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Re: the competition's expm vs ours


From: Jaroslav Hajek
Subject: Re: the competition's expm vs ours
Date: Wed, 3 Dec 2008 08:42:10 +0100

On Wed, Dec 3, 2008 at 8:38 AM, Marco Caliari <address@hidden> wrote:
>> On Wed, Dec 3, 2008 at 1:10 AM, Jordi GutiƩrrez Hermoso
>> <address@hidden> wrote:
>>>
>>> 2008/12/1 Marco Caliari <address@hidden>:
>>>>
>>>> On my laptop, I got the following results for a 500x500 matrix:
>>>>
>>>> Octave 3.0.3 (with ATLAS): 4.3 seconds
>>>> Octave 3.0.3, removing the extra steps: 4.0 seconds
>>>> Matlab 7.6.0: 1.2 seconds
>>>> Octave 3.0.3, rewriting in a better way the Pade' approximation (and
>>>> with
>>>> the extra steps): 3.7 seconds
>>>>
>>>> So, I don't think the extra steps produce the difference and they are
>>>> suggested also in "The scaling and squaring method for the matrix
>>>> exponential revisited" by N.J. Higham.
>>>
>>> Hrm... Are you using sources that incorporate Jaroslav's indexing
>>> improvements? I guess we could profile Octave to see where the actual
>>> slowdown is instead of guessing...
>>>
>>> - Jordi G. H.
>>>
>>
>> Another slowdown in the m-file is caused by the fact that the expressions
>
> Dear Jaroslav,
>
> I computed the cputime of the builtin functions, not the m-file
> implementations.
>

Did you also try the m-file? How does it compare?
Since the whole computation is based on high-level operations like
matrix multiplication, solving, etc, it's an ideal candidate for an
m-file function, provided we can do the elementary operations
efficiently.

> Best regards,
>
> Maco



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



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