The Legendre transforms in the Kit require that a function of bandwidth B be sampled on the 2Bmany Chebyshev points and not the Bmany Gaussian points. Therefore, the number of samples needed is twice the function's bandwidth. This implies that for the spherical transforms in the Kit, a function of bandwidth B is sampled on the equiangular 2Bx2B grid on the sphere.
Some of the algorithms implemented in this package are based on the work of Driscoll and Healy. A preprint that offers a detailed development and description of the algorithms implemented in SpharmonicKit is here.
Caveat emptor  this is research code only and has not been hardened. All the code works quite well on DEC Alpha workstations using OSF1 Versions 3.2 and 4.0. Some code has also been tested and successfully run on Pentiumbased GNU/Linux workstations, SGI workstations using IRIX 5.3 and IRIX 6.4, Sun workstations using SunOS 4.1.2 1, an HP Exemplar XClass running SPPUX 5.2.1, and even a NeXTstation Color Turbo running NeXTStep 3.3!
We would also like to mention that there exists other software for performing spherical transforms. Details on other possibilities may be found here.
What's New  Preprints  Source Code  Other Possibilities 
What's New 
(updated 23 Apr 2008) 
Bug fix  (23 Apr 2008)
A user has recently identified a bug which exists in a source file found in
the SpharmonicKit 2.7, S2kit 1.0 and SOFT 2.0
distributions. (I.e. Slight variations of this file are included in all
three distributions.) Fortunately, the fix is an easy one. The bug's description
and cure may be found in this document.

SOFT 2.0 released 
(16 Sept 2007)
Yes, another shameless plug. SOFT 2.0, a collection of code for taking
Fourier transforms of functions defined on SO(3), has been released and is available
here. The major difference between this release
and the v.1.0 is that the user, with the help of
FFTW, is no longer restricted to doing
transforms at powersof2 bandwidths.

Version 1.0 of S2kit released 
(20 Feb 2004)
S2kit is a lite version of SpharmonicKit.
(Hence the shorter name.)
It is a collection of routines, written in C, which
implement discrete Legendre and spherical harmonic transforms.
In addition to code being cleaned up, S2kit is lite mainly for two reasons.
Firstly, it uses only two types of discrete Legendre transform (DLT) algorithms: the naive and seminaive algorithms. These algorithms are described in the preprint below, as well as this document which is included with the S2kit distribution. Secondly, S2kit absolutely requires version 3 of FFTW. The routines in FFTW are more efficient than our homegrown code, and, perhaps more importantly, the user is no longer restricted to doing transforms at powersof2 bandwidths (which is the case with SpharmonicKit).

Version 2.7 released 
(19 Feb 2004) Bug fix  Thanks to feedback from a user, another (and hopefully
last) scaling
error was identified and fixed. This time, it was in a routine
having to do with convolutions.
Details of the fix may be found in the CHANGES file which accompanies the distribution.

Version 1.0 of SOFT released 
(15 Nov 2003)
Code for taking
Fourier transforms of functions defined on SO(3), aka the
Rotation Group, is available
here. (Yes, this is a shameless plug.)
Included within this distribution are examples of how the code may be
used, e.g. correlating, and rotating, functions defined on the sphere.

Version 2.6 released 
(July 2003)
Bug fix  Thanks to feedback from a user, an ancient scaling
discrepancy has been identified and corrected. Internally,
the normalizations are all consistent with one another and
hence, as far as the code is concerned, correct.
Details of the fix may be found in the CHANGES file which accompanies the distribution.

Version 2.5 released 
Version 2 of SpharmonicKit has been updated and modified to allow
use of a variation of
FFTPACK,
the freely available library of Fortran routines from
NCAR. Use of this modified
library is encouraged (though not required) because its FFT
and DCT routines are noticeably more efficient than those which come
with SpharmonicKit.
If the user does not wish to use the modified FFTPACK, it should now be
(easily) possible for the user to replace our FFT and DCT routines
with their own optimized ones.
Further information concerning the modified FFTPACK, the modified software itself, and substituting other FFT and DCT routines, is available here.

SpharmonicKit 
SpharmonicKit is free software and is distributed under the terms of the
GNU General Public License.
This is the README file from SpharmonicKit 2.7. The source code is available in the following formats:

S2kit 
S2kit is free software and is distributed under the terms of the
GNU General Public License.
This document explains the contents of S2kit 1.0. (It is also included within the distribution.) The source code is available in the following formats: Don't forget that S2kit requires Version 3 of FFTW! Important Note: You should not combine the contents of S2kit with SpharmonicKit in the same directory. While files may share the same name, their contents are almost assuredly different.

FFTPACK 
SpharmonicKit has been designed to allow use of a modified version
of
FFTPACK.
The FFT and DCT routines in FFTPACK are more efficient than
the ones contained in SpharmonicKit. Their use increases the overall
efficiency of the Legendre and spherical transforms and is therefore
encouraged. Easy substitution of our FFT and DCT routines with other,
optimized versions that the user may have should also be possible.
Information regarding how FFTPACK has been modified for use in SpharmonicKit is available here.

Though the spherical transforms in Spherepack are computed using the direct method, the amount of overhead involved in using any nondirect method may make the direct method faster, at least at small enough problem sizes.
There have been 83097 visitors since 18 Jun 2004. They mean you no harm. 
(Visitors to our spherical page) 
Return to Fast Fourier Analysis on Groups.