Re: FYI: optimizing certain matrix arithmetic

[Jaroslav Hajek]

On Tue, Sep 29, 2009 at 1:54 PM, Michael Creel <address@hidden> wrote:
> On Tue, Sep 29, 2009 at 1:44 PM, Jaroslav Hajek <address@hidden> wrote:
>> On Tue, Sep 29, 2009 at 1:34 PM, Michael Creel <address@hidden> wrote:
>>> On Tue, Sep 29, 2009 at 12:47 PM, Jaroslav Hajek <address@hidden> wrote:
>>>> On Tue, Sep 29, 2009 at 12:26 PM, Michael Creel <address@hidden> wrote:
>>>>> On Tue, Sep 29, 2009 at 10:44 AM, Jaroslav Hajek <address@hidden> wrote:
>>>>>> On Tue, Sep 29, 2009 at 10:38 AM, Michael Creel <address@hidden> wrote:
>>>>>>> Hi all,
>>>>>>>
>>>>>>> On an Apple Macbook Pro running Ubuntu Jaunty amd64, using the benchmark
>>>>>>>
>>>>>>> %%%%%%%%%%%%%%%%%%%%%%
>>>>>>> n = 500;
>>>>>>> R = triu (rand (n));
>>>>>>> u = rand (n, 1);
>>>>>>>
>>>>>>> tic; for i = 1:1000; R \ u; endfor; toc
>>>>>>> tic; for i = 1:1000; u' / R; endfor; toc
>>>>>>> tic; for i = 1:1000; R' \ u; endfor; toc
>>>>>>>
>>>>>>> R = tril (rand (n));
>>>>>>> u = rand (n, 1);
>>>>>>>
>>>>>>> tic; for i = 1:1000; R \ u; endfor; toc
>>>>>>> tic; for i = 1:1000; u' / R; endfor; toc
>>>>>>> tic; for i = 1:1000; R' \ u; endfor; toc
>>>>>>>
>>>>>>> u = u + I*rand (n, 1);
>>>>>>> tic; for i = 1:1000; R \ u; endfor; toc
>>>>>>> tic; for i = 1:1000; R' \ u; endfor; toc
>>>>>>>
>>>>>>>
>>>>>>> n = 800;
>>>>>>> a = rand (n);
>>>>>>> b = rand (n) + i*rand (n);
>>>>>>> tic; a * b; toc
>>>>>>> tic; b * a; toc
>>>>>>> tic; a' * b; toc
>>>>>>> tic; b * a'; toc
>>>>>>> tic; a \ b; toc
>>>>>>> tic; b / a; toc
>>>>>>> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>>>>>>>
>>>>>>> Octave3.0.1 that comes with Ubuntu Jaunty amd64, I get
>>>>>>>
>>>>>>>
>>>>>>> octave:4> bench
>>>>>>> Elapsed time is 0.20216 seconds.
>>>>>>> Elapsed time is 1.93894 seconds.
>>>>>>> Elapsed time is 2.33824 seconds.
>>>>>>> Elapsed time is 0.188448 seconds.
>>>>>>> Elapsed time is 1.95657 seconds.
>>>>>>> Elapsed time is 2.43552 seconds.
>>>>>>> Elapsed time is 4.08299 seconds.
>>>>>>> Elapsed time is 7.84752 seconds.
>>>>>>> Elapsed time is 0.213021 seconds.
>>>>>>> Elapsed time is 0.21117 seconds.
>>>>>>> Elapsed time is 0.218387 seconds.
>>>>>>> Elapsed time is 0.217174 seconds.
>>>>>>> Elapsed time is 0.452714 seconds.
>>>>>>> Elapsed time is 0.391383 seconds.
>>>>>>> octave:5>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> Matlab 2008b gives
>>>>>>>>> bench
>>>>>>> Elapsed time is 0.289161 seconds.
>>>>>>> Elapsed time is 0.566446 seconds.
>>>>>>> Elapsed time is 0.562623 seconds.
>>>>>>> Elapsed time is 0.253456 seconds.
>>>>>>> Elapsed time is 0.574304 seconds.
>>>>>>> Elapsed time is 0.570281 seconds.
>>>>>>> Elapsed time is 0.253070 seconds.
>>>>>>> Elapsed time is 0.572601 seconds.
>>>>>>> Elapsed time is 0.102086 seconds.
>>>>>>> Elapsed time is 0.102677 seconds.
>>>>>>> Elapsed time is 0.103080 seconds.
>>>>>>> Elapsed time is 0.103759 seconds.
>>>>>>> Elapsed time is 0.165608 seconds.
>>>>>>> Elapsed time is 0.181704 seconds.
>>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> Octave 3.2.3+ from today, self compiled, gives
>>>>>>> octave:1> bench
>>>>>>> Elapsed time is 0.208794 seconds.
>>>>>>> Elapsed time is 0.189178 seconds.
>>>>>>> Elapsed time is 0.186724 seconds.
>>>>>>> Elapsed time is 0.188649 seconds.
>>>>>>> Elapsed time is 0.192915 seconds.
>>>>>>> Elapsed time is 0.19166 seconds.
>>>>>>> Elapsed time is 0.186277 seconds.
>>>>>>> Elapsed time is 0.19102 seconds.
>>>>>>> Elapsed time is 0.212707 seconds.
>>>>>>> Elapsed time is 0.211013 seconds.
>>>>>>> Elapsed time is 0.210491 seconds.
>>>>>>> Elapsed time is 0.210447 seconds.
>>>>>>> Elapsed time is 0.431791 seconds.
>>>>>>> Elapsed time is 0.367412 seconds.
>>>>>>> octave:2>
>>>>>>>
>>>>>>> Congratulations!
>>>>>>> Michael
>>>>>>>
>>>>>>
>>>>>> It's interesting you didn't get any speed-up in the second part of the
>>>>>> benchmark, compared to 3.0.1...
>>>>>> What BLAS and LAPACK are you using? What's your compiler configuration?
>>>>>> Also, what exactly is your tip? The "3.2.3+" is a bit unclear, did you
>>>>>> mean "3.3.50+", i.e. the development version?
>>>>>>
>>>>>> thanks
>>>>>>
>>>>>> --
>>>>>> RNDr. Jaroslav Hajek
>>>>>> computing expert & GNU Octave developer
>>>>>> Aeronautical Research and Test Institute (VZLU)
>>>>>> Prague, Czech Republic
>>>>>> url: www.highegg.matfyz.cz
>>>>>>
>>>>>
>>>>> Oops, sorry, it's 3.3.50+, updated this morning.
>>>>>
>>>>> I make using
>>>>> make -j2 CFLAGS="-O3 -march=native -funroll-loops" FFLAGS="-O3
>>>>> -march=native -funroll-loops" XTRA_CFLAGS="-O3 -march=native
>>>>> -funroll-loops" XTRA_CXXFLAGS="-O3 -march=native -funroll-loops"
>>>>>
>>>>
>>>> In general, if you're with a newer gcc on a 64-bit architecture, I
>>>> advise you against -funroll-loops. For me, it usually gets some +1% of
>>>> additional speed of some operations, at the cost of increasing the
>>>> binaries' size by more than 50%. Seems like a bad tradeoff.
>>>>
>>>>> ./configure reports
>>>>>  BLAS libraries:       -llapack -lcblas -lf77blas -latlas
>>>>>
>>>>> so I assume that Octave is using Atlas (the atlas dev package that
>>>>> comes with Kubuntu Jaunty amd64).
>>>>>
>>>>> Michael
>>>>>
>>>>
>>>> Apparently, yes. Hmm. It's really weird you got almost exactly the same 
>>>> figures.
>>>> If you apply the attached patch, rebuild and re-run the benchmark,
>>>> what do you get?
>>>>
>>>> --
>>>> RNDr. Jaroslav Hajek
>>>> computing expert & GNU Octave developer
>>>> Aeronautical Research and Test Institute (VZLU)
>>>> Prague, Czech Republic
>>>> url: www.highegg.matfyz.cz
>>>>
>>>
>>> With that patch applied, I get
>>> octave:1> bench
>>> Elapsed time is 0.194493 seconds.
>>> Elapsed time is 0.192309 seconds.
>>> Elapsed time is 0.189026 seconds.
>>> Elapsed time is 0.188679 seconds.
>>> Elapsed time is 0.195958 seconds.
>>> Elapsed time is 0.193521 seconds.
>>> Elapsed time is 0.187596 seconds.
>>> Elapsed time is 0.193254 seconds.
>>> Elapsed time is 0.215135 seconds.
>>> Elapsed time is 0.213705 seconds.
>>> Elapsed time is 0.21341 seconds.
>>> Elapsed time is 0.212501 seconds.
>>> Elapsed time is 0.363992 seconds.
>>> Elapsed time is 0.368094 seconds.
>>>
>>> so there is an improvement in the second to last number.
>>>
>>> Cheers, M.
>>>
>>
>> OK, it's funny. I now understand where the problem is. Just change the line
>>
>> b = rand (n) + i*rand (n);
>>
>> to
>>
>> b = rand (n) + I*rand (n);
>>
>> (note the big I). At this point, i is still defined from the previous
>> loops as a real numeric value (!)
>> And run the benchmarks again. I think this affects Matlab, too.
>> In any case, it is apparent that your Matlab is linked to something
>> faster than ATLAS; probably Intel's MKL.
>>
>> regards
>>
>> --
>> RNDr. Jaroslav Hajek
>> computing expert & GNU Octave developer
>> Aeronautical Research and Test Institute (VZLU)
>> Prague, Czech Republic
>> url: www.highegg.matfyz.cz
>>
>
> That's one of those bugs that causes rockets to go off course, I
> guess!

Yes, definitely. Maybe we could do something about it...

> OK, it makes sense now. Matlab has been available here for a
> while, but I haven't used it much. I don't know the details of what
> libraries it uses - it's v2009b.

You can usually tell by inspecting the binaries using ldd. But it
doesn't matter much.
I will be glad if you post the results of the corrected benchmark.

> The JIT compilation is pretty
> impressive, but the mechanisms for using MPI are not as nice as Octave
> + MPITB.

I definitely need to look at MPITB some day :)

regards

-- 
RNDr. Jaroslav Hajek
computing expert & GNU Octave developer
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz