Re: Status for GSoC project : Improve logm,sqrtm and funm

[Svante Signell]

On Tue, 2016-03-29 at 18:33 +0200, Marco Caliari wrote:
> On Tue, 29 Mar 2016, Svante Signell wrote:
> 
> > Hi, sorry for chiming in here, but anyway. I see that the expm
> implementation in
> > octave only use Pade approximation to calculate the matrix exponential. I
> have
> > an implementation I made in Fortran 77 in the late 90's. It uses scaling,
> pade
> > approximation and squaring.
> 
> Hi,
> 
> the current Octave's expm uses Pade' with scaling and squaring, as well.
> The state of the art for the matrix exponential by Pade approximation is
> 
> A new scaling and squaring algorithm for the matrix exponential, Al-Mohy, 
> A. H. and Higham, N. J., 2009
> 
> which is freely available as a m-file
> 
> http://eprints.ma.man.ac.uk/1442/
> 
> > 1) How much work is it to call that Fortran code from Octave?
> > 2) Do you have some real difficult test examples, including execution times
> and
> > memory requirements?
> > 3) I a .c/.c++ or .m implementation preferred to Fortran?
> 
> A m-file is of course easier to maintain. A standard Pade` approximation 
> with scaling and squaring involves only one or two short, unnested 
> for loops. I can't imagine a Fortran/C++ implementation much faster than a 
> m-file. Did you compare your implementation with Octave's expm? expm.m is 
> a very short file to read and compare with.

Seems like I was doing the right thing, long before Highams work. And long
before Octave really took off too. However, a rewrite that code into C++ or m-
code seems to be an overkill now when the m code from 2009 is available for
integration into Octave.

Thanks!