wigner_functions.h File Reference

#include "rational.h"
#include <cmath>
#include "make_array.h"

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Functions
Numeric	wigner3j (const Rational j1, const Rational j2, const Rational j3, const Rational m1, const Rational m2, const Rational m3)
Numeric	wigner6j (const Rational j1, const Rational j2, const Rational j3, const Rational l1, const Rational l2, const Rational l3)
Numeric	ECS_wigner (Rational L, Rational Nl, Rational Nk, Rational Jk_lower, Rational Jl_lower, Rational Jk_upper, Rational Jl_upper)
Numeric	factorials (const ArrayOfIndex &NomFac, const ArrayOfIndex &DenomFac)
void	primes (ArrayOfIndex &output, const Index input)
void	powers (ArrayOfIndex &output, const ArrayOfIndex primes, const Index input)
Numeric	triangle_coefficient (const Rational a, const Rational b, const Rational c)
bool	triangular_inequality (const Rational x, const Rational y, const Rational z)

Function Documentation

ECS_wigner()

Numeric ECS_wigner	(	Rational	L,
		Rational	Nl,
		Rational	Nk,
		Rational	Jk_lower,
		Rational	Jl_lower,
		Rational	Jk_upper,
		Rational	Jl_upper
	)

Definition at line 185 of file wigner_functions.cc.

References wigner3j(), and wigner6j().

Referenced by test45().

factorials()

Numeric factorials	(	const ArrayOfIndex &	NomFac,
		const ArrayOfIndex &	DenomFac
	)

Definition at line 291 of file wigner_functions.cc.

References max, min, Array< base >::nelem(), powers(), primes(), and temp.

Referenced by triangle_coefficient(), wigner3j(), and wigner6j().

powers()

void powers	(	ArrayOfIndex &	output,
		const ArrayOfIndex	primes,
		const Index	input
	)

Definition at line 271 of file wigner_functions.cc.

References Array< base >::nelem().

Referenced by factorials().

primes()

void primes	(	ArrayOfIndex &	output,
		const Index	input
	)

Definition at line 232 of file wigner_functions.cc.

Referenced by factorials().

triangle_coefficient()

Numeric triangle_coefficient	(	const Rational	a,
		const Rational	b,
		const Rational	c
	)

Definition at line 212 of file wigner_functions.cc.

References factorials(), and Rational::toIndex().

Referenced by wigner6j().

triangular_inequality()

bool triangular_inequality	(	const Rational	x,
		const Rational	y,
		const Rational	z
	)

Definition at line 220 of file wigner_functions.cc.

References abs.

Referenced by wigner3j(), and wigner6j().

wigner3j()

Numeric wigner3j	(	const Rational	j1,
		const Rational	j2,
		const Rational	j3,
		const Rational	m1,
		const Rational	m2,
		const Rational	m3
	)

Equation 34.2.4 in http://dlmf.nist.gov/34.2

Some test cases to simplify the calculations are made for m_i=0.

Definition at line 28 of file wigner_functions.cc.

References abs, factorials(), Rational::toIndex(), and triangular_inequality().

Referenced by ECS_wigner().

wigner6j()

Numeric wigner6j	(	const Rational	j1,
		const Rational	j2,
		const Rational	j3,
		const Rational	J1,
		const Rational	J2,
		const Rational	J3
	)

Equation 34.4.2 in http://dlmf.nist.gov/34.4 may be invalid.

Using Equation 4 in http://mathworld.wolfram.com/Wigner6j-Symbol.html instead

Simplifications are made for J1 = 1.

Definition at line 119 of file wigner_functions.cc.

References factorials(), Rational::toIndex(), Rational::toNumeric(), triangle_coefficient(), and triangular_inequality().

Referenced by ECS_wigner(), and test45().