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---------- Forwarded message ---------
Von: Marc Nieper-Wißkirchen <xxxxxx@nieper-wisskirchen.de>
Date: So., 23. Aug. 2020 um 20:46 Uhr
Subject: Re: Random matrices
To: Linas Vepstas <xxxxxx@gmail.com>

Linas Vepstas <xxxxxx@gmail.com> schrieb am So., 23. Aug. 2020, 19:29:
>
> The python snippet at the bottom-right of page 597 is only 10 lines of code, including documentation and declaration of imports ... The scheme version would be roughly equal in size. ... But it requires a linear-algebra QR decomposition algorithm, which, from what I can tell, there is no srfi ?

I don't think so,  so we would have to write one from scratch, which
could later go into its own SRFI.  The nice thing about writing one
from scratch is that we can do better than the standard libraries for
Python so that our QR decomposition works for reals,  the complex
numbers and quaternions all at once. This way,  we can handle all
three classical groups uniformly.

John, what plans are there for linalg libraries? Preferably over all
three (skew) fields.

Marc

>
> -- Linas
>
> On Thu, Aug 20, 2020 at 4:28 AM Marc Nieper-Wißkirchen <xxxxxx@nieper-wisskirchen.de> wrote:
>>
>> The "make-sphere-generator" is basically a generator on the homogenous
>> space SO(n + 1)/SO(n). I am wondering how complicated it is to add
>> random generators for the elements of SO(n) itself (the probability
>> distribution will be given by the Haar measure, of course).
>>
>> Random generators for the most important compact Lie groups will be
>> quite useful in applications and more than the
>> "make-ellipsoid-generator", which is already in SRFI 194.
>>
>> Some theoretical and implementation background is in the introductory
>> article [1].
>>
>> Marc
>>
>> --
>>
>> [1] http://www.ams.org/notices/200705/fea-mezzadri-web.pdf
>
>
>
> --
> Verbogeny is one of the pleasurettes of a creatific thinkerizer.
>         --Peter da Silva
>