Re: GSoC ode15s

[PhilipNienhuis]

Marco Caliari-4 wrote
> On Sun, 13 Mar 2016, Carlo De Falco wrote:
> 
>>
>> On 11 Mar 2016, at 19:51, Chiara Segala <

> segalachiara92@

> > 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.

Not so fast, please.
Using the test.m supplied with expmv pkg/tarball downloaded from github, I
get:

In Matlab r2016a prerelease:

>> test
Relative differences between vectors from EXPM and EXPMV_TSPAN.
Should be of order  1.11e-16.
 1:   0.00e+00
 2:   1.21e-15
 3:   1.37e-15
 4:   1.67e-15
 5:   1.56e-15
 6:   2.59e-15
 7:   1.40e-15
 8:   3.08e-15
 9:   2.20e-15
10:   4.41e-15
>> 

and in Octave-4.1.0+:

>> test
Relative differences between vectors from EXPM and EXPMV_TSPAN.
Should be of order 1.11e-016.
 1:  0.00e+000
 2:  2.80e-016
 3:  3.82e-016
 4:  7.54e-016
 5:  6.02e-016
 6:  1.44e-015
 7:  1.48e-015
 8:  1.46e-015
 9:  9.28e-016
10:  2.73e-015
>>

....so I'd say Octave behaves slightly better than the competition :-)

Philip




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