pml.c File Reference

Source code for generating table of associated Legendre functions (Pml). More...

#include "s2kit/pml.h"
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "s2kit/chebyshev_nodes.h"
#include "s2kit/pmm.h"
#include "util/l2_norms.h"
#include "util/vector_funcs.h"

Go to the source code of this file.

Functions
void	GeneratePmlTable (const int bw, const int m, double *pml_table, double *workspace)
	Generates all of the Pmls for a specified value of m. More...

Detailed Description

Source code for generating table of associated Legendre functions (Pml).

Definition in file pml.c.

Function Documentation

GeneratePmlTable()

void GeneratePmlTable	(	const int	bw,
		const int	m,
		double *	pml_table,
		double *	workspace
	)

Generates all of the Pmls for a specified value of m.

P(m,l,j) respresents the associated Legendre function P_l^m evaluated at the j-th Chebyshev point (for the bandwidth bw): cos((2 * j + 1) * PI / (2 * bw)).

The array is placed in pml_table as follows:

P(m,m,0)      P(m,m,1)    ...  P(m,m,2*bw-1)
P(m,m+1,0)    P(m,m+1,1)  ...  P(m,m+1,2*bw-1)
P(m,m+2,0)    P(m,m+2,1)  ...  P(m,m+2,2*bw-1)
  ...
P(m,bw-1,0)   P(m,bw-1,1) ...  P(m,bw-1,2*bw-1)

This array will eventually be used by the naive transform algorithm (see naive.c).
This function will precompute the arrays necessary for the algorithm.

Parameters

bw	bandwidth
m	order
pml_table	result array with generated Pmls of size 2*bw*(bw-m)
workspace	space for computations of size 16*bw

Definition at line 41 of file pml.c.