Namespaces
	detail

Classes
class	Permutation
	Permutation of a sequence of objects indexed by base-0 indices. More...

class	PermutationGroup
	Permutation group. More...

class	Representation

class	SymmetricGroup
	Symmetric group. More...

Functions
bool	operator== (const Permutation &p1, const Permutation &p2)
	Permutation equality operator. More...

bool	operator!= (const Permutation &p1, const Permutation &p2)
	Permutation inequality operator. More...

bool	operator< (const Permutation &p1, const Permutation &p2)
	Permutation less-than operator. More...

std::ostream &	operator<< (std::ostream &output, const Permutation &p)
	Add permutation to an output stream. More...

Permutation	operator- (const Permutation &perm)
	Inverse permutation operator. More...

Permutation	operator* (const Permutation &p1, const Permutation &p2)
	Permutation multiplication operator. More...

Permutation &	operator*= (Permutation &p1, const Permutation &p2)
	return *this ^ other More...

Permutation	operator^ (const Permutation &perm, int n)
	Raise `perm` to the n-th power. More...

template<typename T , std::size_t N>
std::array< T, N >	operator* (const Permutation &perm, const std::array< T, N > &a)
	Permute a `std::array`. More...

template<typename T , std::size_t N>
std::array< T, N > &	operator*= (std::array< T, N > &a, const Permutation &perm)
	In-place permute a `std::array`. More...

template<typename T , typename A >
std::vector< T >	operator* (const Permutation &perm, const std::vector< T, A > &v)
	permute a `std::vector<T>` More...

template<typename T , typename A >
std::vector< T, A > &	operator*= (std::vector< T, A > &v, const Permutation &perm)
	In-place permute a `std::array`. More...

bool	operator== (const PermutationGroup &p1, const PermutationGroup &p2)
	PermutationGroup equality operator. More...

bool	operator!= (const PermutationGroup &p1, const PermutationGroup &p2)
	PermutationGroup inequality operator. More...

bool	operator< (const PermutationGroup &p1, const PermutationGroup &p2)
	PermutationGroup less-than operator. More...

std::ostream &	operator<< (std::ostream &output, const PermutationGroup &p)
	Add permutation group to an output stream. More...

template<typename MultiIndex >
bool	is_lexicographically_smallest (const MultiIndex &idx, const PermutationGroup &pg)

PermutationGroup	conjugate (const PermutationGroup &G, const PermutationGroup::Permutation &h)
	Computes conjugate permutation group obtained by the action of a permutation. More...

PermutationGroup	intersect (const PermutationGroup &G1, const PermutationGroup &G2)

template<typename Set >
PermutationGroup	stabilizer (const PermutationGroup &G, const Set &f)
	Computes the largest subgroup of a permutation group that leaves the given set of indices fixed. More...

template<typename T >
T	identity ()
	identity for group of objects of type T More...

Function Documentation

◆ identity()

template<typename T >

T TiledArray::symmetry::identity ( )

identity for group of objects of type T

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◆ operator!=()

bool TiledArray::symmetry::operator!=	(	const Permutation &	p1,
		const Permutation &	p2
	)

inline

Permutation inequality operator.

Parameters

p1	The left-hand permutation to be compared
p2	The right-hand permutation to be compared

Returns: true if any element of p1 is not equal to that of p2, otherwise false.

Definition at line 481 of file permutation.h.

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◆ operator*() [1/3]

Permutation TiledArray::symmetry::operator*	(	const Permutation &	p1,
		const Permutation &	p2
	)

inline

Permutation multiplication operator.

Parameters

p1	The left-hand permutation
p2	The right-hand permutation

Returns: The product of p1 and p2 (which is the permutation of p2 by p1).

Definition at line 523 of file permutation.h.

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◆ operator*() [2/3]

template<typename T , std::size_t N>

std::array<T,N> TiledArray::symmetry::operator*	(	const Permutation &	perm,
		const std::array< T, N > &	a
	)

inline

Permute a std::array.

Template Parameters

T	The element type of the array
N	The size of the array

Parameters

perm	The permutation
a	The array to be permuted

Returns: A permuted copy of a

Exceptions

TiledArray::Exception When the dimension of the permutation is not equal to the size of a.

Definition at line 557 of file permutation.h.

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◆ operator*() [3/3]

template<typename T , typename A >

std::vector<T> TiledArray::symmetry::operator*	(	const Permutation &	perm,
		const std::vector< T, A > &	v
	)

inline

permute a std::vector<T>

Template Parameters

T	The element type of the vector
A	The allocator type of the vector

Parameters

perm	The permutation
v	The vector to be permuted

Returns: A permuted copy of v

Exceptions

TiledArray::Exception When the dimension of the permutation is not equal to the size of v.

Definition at line 589 of file permutation.h.

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◆ operator*=() [1/3]

Permutation& TiledArray::symmetry::operator*=	(	Permutation &	p1,
		const Permutation &	p2
	)

inline

return *this ^ other

Definition at line 529 of file permutation.h.

◆ operator*=() [2/3]

template<typename T , std::size_t N>

std::array<T,N>& TiledArray::symmetry::operator*=	(	std::array< T, N > &	a,
		const Permutation &	perm
	)

inline

In-place permute a std::array.

Template Parameters

T	The element type of the array
N	The size of the array

Parameters

[out]	a	The array to be permuted
[in]	perm	The permutation

Returns: A reference to a

Exceptions

TiledArray::Exception When the dimension of the permutation is not equal to the size of a.

Definition at line 573 of file permutation.h.

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◆ operator*=() [3/3]

template<typename T , typename A >

std::vector<T, A>& TiledArray::symmetry::operator*=	(	std::vector< T, A > &	v,
		const Permutation &	perm
	)

inline

In-place permute a std::array.

Template Parameters

T	The element type of the vector
A	The allocator type of the vector

Parameters

[out]	v	The vector to be permuted
[in]	perm	The permutation

Returns: A reference to v

Exceptions

TiledArray::Exception When the dimension of the permutation is not equal to the size of v.

Definition at line 605 of file permutation.h.

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◆ operator-()

Permutation TiledArray::symmetry::operator- ( const Permutation & perm )

inline

Inverse permutation operator.

Parameters

perm	The permutation to be inverted

Returns: perm.inverse()

Definition at line 513 of file permutation.h.

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◆ operator<()

bool TiledArray::symmetry::operator<	(	const Permutation &	p1,
		const Permutation &	p2
	)

inline

Permutation less-than operator.

Parameters

p1	The left-hand permutation to be compared
p2	The right-hand permutation to be compared

Returns: true if the elements of p1 are lexicographically less than that of p2, otherwise false.

Definition at line 491 of file permutation.h.

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◆ operator<<()

std::ostream& TiledArray::symmetry::operator<<	(	std::ostream &	output,
		const Permutation &	p
	)

inline

Add permutation to an output stream.

Parameters

[out]	output	The output stream
[in]	p	The permutation to be added to the output stream

Returns: The output stream

Definition at line 502 of file permutation.h.

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◆ operator==()

bool TiledArray::symmetry::operator==	(	const Permutation &	p1,
		const Permutation &	p2
	)

inline

Permutation equality operator.

Parameters

p1	The left-hand permutation to be compared
p2	The right-hand permutation to be compared

Returns: true if all elements of p1 and p2 are equal and in the same order, otherwise false.

Definition at line 470 of file permutation.h.

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◆ operator^()

Permutation TiledArray::symmetry::operator^	(	const Permutation &	perm,
		int	n
	)

inline

Raise perm to the n-th power.

Constructs the permutation $ P^n $ , where $ P $ is the permutation perm.

Parameters

perm	The base permutation
n	Exponent value

Returns: This permutation raised to the n-th power

Definition at line 540 of file permutation.h.

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Namespaces

Classes

Functions

Function Documentation

◆ identity()

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/3]

◆ operator*=() [2/3]

◆ operator*=() [3/3]

◆ operator-()

◆ operator<()

◆ operator<<()

◆ operator==()

◆ operator^()