weights.c File Reference

Contains the function that generates the weights for a Legendre transform. More...

#include "s2kit/weights.h"
#include <math.h>

Go to the source code of this file.

Functions
void	GenerateWeightsForDLT (const int bw, double *weights)
	Generates weights for both even and odd order Legendre transforms for a given bandwidth. More...

Detailed Description

Contains the function that generates the weights for a Legendre transform.

Basically, it contains the implementation of the formula as defined in the tensor paper, and also given in the so(3) paper and is mentioned in the s^2 paper! // TODO find these pages

This formula is slightly different from the one given in the original Driscoll and Healy paper because they were sampling at the poles, and now we're not.

In pseudo-TeX, the formula for the bandwidth B weights is:

w_B(j) = 2/B sin((pi*(2j+1))/(4B)) *
    sum_{k=0}^{B-1} 1/(2k+1)*sin((2j+1)(2k+1)pi/(4B))
where j = 0, 1, ..., 2 B - 1 

Definition in file weights.c.

Function Documentation

GenerateWeightsForDLT()

void GenerateWeightsForDLT	(	const int	bw,
		double *	weights
	)

Generates weights for both even and odd order Legendre transforms for a given bandwidth.

Parameters

bw	bandwidth of transform
weights	array of size 4*bw which will contain the weights for both even (starting at weights[0]) and odd (weights[2*bw]) transforms

Note

If you want to use these weights for an odd order transform, given the way the code is set up, you have to multiply the j-th weight by sin(pi*(2j+1)/(4B)).
It is taken into account in this library functions.

Definition at line 32 of file weights.c.