GSoC 2015: improving matrix funtcions

[Antonio Pino]

Hello,

I have been using octave for a couple of years now for my university
courses as a replacement for That Other Software.

Last year we had the chance to take a closer look at the Moler-Van Loan
paper [1] when we studied non-linear dynamics. The exponential of a
matrix was also the basic tool we used to solve the Automatic Control
course's problems.

That said, I would like to contribute to the gnu-octave project by
improving the matrix functions as cited in the ideas[2] page.

I would like to know what is the (estimated) scope of the improvement to
be made and see whether my ''some mathematics'' level is up to the
challenge.

Thank you in advance for further suggestions.


[1] www.cs.cornell.edu/cv/researchpdf/19ways+.pdf
[2]
http://wiki.octave.org/Summer_of_Code_Project_Ideas#Improve_logm.2C_sqrtm.2C_funm

[Jordi Gutiérrez Hermoso-2]

On Mon, 2015-03-16 at 18:31 +0100, Antonio Pino wrote:
> I have been using octave for a couple of years now for my university
> courses as a replacement for That Other Software.

You can say "Matlab". It's evil, but it's not Lord Voldermort.

> I would like to know what is the (estimated) scope of the
> improvement to be made and see whether my ''some mathematics'' level
> is up to the challenge.

Can you understand any of the papers in this website?

    http://www.maths.manchester.ac.uk/~higham/NAMF/

All the links are dead, but perhaps you can still find the articles
otherwise.

- Jordi G. H.

[Antonio Pino]

al., 2015.eko marren 16a 21:28(e)an, Jordi Gutiérrez Hermoso igorleak
idatzi zuen:
> You can say "Matlab". It's evil, but it's not Lord Voldermort.

Understood, I will bear that in mind from now on.

> Can you understand any of the papers in this website?
>
>     http://www.maths.manchester.ac.uk/~higham/NAMF/

These are the reason it took me a while to answer: I wanted to spend a
little time reading them. That said, I think I will be able to implement
the algorithms described there to improve the functions.

Now, before doing anything else I will build octave. Any suggestions
will be welcomed.

Regards,

Antonio P.R.

PS:

> All the links are dead, but perhaps you can still find the articles
> otherwise.

I found the articles quite easily (freely available) from either the
authors' pages or public academic databases (citeseerX/science direct).
I may provide you with them if asked.

[Antonio Pino]

al., 2015.eko marren 16a 21:28(e)an, Jordi Gutiérrez Hermoso igorleak
idatzi zuen:
> Can you understand any of the papers in this website?
>
>     http://www.maths.manchester.ac.uk/~higham/NAMF/
>
> All the links are dead, but perhaps you can still find the articles
> otherwise.

I wanted to go deep into at least one of the articles to further
responding. The one I have chosen is the one named "Computing the Matrix
Cosine" by N.J. Higham and M.I. Smith.

After compiling octave, I have written a draft of a would be cosm
function. It seems to compare well to the actual funm in octave and
real(expm()).

This has brought up to a couple of questions about testing matrix
funcions: is there any way to systematically test a (matrix) function?
The second one is about Padé approximations in octave, right now I am
using sympy (sympy.org) for that purpose.

Either way, my plan for the gsoc is to follow the articles and try to
effectively implement and test all of them.

Finally, I provide you with the m file and new (working) links to the
articles.

Regards,

Antonio PR