About improving sqrtm

[Marco Caliari]

Dear all,

Mudit Sharma started to work on matrix functions last October, under my 
mild supervision. For expm and logm he used the free code available here

http://eprints.ma.man.ac.uk/1442/

and here

http://eprints.ma.man.ac.uk/1851/

Then he moved to sqrtm. On January 12th I wrote him

> Dear Mudit,

> you can go with sqrtm. If I remember it correctly, sqrtm in Octave 
> (whose code is in libinterp/corefcn/sqrtm.cc) should already be aligned with the 
> state of the art
>
> www.maths.manchester.ac.uk/~higham/narep/narep336.ps.gz
>
> On the other hand, Matlab's sqrtm allows three output arguments, while 
> Octave's sqrtm only two. This should be fixed. So, the plan for sqrtm 
> could be:
>
> 1) check that narep336 is still the state of the art (I mean, no more 
> recent Higham's paper on sqrtm)
>
> 2) fix the output to align with Matlab

He asked Carnë for some "advice in setting up the environment for C 
coding for Octave in Windows". Then he proposed (January 17th)

> Here's a brief summary I would do:
> 1) Set up Octave's C code environment in Visual Studio.
> 2) Align sqrtm.cc in C with 3 outputs just like Matlab.

In the meantime, we moved to funm, which requires only m-files.

So, I believe Mudit did not try to use Matlab's m-file. He was not aware 
of sqrtm2.m Carnë got by Higham. He was really waiting for some help in 
modifying sqrtm.cc. I apologize with the maintainers for not being clear 
enough with Mudit that he should not even open Matlab copyrighted m-files.

Best regards,

Marco