Re: GSOC 16, Improvements to sqrtm,logm and funm

[Carnë Draug]

March 2016 at 02:52, Jordi Gutiérrez Hermoso <address@hidden> wrote:
> On Thu, 2016-03-03 at 14:09 +0100, Marco Caliari wrote:
>> In my humble opinion what is left is not enough for a GSOC. Jordi,
>> you are indicated a potential mentor, what do you think? Carnë?
>
> I think there's still lots of work to be done. Although Higham has
> published a lot of code, there are still things to be done. Not all of
> the work he and his colleagues have published has made it into free
> code; a lot of it is only in proprietary Matlab code. This includes
> some of the most interesting things, such as the funm function. We are
> in effect reproducing many years of work by a large team of
> researchers. We're lucky that the papers all published; "all" that has
> to be done is distill the knowledge into Octave code. There's plenty
> of meat here for a GSoC project and beyond.
>
> For example, how much more work is there before the `mft_test` command
> available here passes on Octave? How about making it pass with speed
> comparable to Matlab?
>
>     http://www.maths.manchester.ac.uk/~higham/mftoolbox/
>
> This seems like a very nice, concrete goal to aim for. What do you
> think?

Here's my notes from the few meetings we had last year with Antonio
Pino (the GSoC student that disappeared after the initial payment).

This was going to be the work plan (I don't see reason to deviate
much from it):

* Create repositories for Higham's toolboxes, and code from his papers.
* We don't know which of his code works, and which does not, in Octave.
  So start by writing several Octave tests for all this functions.  In many
  cases, tests are described on the papers and reports.
* Do not modify the code to it work in Octave.  We have more interest in
  improving Octave so that it works out of the box.  That maximizes the use
  of the work done for all the community.  Only change code to work around
  undocumented Matlab features that we do not want in Octave such as for
  loop to "Inf", or "superiorfloat" (but still report them in Octave bug
  tracker).
* Higham's code uses a lot of loops that will not be accepted in core.
  Vectorize those operations (likely to not be possible), or reimplement
  them in C++.  Use the tests that are already written.

Some notes from other meetings:

* sqrtm.cc already implements Higham's code.  Compare with his published
  code and write tests for this.  Read section 6 of Numerical Analysis
  Report 336.
* Add sqrtm tests for %!warning
* Get familiar with xpow.cc since there will be a lot of work done in
  that file.
* Write tests for gallery().
* Start by working on the Test Matrix Toolbox which seems to be the easiest
  and mostly working out of the box.

Carnë