SphericalHarmonics.h File Reference

#include <core/vector3.h>

Classes
struct	YlmProdTerm
	Term in real spherical harmonic expansion of a product of two real spherical harmonics. More...

Namespaces
	YlmInternal

Macros
#define	Power   pow
#define	DECLARE_Ylm(lm, code)   template<> __hostanddev__ double Ylm<lm>(double x, double y, double z) { return code; }
#define	SwitchTemplate_lm(l, m, fTemplate, argList)
	Switch a function templated over l,m for all supported l,m with parenthesis enclosed argument list argList.
#define	ADD(l, m, coeff)   result.push_back(YlmProdTerm(l,m,coeff))

Functions
double	bessel_jl (int l, double x)
	Spherical bessel function.
template<int lm>
__hostanddev__ double	YlmInternal::Ylm (double x, double y, double z)
	YlmInternal::DECLARE_Ylm (6,-0.31539156525252005 *(Power(x, 2)+Power(y, 2)-2.*Power(z, 2))) DECLARE_Ylm(8
*x y *x y	YlmInternal::DECLARE_Ylm (9,-0.5900435899266435 *y *(-3.*Power(x, 2)+Power(y, 2))) DECLARE_Ylm(11
*x y *x y *y *	YlmInternal::Power (x, 2)+Power(y
*x y *x y *y *	YlmInternal::Power (z, 2))) DECLARE_Ylm(12
*x y *x y *y *z *x *x y *x y *z	YlmInternal::DECLARE_Ylm (15, 0.5900435899266435 *x *(Power(x, 2)-3.*Power(y, 2))) DECLARE_Ylm(16
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y	YlmInternal::DECLARE_Ylm (17,-1.7701307697799304 *y *(-3.*Power(x, 2)+Power(y, 2))*z) DECLARE_Ylm(18
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y *x *y *y *z **	YlmInternal::Power (Power(x, 2)+Power(y, 2), 2)-72.*(Power(x
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y *x *y *y *z	YlmInternal::Power (y, 2))*Power(z
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y *x *y *y *z *	YlmInternal::Power (z, 4))) DECLARE_Ylm(21
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y *x *y *y *z *x *z *x y *x y *x *z	YlmInternal::DECLARE_Ylm (24, 0.6258357354491761 *(Power(x, 4)-6.*Power(x, 2)*Power(y, 2)+Power(y, 4))) DECLARE_Ylm(25
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y *x *y *y *z *x *z *x y *x y *x *z *y **	YlmInternal::Power (x, 4)-10.*Power(x
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y *x *y *y *z *x *z *x y *x y *x *z *y	YlmInternal::DECLARE_Ylm (26, 8.302649259524166 *x *(x-y)*y *(x+y)*z) DECLARE_Ylm(27
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y *x *y *y *z *x *z *x y *x y *x *z *y *y *x *y *z *y *z *x *x y *x y *z *x *z	YlmInternal::DECLARE_Ylm (35, 0.6563820568401701 *x *(Power(x, 4)-10.*Power(x, 2)*Power(y, 2)+5.*Power(y, 4))) DECLARE_Ylm(36
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y *x *y *y *z *x *z *x y *x y *x *z *y *y *x *y *z *y *z *x *x y *x y *z *x *z *x *y	YlmInternal::DECLARE_Ylm (37, 2.366619162231752 *y *(5.*Power(x, 4)-10.*Power(x, 2)*Power(y, 2)+Power(y, 4))*z) DECLARE_Ylm(38
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y *x *y *y *z *x *z *x y *x y *x *z *y *y *x *y *z *y *z *x *x y *x y *z *x *z *x *y *x *x y *y *x y *y *z *x *y *y *z **	YlmInternal::Power (Power(x, 2)+Power(y, 2), 3)+90.*Power(Power(x
*x y *x y *y *z *x *x y *x y *z *x *x y *y *x y *x *y *y *z *x *z *x y *x y *x *z *y *y *x *y *z *y *z *x *x y *x y *z *x *z *x *y *x *x y *y *x y *y *z *x *y *y *z *	YlmInternal::Power (z, 6))) DECLARE_Ylm(43
template<int lm>
__hostanddev__ double	Ylm (const vector3<> &qhat)
	Index by combined lm := l*(l+1)+m index (useful when static-looping over all l,m)
template<int l, int m>
__hostanddev__ double	Ylm (const vector3<> &qhat)
	Index by l and m separately.
template<int l, int m>
void	set_Ylm (const vector3<> qHat, double &result)
	Use above macro to provide a non-templated version of the function.
double	Ylm (int l, int m, const vector3<> &qHat)
std::vector< YlmProdTerm >	expandYlmProd (int lm1, int lm2)
std::vector< YlmProdTerm >	expandYlmProd (int l1, int m1, int l2, int m2)
	Wrapper function expandYlmProd with individual indices.

Detailed Description

Real spherical Harmonics and spherical bessel functions