This is the README file for libftsh, a library that implements a fast transform for spherical harmonics.

Further information may be found at http://www.ohiouniversityfaculty.com/mohlenka/ Please report bugs, missing/confusing instructions, suggested improvements, etc. to mohle.nosp@m.nka@.nosp@m.ohio..nosp@m.edu .

What it does:

The library libftsh implements a fast transform for spherical harmonics. The difficult part of the transform is the Associated Legendre Transform portion, and this library only does that portion. The rest of the transform, such as the fourier transform in longitude, transpose, and overall data organization, is left up to the user.

The fast transform implemented is based on the paper: A Fast Transform for Spherical Harmonics Martin J. Mohlenkamp Journal of Fourier Analysis and Applications, 5(2/3):159-184, 1999.

Key points:

This is not a simple, user-friendly program for the spherical harmonic novice.
This transform is approximate, but allows you to set the precision needed. This does not cause any difficulties, but does require you to think about the precision needed.
This transform has a slow initialization phase. If you plan to do only a few transforms of a given size, do the direct transform instead. For precision 1e-6 this transform breaks even at around degree 100 (200x100 grid). If you are doing small transforms, do not use this algorithm.
It is numerically stable, and can be used at large degrees/orders and at high precision.
It is not the full transform. It only does the hard part, which is the Associated Legendre Transform portion. By not doing the easy part, it allows the user greater flexibility.

Installation:

Install the fftw library (version >= 2.1.3), available from www.fftw.org.
Adjust make.inc for your local system. Choose you favorite compiler options, decide where the compiled library will go, choose your precision, etc.
If you want to run in single precision, adjust the USE_double flag in libftsh.h and make sure the appropriate fftw headers are selected.
Run 'make'.
Move to the TEST directory and run the tests as directed by the README file there.

Usage:

Within the TEST directory are examples of how to use these routines. The TEST/README file there will direct you to the proper files and run you through an example session.

Acknowledgements:

Thanks to Ronald Coifman (Yale U) for advising me on this (my thesis) project.

Thanks to Gregory Beylkin (U of Colorado) for helping me improve the implementation.

Thanks to Andrew DienstFrey (NIST) and Bill Spotz (NCAR) for helping test the code.

Thanks to Dean Allen Provins (U of Calgary) and Yue Shi Lai (Columbia U) for pointing out bugs.

This material is based upon work supported by the National Science Foundation.