TEST/initialize_f1.c File Reference

Precompute data for the fast1 algorithm. More...

#include "../libftsh.h"

Functions
int	main (int argc, char *argv[])

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Detailed Description

Precompute data for the fast1 algorithm.

This program initializes the fast transform for spherical harmonics

A Fast Transform for Spherical Harmonics Martin J. Mohlenkamp Journal of Fourier Analysis and Applications, 5(2/3):159-184, 1999

This version is the simplest, both from an algorithmic standpoint and a user standpoint. Algorithmicly, it does the single partition version, which should have the lowest break-even point, but will be slower asymptotically. For the user, it provides routines with the fewest parameters to worry about. This is easier, but does not allow tuning.

This initialization algorithm is slow. For a degree N spherical harmonic representation it will take (O(N^3 log(N))). The idea is to initialize only once (for some set of parameters) and save it to a file.

Usage: call this routine with 4 command-line arguments: numpts band_limit epsilon out_file

• numpts -- the number of latitude points. We construct a gaussian quadrature for this number of points, although other node/weight combinations could be used. In this version, the number of points must be divisible by 4. Additional factors of 2 will improve performance. In general you should have a power of 2 times a factor smaller than 10.
• band_limit -- The restriction on the degree of the expansion (n in P^m_n notation). For gaussian nodes this must be less than numpts.
• epsilon -- The target precision. 1 > epsilon >0 This algorithm gives an approximate transform, but allows you to control the error. The idea is to choose the error here slightly smaller than the errors in the rest of your program. The larger the allowed error, the faster the algorithm will run. As you make the error smaller, the slow-down is not dramatic, so do not be afraid to ask for somewhat smaller error than you think you need.
• out_file -- The name of the file in which to put results of the initialization

Notes:

• epsilon directly controls the level of truncation of entries. By fiddling with the normalization, we think we now have it bounding the overall, accumulated (L^2) error.