From: Patrick Alken <patrick.alken@colorado.edu>
To: gsl-discuss@sourceware.org
Subject: New extension for Associated Legendre Functions (ALFs)
Date: Mon, 16 Mar 2009 21:29:00 -0000 [thread overview]
Message-ID: <20090316213137.GA4277@hippogriff.homeunix.org> (raw)
Hello all,
Most current implementations of associated Legendre functions
(ALFs), including the current GSL version fail due to underflow
above degree and order (L,M) 1900. A 2002 paper by Holmes and
Featherstone shows that with a very simple scaling modification
this limit can be extended to 2700 in double precision. I have
recently needed to compute high degree ALFs so I have implemented
their algorithm and made a new GSL extension if others are interested.
There are several other advantages in this extension over the
current GSL implementation:
1) I have included support for several normalization conventions:
- Schmidt semi-normalized ALFs
- Spherical harmonic normalized ALFs (GSL already has this)
- Fully normalized ALFs
- Unnormalized ALFs (GSL has this)
2) The user can choose whether to compute the Condon-Shortley
phase of (-1)^m
3) The GSL array versions currently only compute ALFs for a fixed
order m and multiple degrees l. This extension now efficiently
computes all ALFs for a given maximum degree lmax for all
(l,m) up to lmax.
4) The routines in this extension use a workspace which precomputes
various factors in the recurrence relations which should lead
to a (minor) speedup in the calculations.
This extension includes a complete test suite and documentation.
The docs contain a plot which shows how the current GSL
implementation fails for L,M = 2700.
I have put a link on the main GSL webpage for the extension.
Patrick Alken
next reply other threads:[~2009-03-16 21:29 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2009-03-16 21:29 Patrick Alken [this message]
2009-03-17 11:37 ` Brian Gough
2009-03-17 16:23 ` Patrick Alken
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