do dense axpy
>>>>>>>> > - scalable PtAP:       do sparse axpy without use of PN array
>>>>>>>> >
>>>>>>>> > What PN means here?
>>>>>>>> > Global number of columns of P.
>>>>>>>> >
>>>>>>>> > - hypre PtAP.
>>>>>>>> >
>>>>>>>> > The results are attached. Summary:
>>>>>>>> > - nonscalable PtAP is 2x faster than scalable, 8x faster than
>>>>>>>> hypre PtAP
>>>>>>>> > - scalable PtAP is 4x faster than hypre PtAP
>>>>>>>> > - hypre uses less memory (see job.ne399.n63.np1000.sh)
>>>>>>>> >
>>>>>>>> > I was wondering how much more memory PETSc PtAP uses than hypre?
>>>>>>>> I am implementing an AMG algorithm based on PETSc right now, and it is
>>>>>>>> working well. But we find some a bottleneck with PtAP. For the same P and
>>>>>>>> A, PETSc PtAP fails to generate a coarse matrix due to out of memory, while
>>>>>>>> hypre still can generates the coarse matrix.
>>>>>>>> >
>>>>>>>> > I do not want to just use the HYPRE one because we had to
>>>>>>>> duplicate matrices if I used HYPRE PtAP.
>>>>>>>> >
>>>>>>>> > It would be nice if you guys already have done some compassions
>>>>>>>> on these implementations for the memory usage.
>>>>>>>> > Do you encounter memory issue with  scalable PtAP?
>>>>>>>> >
>>>>>>>> > By default do we use the scalable PtAP?? Do we have to specify
>>>>>>>> some options to use the scalable version of PtAP?  If so, it would be nice
>>>>>>>> to use the scalable version by default.  I am totally missing something
>>>>>>>> here.
>>>>>>>> >
>>>>>>>> > Thanks,
>>>>>>>> >
>>>>>>>> > Fande
>>>>>>>> >
>>>>>>>> >
>>>>>>>> > Karl had a student in the summer who improved MatPtAP(). Do you
>>>>>>>> use the latest version of petsc?
>>>>>>>> > HYPRE may use less memory than PETSc because it does not save and
>>>>>>>> reuse the matrices.
>>>>>>>> >
>>>>>>>> > I do not understand why generating coarse matrix fails due to out
>>>>>>>> of memory. Do you use direct solver at coarse grid?
>>>>>>>> > Hong
>>>>>>>> >
>>>>>>>> > Based on above observation, I set the default PtAP algorithm as
>>>>>>>> 'nonscalable'.
>>>>>>>> > When PN > local estimated nonzero of C=PtAP, then switch default
>>>>>>>> to 'scalable'.
>>>>>>>> > User can overwrite default.
>>>>>>>> >
>>>>>>>> > For the case of np=8000, ne=599 (see job.ne599.n500.np8000.sh),
>>>>>>>> I get
>>>>>>>> > MatPtAP                   3.6224e+01 (nonscalable for small mats,
>>>>>>>> scalable for larger ones)
>>>>>>>> > scalable MatPtAP     4.6129e+01
>>>>>>>> > hypre                        1.9389e+02
>>>>>>>> >
>>>>>>>> > This work in on petsc-master. Give it a try. If you encounter any
>>>>>>>> problem, let me know.
>>>>>>>> >
>>>>>>>> > Hong
>>>>>>>> >
>>>>>>>> > On Wed, May 3, 2017 at 10:01 AM, Mark Adams <mfadams at lbl.gov>
>>>>>>>> wrote:
>>>>>>>> > (Hong), what is the current state of optimizing RAP for scaling?
>>>>>>>> >
>>>>>>>> > Nate, is driving 3D elasticity problems at scaling with GAMG and
>>>>>>>> we are working out performance problems. They are hitting problems at ~1.5B
>>>>>>>> dof problems on a basic Cray (XC30 I think).
>>>>>>>> >
>>>>>>>> > Thanks,
>>>>>>>> > Mark
>>>>>>>> >
>>>>>>>>
>>>>>>>>
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