Angular::SixJTable

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Lookup table for Wigner 6j symbols.

Pre-computes and caches Wigner 6j symbols \(\sixj{a/2}{b/2}{c/2}{d/2}{e/2}{f/2}\). All public functions accept arguments as \(2j\) or \(2k\) (integers), so that half-integer spins are handled exactly.

Storage exploits symmetry: the six entries of each symbol are permuted into a canonical "normal order" before lookup, so each physically distinct symbol is stored only once.

Note

• Call fill() (or the constructor) with the maximum \(2j\) or \(k\) that will be needed; the table can be extended at any time.
• Requesting a symbol outside the stored range returns 0 without warning.
• Non-mutable accessors are thread-safe once the table is fully built.

Warning

Symbols are stored up to the value passed to fill(); calls with larger arguments silently return 0.

#include <SixJTable.hpp>

Public Member Functions
	SixJTable ()=default
	Constructs an empty table; extend later with fill() or get().
	SixJTable (int max_2j_k)
	Constructs the table, pre-filling all symbols up to max_2j_k.
int	max_2jk () const
	Returns the maximum 2j (or k) currently stored; max(k) = 2*max(j).
std::size_t	size () const
	Returns the number of non-zero symbols stored in the table.
double	get_2 (int a, int b, int c, int d, int e, int f) const
	Returns 6j symbol {a/2, b/2, c/2; d/2, e/2, f/2}.
template<class A , class B , class C , class D , class E , class F >
double	get (const A &a, const B &b, const C &c, const D &d, const E &e, const F &f) const
	"Magic" table lookup: pass integers (for k) or DiracSpinors (for j).
bool	contains (int a, int b, int c, int d, int e, int f) const
	Returns true if the symbol is present in the table (absent symbols may be zero or simply out of range).
void	fill (int max_2j_k)
	Extends the table to cover all symbols up to max_2j_k.

Constructor & Destructor Documentation

SixJTable() [1/2]

Angular::SixJTable::SixJTable ( )

default

Constructs an empty table; extend later with fill() or get().

SixJTable() [2/2]

Angular::SixJTable::SixJTable ( int  max_2j_k )

inline

Constructs the table, pre-filling all symbols up to max_2j_k.

Calls fill() internally. Typically max_2j_k is the maximum \(2j\) of the orbital set; all symbols with every argument \(\le 2 \times \texttt{max\_2j\_k}\) are stored.

Parameters

max_2j_k

Maximum value of \(2j\) (or \(k\)) to pre-compute.

Member Function Documentation

max_2jk()

int Angular::SixJTable::max_2jk ( ) const

inline

Returns the maximum 2j (or k) currently stored; max(k) = 2*max(j).

size()

std::size_t Angular::SixJTable::size ( ) const

inline

Returns the number of non-zero symbols stored in the table.

get_2()

double Angular::SixJTable::get_2 ( int  a, int  b, int  c, int  d, int  e, int  f  ) const

inline

Returns 6j symbol {a/2, b/2, c/2; d/2, e/2, f/2}.

Arguments are \(2j\) or \(2k\) as integers. Returns 0 without warning if the symbol is outside the stored range.

Parameters

a,b,c,d,e,f

Twice the top/bottom rows of the 6j symbol.

get()

template<class A , class B , class C , class D , class E , class F >

double Angular::SixJTable::get ( const A &  a, const B &  b, const C &  c, const D &  d, const E &  e, const F &  f  ) const

inline

"Magic" table lookup: pass integers (for k) or DiracSpinors (for j).

Converts each argument via twojk() then delegates to get_2(). Example: get(Fa, Fb, k, Fc, Fd, k) returns \(\{j_a,j_b,k;j_c,j_d,k\}\). Returns 0 without warning if the symbol is outside the stored range.

Warning

Do not pre-multiply by 2.

contains()

bool Angular::SixJTable::contains ( int  a, int  b, int  c, int  d, int  e, int  f  ) const

inline

Returns true if the symbol is present in the table (absent symbols may be zero or simply out of range).

fill()

void Angular::SixJTable::fill ( int  max_2j_k )

inline

Extends the table to cover all symbols up to max_2j_k.

Called automatically by the constructor. Only needed explicitly when the required \(2j\) grows beyond the original maximum. No-op if max_2j_k does not exceed the current maximum.

Parameters

max_2j_k

New maximum value of \(2j\) (or \(k\)).

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The documentation for this class was generated from the following file:

• Angular/SixJTable.hpp