[SciPy-dev] Re: [SciPy-user] Matrix square root
Travis Oliphant
oliphant at ee.byu.edu
Tue Oct 5 04:26:52 CDT 2004
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.
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