Namespaces
	TiledArray::symmetry

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

class	TiledArray::symmetry::PermutationGroup
	Permutation group. More...

class	TiledArray::symmetry::SymmetricGroup
	Symmetric group. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

PermutationGroup	TiledArray::symmetry::intersect (const PermutationGroup &G1, const PermutationGroup &G2)

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

Detailed Description

Function Documentation

◆ conjugate()

PermutationGroup TiledArray::symmetry::conjugate	(	const PermutationGroup &	G,
		const PermutationGroup::Permutation &	h
	)

inline

Computes conjugate permutation group obtained by the action of a permutation.

Conjugate of group $ G $ under the action of element $ h $ is a group $\{ a: a = h g h^{-1}, \forall g \in G \}$ .

Note: Since all permutation groups are subgroups of the symmetric group on the "infinite" set $\{ 0, 1, \dots \}$ , this can be used to "shift" the domain of G by action of h that permutes elements in the domain of G with those outside its domain, e.g. if on domain $\{0,1\}$ , conjugation with will produce on domain $\{0,2\}$ .

Parameters

G	input PermutationGroup
h	input Permutation

Returns: conjugate PermutationGroup

Definition at line 381 of file permutation_group.h.

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◆ intersect()

PermutationGroup TiledArray::symmetry::intersect	(	const PermutationGroup &	G1,
		const PermutationGroup &	G2
	)

inline

Computes intersect of 2 PermutationGroups

Note: The intersect is guaranteed to be a subgroup for both groups, hence this is the largest common subgroup.

Parameters

G1	PermutationGroup
G2	PermutationGroup

Returns: PermutationGroup

Definition at line 395 of file permutation_group.h.

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◆ is_lexicographically_smallest()

template<typename MultiIndex >

bool TiledArray::symmetry::is_lexicographically_smallest	(	const MultiIndex &	idx,
		const PermutationGroup &	pg
	)

determines whether a given MultiIndex is lexicographically smallest among all indices generated by the action of pg.

Template Parameters

MultiIndex a sequence type that is directly addressable, i.e. has a fast operator[]

Parameters

idx	an Index object
pg	the PermutationGroup

Returns: false if action of a permutation in pg can produce an Index that is lexicographically smaller than idx (i.e. there exists i such that pg[i]*idx is lexicographically less than idx), true otherwise

Definition at line 353 of file permutation_group.h.

◆ operator!=() [1/2]

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

inline

PermutationGroup inequality operator.

Parameters

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

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

Definition at line 225 of file permutation_group.h.

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◆ operator!=() [2/2]

bool TiledArray::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 406 of file permutation.h.

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◆ operator*()

Permutation TiledArray::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 450 of file permutation.h.

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◆ operator*=()

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

inline

return *this ^ other

Definition at line 456 of file permutation.h.

◆ operator-()

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

inline

Inverse permutation operator.

Parameters

perm	The permutation to be inverted

Returns: perm.inverse()

Definition at line 440 of file permutation.h.

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◆ operator<() [1/2]

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

inline

PermutationGroup less-than operator.

Parameters

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

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

Definition at line 235 of file permutation_group.h.

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◆ operator<() [2/2]

bool TiledArray::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 416 of file permutation.h.

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◆ operator<<() [1/2]

std::ostream & TiledArray::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 426 of file permutation.h.

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◆ operator<<() [2/2]

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

inline

Add permutation group to an output stream.

Parameters

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

Returns: The output stream

Definition at line 245 of file permutation_group.h.

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◆ operator==() [1/2]

bool TiledArray::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 395 of file permutation.h.

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◆ operator==() [2/2]

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

inline

PermutationGroup equality operator.

Parameters

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

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

Definition at line 214 of file permutation_group.h.

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◆ operator^()

Permutation TiledArray::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 467 of file permutation.h.

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◆ stabilizer()

template<typename Set >

PermutationGroup TiledArray::symmetry::stabilizer	(	const PermutationGroup &	G,
		const Set &	f
	)

inline

Computes the largest subgroup of a permutation group that leaves the given set of indices fixed.

Template Parameters

Set	a set of indices

Parameters

G	input PermutationGroup
f	input Set

Returns: the fixed set subgroup of G

Definition at line 411 of file permutation_group.h.

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Namespaces

Classes

Functions

Detailed Description

Function Documentation

◆ conjugate()

◆ intersect()

◆ is_lexicographically_smallest()

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator*()

◆ operator*=()

◆ operator-()

◆ operator<() [1/2]

◆ operator<() [2/2]

◆ operator<<() [1/2]

◆ operator<<() [2/2]

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator^()

◆ stabilizer()