Detailed Description

Tools to create and work with permutations.

Functions
template<typename T, std::integral Int, size_t N>
constexpr std::array< T, N >	nda::permutations::apply (std::array< Int, N > const &p, std::array< T, N > const &a)
	Apply a permutation to a std::array.
template<typename T, std::integral Int, size_t N>
constexpr std::array< T, N >	nda::permutations::apply_inverse (std::array< Int, N > const &p, std::array< T, N > const &a)
	Apply the inverse of a permutation to a std::array.
template<std::integral Int, size_t N>
constexpr std::array< Int, N >	nda::permutations::compose (std::array< Int, N > const &p1, std::array< Int, N > const &p2)
	Composition of two permutations.
template<size_t N>
constexpr std::array< int, N >	nda::permutations::cycle (int p, int pos=N)
	Perform a forward (partial) cyclic permutation of the identity p times.
template<size_t N>
constexpr std::array< int, N >	nda::decode (uint64_t binary_representation)
	Decode a uint64_t into a std::array<int, N>.
template<size_t N>
constexpr uint64_t	nda::encode (std::array< int, N > const &a)
	Encode a std::array<int, N> in a uint64_t.
template<size_t N>
constexpr std::array< int, N >	nda::permutations::identity ()
	Get the identity permutation.
template<std::integral Int, size_t N>
constexpr std::array< Int, N >	nda::permutations::inverse (std::array< Int, N > const &p)
	Inverse of a permutation.
template<std::integral Int, size_t N>
constexpr bool	nda::permutations::is_valid (std::array< Int, N > const &p)
	Check if a given array is a valid permutation.
template<size_t N>
constexpr std::array< int, N >	nda::permutations::reverse_identity ()
	Get the reverse identity permutation.
template<size_t N>
constexpr std::array< int, N >	nda::permutations::transposition (int i, int j)
	Get the permutation representing a single given transposition.

Function Documentation

◆ apply()

template<typename T, std::integral Int, size_t N>

std::array< T, N > nda::permutations::apply	(	std::array< Int, N > const &	p,
		std::array< T, N > const &	a )

constexpr

#include <nda/layout/permutation.hpp>

Apply a permutation to a std::array.

The application of a permutation p to an array a results in a new array b such that b[i] = a[p[i]].

Template Parameters

T	Value type of the array.
Int	Integral type.
N	Size/Degree of the array/permutation.

Parameters

p	Permutation to apply.
a	std::array to apply the permutation to.

Returns: Result of applying the permutation to the array.

Definition at line 175 of file permutation.hpp.

◆ apply_inverse()

template<typename T, std::integral Int, size_t N>

std::array< T, N > nda::permutations::apply_inverse	(	std::array< Int, N > const &	p,
		std::array< T, N > const &	a )

constexpr

#include <nda/layout/permutation.hpp>

Apply the inverse of a permutation to a std::array.

Template Parameters

T	Value type of the array.
Int	Integral type.
N	Size/Degree of the array/permutation.

Parameters

p	Permutation to invert and apply.
a	std::array to apply the inverse permutation to.

Returns: Result of applying the inverse permutation to the array.

Definition at line 154 of file permutation.hpp.

◆ compose()

template<std::integral Int, size_t N>

std::array< Int, N > nda::permutations::compose	(	std::array< Int, N > const &	p1,
		std::array< Int, N > const &	p2 )

constexpr

#include <nda/layout/permutation.hpp>

Composition of two permutations.

The second argument is applied first. Composition is not commutative in general, i.e. compose(p1, p2) != compose(p2, p1).

Template Parameters

Int	Integral type.
N	Degree of the permutations.

Parameters

p1	Permutation to apply second.
p2	Permutation to apply first.

Returns: Composition of the two permutations.

Definition at line 114 of file permutation.hpp.

◆ cycle()

template<size_t N>

std::array< int, N > nda::permutations::cycle	(	int	p,
		int	pos = N )

constexpr

#include <nda/layout/permutation.hpp>

Perform a forward (partial) cyclic permutation of the identity p times.

The permutation is partial if pos >= 0 && pos < N. In this case, only the first pos elements are permuted, while the rest is left unchanged w.r.t the identity.

Template Parameters

N	Degree of the permutation.

Parameters

p	Number of times to perform the cyclic permutation.
pos	Number of elements to permute. If pos < N, the permutation is partial.

Returns: Result of the cyclic permutation.

Definition at line 238 of file permutation.hpp.

◆ decode()

template<size_t N>

std::array< int, N > nda::decode ( uint64_t binary_representation )

constexpr

#include <nda/layout/permutation.hpp>

Decode a uint64_t into a std::array<int, N>.

The 64-bit code is split into 4-bit chunks, and each chunk is then decoded into a value in the range [0, 15]. The 4 least significant bits are decoded into the first element, the next 4-bits into second element, and so on.

Template Parameters

N	Size of the array.

Parameters

binary_representation 64-bit code.

Returns: std::array<int, N> containing values in the range [0, 15].

Definition at line 43 of file permutation.hpp.

◆ encode()

template<size_t N>

uint64_t nda::encode ( std::array< int, N > const & a )

constexpr

#include <nda/layout/permutation.hpp>

Encode a std::array<int, N> in a uint64_t.

The values in the array are assumed to be in the range [0, 15]. Then each value is encoded in 4 bits, i.e. the first element is encoded in the 4 least significant bits, the second element in the next 4 bits, and so on.

Template Parameters

N	Size of the array.

Parameters

a	std::array<int, N> to encode.

Returns: 64-bit code.

Definition at line 60 of file permutation.hpp.

◆ identity()

template<size_t N>

std::array< int, N > nda::permutations::identity ( )

constexpr

#include <nda/layout/permutation.hpp>

Get the identity permutation.

Template Parameters

N	Degree of the permutation.

Returns: Identity permutation of degree N.

Definition at line 189 of file permutation.hpp.

◆ inverse()

template<std::integral Int, size_t N>

std::array< Int, N > nda::permutations::inverse ( std::array< Int, N > const & p )

constexpr

#include <nda/layout/permutation.hpp>

Inverse of a permutation.

The inverse, inv, of a permutation p is defined such that compose(p, inv) == compose(inv, p) == identity.

Template Parameters

Int	Integral type.
N	Degree of the permutations.

Parameters

p	Permutation to invert.

Returns: Inverse of the permutation.

Definition at line 134 of file permutation.hpp.

◆ is_valid()

template<std::integral Int, size_t N>

bool nda::permutations::is_valid ( std::array< Int, N > const & p )

constexpr

#include <nda/layout/permutation.hpp>

Check if a given array is a valid permutation.

A valid permutation is an array of integers with values in the range [0, N - 1] where each value appears exactly once.

Template Parameters

Int	Integral type.
N	Degree of the permutation.

Parameters

p	std:::array to check.

Returns: True if the array is a valid permutation, false otherwise.

Definition at line 92 of file permutation.hpp.

◆ reverse_identity()

template<size_t N>

std::array< int, N > nda::permutations::reverse_identity ( )

constexpr

#include <nda/layout/permutation.hpp>

Get the reverse identity permutation.

Template Parameters

N	Degree of the permutation.

Returns: Reverse of the identity permutation of degree N.

Definition at line 202 of file permutation.hpp.

◆ transposition()

template<size_t N>

std::array< int, N > nda::permutations::transposition	(	int	i,
		int	j )

constexpr

#include <nda/layout/permutation.hpp>

Get the permutation representing a single given transposition.

A transposition is a permutation in which only two elements are different from the identity permutation.

Template Parameters

N	Degree of the permutation.

Parameters

i	First index to transpose.
j	Second index to transpose.

Returns: Permutation corresponding to the transposition of i and j.

Definition at line 219 of file permutation.hpp.

Detailed Description

Functions

Function Documentation

◆ apply()

◆ apply_inverse()

◆ compose()

◆ cycle()

◆ decode()

◆ encode()

◆ identity()

◆ inverse()

◆ is_valid()

◆ reverse_identity()

◆ transposition()