the competition's expm vs ours

[Marco Caliari]

Dear Jordi,

> Thank you for the explanation. Now, am I correct in inferring that the
> extra steps that Octave does for this function (whose implementation I
> think I finally found after Doxygenising the sources, yay!) produce a
> noticeable performance hit as compared to Matlab's? Is this
> performance hit acceptable?

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.

Best regards,

Marco