Re: logm, funm, sqrtm

[Philip Nienhuis]

Tommy Guy wrote:
> Phillip wrote:
>
> > FWIW, one of the authors of your literature ref provides a (basic) matrix
> > functions toolbox under the GPL v. 3 license:
> > http://www.maths.manchester.ac.uk/~higham/mftoolbox/
>
> > Another (significantly more involved) one is on this web page:
> > http://www.maths.manchester.ac.uk/~higham/NAMF/
> > There's no mentioning of any license, only a note on the web page of the
> > institution that supplied the grant for the research that led to this
> > toolbox, that Intellectual Property is a responsibility of the researchers
> > in question.
>
> > Philip
>
> There is a package available through Higham's lab.

I suppose that's the one in the second link I mentioned.

>                                                    I am new to Octave
> hacking and I am not sure what, legally, we are allowed to do with
> this code.  If we are allowed to adapt what we need for logarithms, we
> could add that to the trunk.  Should someone contact him?

Yes I think so. Will you do that?
I have the impression that Higham's group worked closely with The 
Mathworks (who implemented it immediately), so for octave we must be 
very sure that we are allowed to use Higham's code & under what conditions.

I'm no license expert but there are people on this list who know exactly 
how & what to ask for.

> Regarding the development of a funm function like the one in the
> competition, logm has a few peculiarities due to the fact that the
> Taylor expansion is not globally convergent.  This suggests that while
> funm would be a good idea, logm as a separate unit is also probably
> necessary.

After perusing the code that's my impression, too.

As regards funm:
IMO (but please correct me if I'm wrong) getting the eigen stuff done 
properly and stable (Schur etc) is probably the most CPU-time consuming 
& critical part of a matrix function template. Application of the 
desired function to the diagonal elements (eigenvalues) followed by back 
transformation seems fairly trivial in comparison.

As a sidenote, while googleing the last evenings for this matrix 
function stuff I stumbled upon a phrase from C. Moler (ML creator) that 
in his idea "existence of funm had clearly helped ML to quickly become a 
success" (not his exact wording, but reproduced from my memory).

For myself I only needed a funm to be able to apply a.o. Bessel 
functions to matrix arguments (i.e. decoupling a fairly simple system of 
linear equations for multi-aquifer groundwater flow). The basic version 
we have in octave-forge proved good enough for that.

Philip