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

[Marco Caliari]

On Tue, 29 Mar 2016, Svante Signell wrote:

> On Tue, 2015-10-20 at 18:40 +0100, Carnë Draug wrote:
> > On 20 October 2015 at 16:07, Mudit Sharma <address@hidden> wrote:
> > > All,
> > > I would like to know the status of
> > > the project:Improve logm,sqrt,funmn
> > >  as it was being done for GSoC'15.
> > > I am concerned for it as I have interests in doing it even without any
> > > funding.
> > Hi Mudit
> >
> > The student stopped replying 1-2 weeks after the start and we never heard
> > from him again.  He failed on the midterm evaluation, having made pretty
> > much no work.
> >
> > If you wish to work on this, you should speak with Marco Caliari
> > (cc'ed on this email) as he has details on what algorithms to try
> > to implement, including source code to start the work.
>
> 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.

Best regards,

Marco