Wigner symbol interactions. More...

#include "rational.h"
#include <wigner/wigxjpf/inc/wigxjpf.h>
#include <algorithm>
#include <array>

Macros
#define	DO_FAST_WIGNER 0

Functions
std::pair< Rational, Rational >	wigner_limits (std::pair< Rational, Rational > a, std::pair< Rational, Rational > b)

template<Index pos>
constexpr std::pair< Rational, Rational >	wigner3j_limits (const Rational a=0, const Rational b=0, const Rational c=0, const Rational d=0, const Rational e=0)

Numeric	wigner3j (const Rational j1, const Rational j2, const Rational j3, const Rational m1, const Rational m2, const Rational m3)
	Wigner 3J symbol.

Numeric	wigner6j (const Rational j1, const Rational j2, const Rational j3, const Rational l1, const Rational l2, const Rational l3)
	Wigner 6J symbol.

Index	make_wigner_ready (int largest, int fastest, int size)
	Ready Wigner.

bool	is_wigner_ready (int j)
	Tells if the function can deal with the input integer.

bool	is_wigner3_ready (const Rational &J)
	Tells if the function is ready for Wigner 3J calculations.

bool	is_wigner6_ready (const Rational &J)
	Tells if the function is ready for Wigner 6J calculations.

template<class ... Integer>
constexpr int	temp_init_size (Integer... vals) noexcept

Numeric	dwigner3j (Index M, Index J1, Index J2, Index J)
	Computes the wigner 3J symbol with floating point precision.

Numeric	dwigner6j (Index A, Index B, Index C, Index D, Index F)
	Computes the wigner 6J symbol with floating point precision.

Detailed Description

Wigner symbol interactions.

Author: Richard Larsson

Date: 2013-06-19

Definition in file wigner_functions.h.

Macro Definition Documentation

◆ DO_FAST_WIGNER

#define DO_FAST_WIGNER 0

Definition at line 23 of file wigner_functions.h.

Function Documentation

◆ dwigner3j()

Numeric dwigner3j	(	Index	M,
		Index	J1,
		Index	J2,
		Index	J
	)

Computes the wigner 3J symbol with floating point precision.

 /               \
 |  J1   J2   J  |

output = | | | M -M 0 | \ /

Parameters

M	Input as above
J1	Input as above
J2	Input as above
J	Input as above

Returns: Numeric

Definition at line 152 of file wigner_functions.cc.

◆ dwigner6j()

Numeric dwigner6j	(	Index	A,
		Index	B,
		Index	C,
		Index	D,
		Index	F
	)

Computes the wigner 6J symbol with floating point precision.

 /             \
 |  A   B   1  |

output = < > | D C F | \ /

Parameters

A	Input as above
B	Input as above
C	Input as above
D	Input as above
F	Input as above

Returns: Numeric

Definition at line 196 of file wigner_functions.cc.

References pow_negative_one().

◆ is_wigner3_ready()

bool is_wigner3_ready ( const Rational & J )

Tells if the function is ready for Wigner 3J calculations.

Parameters

[in] J Largest input into a Wigner 3J function call

Returns: true If is_wigner_ready(3J + 1) does; false Otherwise

Definition at line 142 of file wigner_functions.cc.

References is_wigner_ready().

Referenced by lbl_checkedCalc().

◆ is_wigner6_ready()

bool is_wigner6_ready ( const Rational & J )

Tells if the function is ready for Wigner 6J calculations.

Parameters

[in] J Largest input into a Wigner 6J function call

Returns: true If is_wigner_ready(4J + 1); false Otherwise

Definition at line 147 of file wigner_functions.cc.

References is_wigner_ready().

◆ is_wigner_ready()

bool is_wigner_ready ( int j )

Tells if the function can deal with the input integer.

Parameters

[in] j

Returns: true If j is less than max allowed j; false Otherwise

Definition at line 137 of file wigner_functions.cc.

Referenced by is_wigner3_ready(), and is_wigner6_ready().

◆ make_wigner_ready()

Index make_wigner_ready	(	int	largest,
		int	fastest,
		int	size
	)

Ready Wigner.

Parameters

[in]	largest
[in]	fastest
[in]	size	[3 or 6]

Returns: largest if successful

Definition at line 102 of file wigner_functions.cc.

Referenced by Wigner3Init(), and Wigner6Init().

◆ temp_init_size()

template<class ... Integer>

constexpr int temp_init_size ( Integer... vals )

constexprnoexcept

Definition at line 197 of file wigner_functions.h.

References v.

Referenced by Absorption::LineMixing::Makarov2020etal::relaxation_matrix_offdiagonal().

◆ wigner3j()

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

Wigner 3J symbol.

Run wigxjpf wig3jj for Rational symbol

/ \

j1 j2 j3
m1 m2 m3

\ /

See for definition: http://dlmf.nist.gov/34.2

Parameters

[in]	j1	as above
[in]	j2	as above
[in]	j3	as above
[in]	m1	as above
[in]	m2	as above
[in]	m3	as above

Returns: Numeric Symbol value

Definition at line 27 of file wigner_functions.cc.

References a, ARTS_USER_ERROR, b, c, d, and WIGNER3.

Referenced by Absorption::reduced_rovibrational_dipole(), Absorption::LineMixing::LinearRovibErrorCorrectedSudden::relaxation_matrix_offdiagonal(), and Zeeman::Model::Strength().

◆ wigner3j_limits()

template<Index pos>

constexpr std::pair< Rational, Rational > wigner3j_limits	(	const Rational	a = `0`,
		const Rational	b = `0`,
		const Rational	c = `0`,
		const Rational	d = `0`,
		const Rational	e = `0`
	)

constexpr

Return the limits where a wigner3j symbol can be non-zero

The values a-e are as in a call to wigner3j with pos determining the offset. The output is the range of valid values at the offset position given the relevant triangle equaility |x - y| <= z <= x + y and that the m1 + m2 = -m3 condition for the lower row values

Positional information: pos == 1: wigner3j(X, a, b, c, d, e): b <= X + a -> X <= b - a, and |X - a| <= b -> a - b <= X <= a + b pos == 2: wigner3j(a, X, b, c, d, e): b <= a + X -> X <= b - a, and |a - X| <= b -> a + b <= X <= a - b pos == 3: wigner3j(a, b, X, c, d, e): |a - b| <= X <= a + b -> X <= b - a pos == 4: wigner3j(a, b, c, X, d, e): -|a| <= X <= |a|, and X + d = - e -> X = - e - d pos == 5: wigner3j(a, b, c, d, X, e): -|b| <= X <= |b|, and d + X = - e -> X = - e - d pos == 6: wigner3j(a, b, c, d, e, X): -|c| <= X <= |c|, and d + e = - X -> X = - e - d

If there is no valid range, the function returns {RATIONAL_UNDEFINED, RATIONAL_UNDEFINED}

Parameters

[in]	pos	Position of value
[in]	a	An input
[in]	b	An input
[in]	c	An input
[in]	d	An input
[in]	e	An input

Returns: A valid range where both start and end are valid, or invalid numbers

Definition at line 80 of file wigner_functions.h.

References a, b, c, and d.

◆ wigner6j()

Numeric wigner6j	(	const Rational	j1,
		const Rational	j2,
		const Rational	j3,
		const Rational	l1,
		const Rational	l2,
		const Rational	l3
	)

Wigner 6J symbol.

Run wigxjpf wig6jj for Rational symbol

/ \ | j1 j2 j3 | < > | l1 l2 l3 | \ /

See for definition: http://dlmf.nist.gov/34.4

Parameters

[in]	j1	as above
[in]	j2	as above
[in]	j3	as above
[in]	l1	as above
[in]	l2	as above
[in]	l3	as above

Returns: Numeric Symbol value

Definition at line 59 of file wigner_functions.cc.

References a, ARTS_USER_ERROR, b, c, d, and WIGNER6.

Referenced by Absorption::LineMixing::Makarov2020etal::reduced_dipole(), Absorption::reduced_magnetic_quadrapole(), and Absorption::LineMixing::LinearRovibErrorCorrectedSudden::relaxation_matrix_offdiagonal().

◆ wigner_limits()

std::pair< Rational, Rational > wigner_limits	(	std::pair< Rational, Rational >	a,
		std::pair< Rational, Rational >	b
	)

Refine limits from multiple inputs

Parameters

[in]	a	A limit
[in]	a	Another limit

Returns: [low, high] for valid ranges of numbers or two undefined rationals

Definition at line 89 of file wigner_functions.cc.

References a, b, max(), and min().

Referenced by Absorption::LineMixing::Makarov2020etal::relaxation_matrix_offdiagonal().

Macros

Functions

Detailed Description

Macro Definition Documentation

◆ DO_FAST_WIGNER

Function Documentation

◆ dwigner3j()

◆ dwigner6j()

◆ is_wigner3_ready()

◆ is_wigner6_ready()

◆ is_wigner_ready()

◆ make_wigner_ready()

◆ temp_init_size()

◆ wigner3j()

◆ wigner3j_limits()

◆ wigner6j()

◆ wigner_limits()