Re: FYI: optimizing certain matrix arithmetic

[Michael Creel]

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