Re: FYI: optimizing certain matrix arithmetic

[Jaroslav Hajek]

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