the competition's expm vs ours

[David Bateman]

Kai Habel wrote:
> Jordi Gutiérrez Hermoso schrieb:
>   
>> 2008/11/12 David Bateman <David.Bateman at motorola.com>:
>>   
>>     
>>> Jordi Gutiérrez Hermoso wrote:
>>>     
>>>       
>>>> I just ran into a "benchmark" in a blog somewhere that suggests that
>>>> our expm is slower than Matlab's.
>>>>
>>>>       
>>>>         
>>> Jaroslav can probably do a better job at that than I can as he worked on
>>> this part of the code... However, can you put us to the benchmark?
>>>     
>>>       
>> It wasn't anything impressive. Just ran expm a couple of times on
>> rand(300), and we lost by a factor of 8 or so. I can't find it again.
>> :-/
>>
>> I just want to confirm if we are indeed this slow. And also some
>> hints, because I can't find the actual implementation.
>>
>> - Jordi G. H.
>>   
>>     
>
> Looking for 'expm matlab octave' Google gave back this thread [1].
>
> I ran a quick benchmark on a 1.4GHz Pentium M using today's tip and
> matlab 7.6.0
>
> matlab 7.6.0
>   
>>> M = rand(300,300);
>>>       
> t=0.25; T=2;
> tic; inv(M) * (expm(-t*M) - expm(-T*M)); toc;
> Elapsed time is 2.799052 seconds.
>   
>>> tic; inv(M) * (expm(-t*M) - expm(-T*M)); toc;
>>>       
> Elapsed time is 1.789023 seconds.
>   
>>> tic; inv(M) * (expm(-t*M) - expm(-T*M)); toc;
>>>       
> Elapsed time is 1.611524 seconds.
>   
>>> tic; inv(M) * (expm(-t*M) - expm(-T*M)); toc;
>>>       
> Elapsed time is 1.607993 seconds.
>   
>>> tic; inv(M) * (expm(-t*M) - expm(-T*M)); toc;
>>>       
> Elapsed time is 1.750429 seconds.
>
>
> octave:15> clear all
> octave:16> M = rand(300,300);
> octave:17> t=0.25; T=2;
> octave:18> tic; inv(M) * (expm(-t*M) - expm(-T*M)); toc;
> Elapsed time is 4.506 seconds.
> octave:19> tic; inv(M) * (expm(-t*M) - expm(-T*M)); toc;
> Elapsed time is 4.303 seconds.
> octave:20> tic; inv(M) * (expm(-t*M) - expm(-T*M)); toc;
> Elapsed time is 4.374 seconds.
> octave:21> tic; inv(M) * (expm(-t*M) - expm(-T*M)); toc;
> Elapsed time is 4.457 seconds.
>
> So, I see a factor of 2...3 for this particular code - without ATLAS if
> its relevant here.
>
>   
Yes the absence of ATLAS is important as we use xLANGE and xGEBAL in the 
expm that are part of LAPACK. So we need to compare with ATLAS installed..

Regards
D.


> Kai
>
> [1]
> http://www.wilmott.com/messageview.cfm?catid=19&threadid=41499&STARTPAGE=2
>
>   


-- 
David Bateman                                David.Bateman at motorola.com
Motorola Labs - Paris                        +33 1 69 35 48 04 (Ph) 
Parc Les Algorithmes, Commune de St Aubin    +33 6 72 01 06 33 (Mob) 
91193 Gif-Sur-Yvette FRANCE                  +33 1 69 35 77 01 (Fax) 

The information contained in this communication has been classified as: 

[x] General Business Information 
[ ] Motorola Internal Use Only 
[ ] Motorola Confidential Proprietary