saf_sh_internal.c File Reference

Internal source for the Spherical Harmonic Transform and Spherical Array Processing module (SAF_SH_MODULE) More...

#include "saf_sh.h"
#include "saf_sh_internal.h"

Go to the source code of this file.

Functions
float	wigner_3j (int j1, int j2, int j3, int m1, int m2, int m3)
	Computes the Wigner 3j symbol through the Racah formula found in http://mathworld.wolfram.com/Wigner3j-Symbol.html, Eq.7.
void	gaunt_mtx (int N1, int N2, int N, float *A)
	Constructs a matrix of Guant coefficients.
float	getP (int M, int i, int l, int a, int b, float R_1[3][3], float *R_lm1)
	Helper function for getSHrotMtxReal()
float	getU (int M, int l, int m, int n, float R_1[3][3], float *R_lm1)
	Helper function for getSHrotMtxReal()
float	getV (int M, int l, int m, int n, float R_1[3][3], float *R_lm1)
	Helper function for getSHrotMtxReal()
float	getW (int M, int l, int m, int n, float R_1[3][3], float *R_lm1)
	Helper function for getSHrotMtxReal()
void	getWnimu (int order, int mm, int ni, int mu, double *Wnimu)
	Helper function for sphESPRIT_create()
void	getVnimu (int order, int ni, int mu, double *Vnimu)
	Helper function for sphESPRIT_create()
void	muni2q (int order, int ni, int mu, int *idx_nimu, int *idx_nm)
	Helper function for sphESPRIT_create()

Detailed Description

Internal source for the Spherical Harmonic Transform and Spherical Array Processing module (SAF_SH_MODULE)

A collection of spherical harmonic related functions. Many of which have been derived from the MATLAB libraries found in [1-3].

See also

[1] https://github.com/polarch/Spherical-Harmonic-Transform Copyright (c) 2015, Archontis Politis, BSD-3-Clause License

[2] https://github.com/polarch/Array-Response-Simulator Copyright (c) 2015, Archontis Politis, BSD-3-Clause License

[3] https://github.com/polarch/Spherical-Array-Processing Copyright (c) 2016, Archontis Politis, BSD-3-Clause License

Author

Leo McCormack

Date

22.05.2016

License

ISC

Definition in file saf_sh_internal.c.

Function Documentation

gaunt_mtx()

void gaunt_mtx	(	int	N1,
		int	N2,
		int	N,
		float *	A )

Constructs a matrix of Guant coefficients.

Constructs the (N1+1)^2 x (N2+1)^2 x (N+1)^2 matrix of Gaunt coefficients which represent the integral of three spherical harmonics, such as G^q_{q',q''} = int_Omega Y_{q'}Y_{q''}Y^*_{q} mathrm{d} Omega.

With Gaunt coefficients, the spherical harmonic coefficients of the product of two spherical functions can be given directly as a linear relationship between the harmonic coefficients of the two functions.

Parameters

[in]	N1	Order of first harmonic coeffient
[in]	N2	Order of second harmonic coefficient
[in]	N	Target order
[out]	A	Gaunt matrix; FLAT: (N1+1)^2 x (N2+1)^2 x (N+1)^2

Definition at line 100 of file saf_sh_internal.c.

getP()

float getP	(	int	M,
		int	i,
		int	l,
		int	a,
		int	b,
		float	R_1[3][3],
		float *	R_lm1 )

Helper function for getSHrotMtxReal()

Definition at line 151 of file saf_sh_internal.c.

getU()

float getU	(	int	M,
		int	l,
		int	m,
		int	n,
		float	R_1[3][3],
		float *	R_lm1 )

Helper function for getSHrotMtxReal()

Definition at line 182 of file saf_sh_internal.c.

getV()

float getV	(	int	M,
		int	l,
		int	m,
		int	n,
		float	R_1[3][3],
		float *	R_lm1 )

Helper function for getSHrotMtxReal()

Definition at line 197 of file saf_sh_internal.c.

getVnimu()

void getVnimu	(	int	order,
		int	ni,
		int	mu,
		double *	Vnimu )

Helper function for sphESPRIT_create()

Definition at line 315 of file saf_sh_internal.c.

getW()

float getW	(	int	M,
		int	l,
		int	m,
		int	n,
		float	R_1[3][3],
		float *	R_lm1 )

Helper function for getSHrotMtxReal()

Definition at line 235 of file saf_sh_internal.c.

getWnimu()

void getWnimu	(	int	order,
		int	mm,
		int	ni,
		int	mu,
		double *	Wnimu )

Helper function for sphESPRIT_create()

Definition at line 268 of file saf_sh_internal.c.

muni2q()

void muni2q	(	int	order,
		int	ni,
		int	mu,
		int *	idx_nimu,
		int *	idx_nm )

Helper function for sphESPRIT_create()

+1

Definition at line 353 of file saf_sh_internal.c.

wigner_3j()

float wigner_3j	(	int	j1,
		int	j2,
		int	j3,
		int	m1,
		int	m2,
		int	m3 )

Computes the Wigner 3j symbol through the Racah formula found in http://mathworld.wolfram.com/Wigner3j-Symbol.html, Eq.7.

Parameters

[in]	j1	Wigner 3 j-symbol, j1
[in]	j2	Wigner 3 j-symbol, j2
[in]	j3	Wigner 3 j-symbol, j3
[in]	m1	Wigner 3 j-symbol, m1
[in]	m2	Wigner 3 j-symbol, m2
[in]	m3	Wigner 3 j-symbol, m3

Returns

wigner_3j symbol

Definition at line 45 of file saf_sh_internal.c.