Re: GSoC ode15s

[Marco Caliari]

On Sun, 13 Mar 2016, Carlo De Falco wrote:

> On 11 Mar 2016, at 19:51, Chiara Segala <address@hidden> wrote:
>
> > As another project idea I would like to work on Exponential Integrators. It 
> > could be an idea to implement, for example, the Exponential Euler and 
> > Rosenbrock methods. But I don't know if it can be an interesting proposal since 
> > these functions are not well defined even in Matlab.
>
> Chira,
>
> I lke this project proposal, I would be interested in mentoring (or rather 
> co-mentoring) on it.
>
> As you also stated I think it should have lower priority with implementation of 
> ode15s,
> because it is not a functionality for which there as much demand.
>
> Definitely an implementation of this feature should go iinto odepkg and not in 
> core-Octave.
>
> That said, I do encourage you to submit an application for GSOC about this.
>
> The first point to investigate before starting development would be what is the 
> state of
> algorithms for computing matrix exponential in Octave and how that compares to 
> Matlab.
>
> I know there is another project being considered about matrix functions and I 
> am not fully
> aware of its state of advancement but I have seen that discussed on the list 
> recently, I suggest you
> look at those discussion threads.

Dear Chiara,

I like too your idea on exponential integrators and I would be available 
as co-mentor. About the other project on matrix functions, it would be 
completely different. In fact, in exponential integrators it is required 
only the action of the matrix exponential to a vector. To this purpose, 
one of the best (fast, reliable) methods available is the one developed by 
Nick Higham (Computing the action of the matrix exponential with an 
application to exponential integrators). He very recently made his code 
available with a free license

https://github.com/higham/expmv

Of course, this is just a small ingredient of an exponential integrators 
package. Anyway, I'm pretty sure it does not work in Octave as is. Can you 
please verify and fix it (or report what does not work and why)?

Moreover, the two methods you mentioned (exp. Euler and exp. 
Rosenbrock-Euler) are very basic methods with no adaptive time step. Can 
you find the relevant references for exponential integrators?

Best regards,

Marco