[SciPy-user] Matrix square root

[Travis Oliphant]

Pearu Peterson wrote:

>
>
> On Mon, 4 Oct 2004, Nils Wagner wrote:
>
>> AFAIK there is no direct support for sqrtm but you may use funm.
>
>
> I just discovered that there might be a bug in funm. I have added
> a test to scipy.linalg.test_matfuncs that demonstrates the bug.
> So, be aware to check the results of funm(..,sqrt).

As far as I undertand, the idea of a general purpose matrix function has 
precision problems.   The algorithm in scipy is based on a published 
algorithm using the Schur decomposition.   That is why it is usually a 
good idea to write separate algorithms for special matrix functions if 
possible.

Is this really a bug, or just a problem with using the generic funm 
algorithm when a more accurate algorithm exists.

The fact that you can return a reasonable square root for non-special 
matrices makes me believe that it is not a bug in funm, but a 
demonstration that the generic funm algorithm does not always produce 
the best results for specific functions of matrices.  



-Travis O.