Re: FYI: optimizing certain matrix arithmetic

[Michael Creel]

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"

./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