Documentation

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

Permutation class is used as an argument in all permutation operations on other objects. Permutations can be applied to sequences of objects:

b = p * a; // apply permutation p to sequence a and assign the result to

sequence b. a *= p; // apply permutation p (in-place) to sequence a.

Permutations can also be composed, e.g. multiplied and inverted:

p3 = p1 * p2; // computes product of permutations of p1 and p2

p1_inv = p1.inv(); // computes inverse of p1

Definition at line 117 of file permutation.h.

Public Types
typedef Permutation Permutation_

typedef unsigned int index_type

template<typename T >
using vector = container::svector< T >

typedef std::map< index_type, index_type > Map

typedef Map::const_iterator const_iterator

Public Member Functions
Permutation ()=default

Permutation (const Permutation &)=default

Permutation (Permutation &&)=default

~Permutation ()=default

Permutation & operator= (const Permutation &)=default

Permutation & operator= (Permutation &&other)=default

template<typename InIter , typename std::enable_if< TiledArray::detail::is_input_iterator< InIter >::value >::type * = nullptr>
Permutation (InIter first, InIter last)
Construct permutation using its 1-line form given by range [first,last) More...

template<typename Index , typename std::enable_if< TiledArray::detail::is_integral_range_v< Index >, bool >::type * = nullptr>
Permutation (Index &&a)
Construct permutation using 1-line form given as an integral range. More...

template<typename Integer , std::enable_if_t< std::is_integral_v< Integer >> * = nullptr>
Permutation (std::initializer_list< Integer > list)
Construct permutation with an initializer list. More...

Permutation (Map p)
Construct permutation using its compressed 2-line form given by std::map. More...

unsigned int domain_size () const
Permutation domain size. More...

index_type operator[] (index_type e) const
Computes image of an element under this permutation. More...

template<typename Set >
Set domain () const
Computes the domain of this permutation. More...

template<typename Integer , typename std::enable_if< std::is_integral< Integer >::value >::type * = nullptr>
bool is_in_domain (Integer i) const
Test if an index is in the domain of this permutation. More...

vector< vector< index_type > > cycles () const
Cycles decomposition. More...

Permutation mult (const Permutation &other) const
Product of this permutation by `other`. More...

Permutation inv () const
Construct the inverse of this permutation. More...

Permutation pow (int n) const
Raise this permutation to the n-th power. More...

const Map & data () const
Data accessor. More...

Permutation identity () const
Idenity permutation factory method. More...

template<typename Archive >
void serialize (Archive &ar)
Serialize permutation. More...

Iterator accessors
Permutation iterators dereference into `std::pair<index_type,index_type>`, where `first` is the domain index, `second` is its image E.g. `Permutation::begin()` of $\{1->3, 2->1, 3->2\}$ dereferences to `std::pair` {1,3} .
const_iterator begin () const
Begin element iterator factory function. More...

const_iterator cbegin () const
Begin element iterator factory function. More...

const_iterator end () const
End element iterator factory function. More...

const_iterator cend () const
End element iterator factory function. More...

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

Member Typedef Documentation

◆ const_iterator

typedef Map::const_iterator TiledArray::symmetry::Permutation::const_iterator

Definition at line 124 of file permutation.h.

◆ index_type

typedef unsigned int TiledArray::symmetry::Permutation::index_type

Definition at line 120 of file permutation.h.

◆ Map

typedef std::map<index_type, index_type> TiledArray::symmetry::Permutation::Map

Definition at line 123 of file permutation.h.

◆ Permutation_

typedef Permutation TiledArray::symmetry::Permutation::Permutation_

Definition at line 119 of file permutation.h.

◆ vector

template<typename T >

using TiledArray::symmetry::Permutation::vector = container::svector<T>

Definition at line 122 of file permutation.h.

Constructor & Destructor Documentation

◆ Permutation() [1/7]

TiledArray::symmetry::Permutation::Permutation ( )

default

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◆ Permutation() [2/7]

TiledArray::symmetry::Permutation::Permutation ( const Permutation & )

default

◆ Permutation() [3/7]

TiledArray::symmetry::Permutation::Permutation ( Permutation && )

default

◆ ~Permutation()

TiledArray::symmetry::Permutation::~Permutation ( )

default

◆ Permutation() [4/7]

template<typename InIter , typename std::enable_if< TiledArray::detail::is_input_iterator< InIter >::value >::type * = nullptr>

TiledArray::symmetry::Permutation::Permutation	(	InIter	first,
		InIter	last
	)

inline

Construct permutation using its 1-line form given by range [first,last)

Template Parameters

InIter An input iterator type

Parameters

first	The beginning of the iterator range
last	The end of the iterator range

Exceptions

TiledArray::Exception if invalid input is given.

See also: valid_permutation(first,last)

Definition at line 200 of file permutation.h.

◆ Permutation() [5/7]

template<typename Index , typename std::enable_if< TiledArray::detail::is_integral_range_v< Index >, bool >::type * = nullptr>

TiledArray::symmetry::Permutation::Permutation ( Index && a )

inlineexplicit

Construct permutation using 1-line form given as an integral range.

Template Parameters

Index An integral range type

Parameters

a	range that specifies permutation in 1-line form

Definition at line 216 of file permutation.h.

◆ Permutation() [6/7]

template<typename Integer , std::enable_if_t< std::is_integral_v< Integer >> * = nullptr>

TiledArray::symmetry::Permutation::Permutation ( std::initializer_list< Integer > list )

inlineexplicit

Construct permutation with an initializer list.

Template Parameters

Integer an integral type

Parameters

list	An initializer list of integers

Definition at line 224 of file permutation.h.

◆ Permutation() [7/7]

TiledArray::symmetry::Permutation::Permutation ( Map p )

inline

Construct permutation using its compressed 2-line form given by std::map.

Parameters

p the map

Definition at line 230 of file permutation.h.

Member Function Documentation

◆ begin()

const_iterator TiledArray::symmetry::Permutation::begin ( ) const

inline

Begin element iterator factory function.

Returns: An iterator that points to the beginning of the range

Definition at line 249 of file permutation.h.

◆ cbegin()

const_iterator TiledArray::symmetry::Permutation::cbegin ( ) const

inline

Begin element iterator factory function.

Returns: An iterator that points to the beginning of the range

Definition at line 254 of file permutation.h.

◆ cend()

const_iterator TiledArray::symmetry::Permutation::cend ( ) const

inline

End element iterator factory function.

Returns: An iterator that points to the end of the range

Definition at line 264 of file permutation.h.

◆ cycles()

vector<vector<index_type> > TiledArray::symmetry::Permutation::cycles ( ) const

inline

Cycles decomposition.

Certain algorithms are more efficient with permutations represented as a set of cyclic transpositions. This function returns the set of cycles that represent this permutation. For example, permutation $\{3, 2, 1, 0 \}$ is represented as the following set of cycles: (0,3)(1,2). The canonical format for the cycles is:

Cycles of length 1 are skipped.
Each cycle is in order of increasing elements.
Cycles are in the order of increasing first elements.

Returns: the set of cycles (in canonical format) that represent this permutation

Definition at line 320 of file permutation.h.

◆ data()

const Map& TiledArray::symmetry::Permutation::data ( ) const

inline

Data accessor.

gives direct access to std::map that encodes the Permutation

Returns: std::map<index_type,index_type> object encoding the permutation in compressed two-line form

Definition at line 425 of file permutation.h.

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◆ domain()

template<typename Set >

Set TiledArray::symmetry::Permutation::domain ( ) const

inline

Computes the domain of this permutation.

Template Parameters

Set	a container type in which the result will be returned

Returns: the domain of this permutation, as a Set

Definition at line 286 of file permutation.h.

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◆ domain_size()

unsigned int TiledArray::symmetry::Permutation::domain_size ( ) const

inline

Permutation domain size.

Returns: The number of elements in the domain of permutation

Definition at line 235 of file permutation.h.

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◆ end()

const_iterator TiledArray::symmetry::Permutation::end ( ) const

inline

End element iterator factory function.

Returns: An iterator that points to the end of the range

Definition at line 259 of file permutation.h.

◆ identity()

Permutation TiledArray::symmetry::Permutation::identity ( ) const

inline

Idenity permutation factory method.

Returns: the identity permutation

Definition at line 430 of file permutation.h.

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◆ inv()

Permutation TiledArray::symmetry::Permutation::inv ( ) const

inline

Construct the inverse of this permutation.

The inverse of permutation $ P $ is defined as $P \times P^{-1} = P^{-1} \times P = I$ , where $ I $ is the identity permutation.

Returns: The inverse of this permutation

Definition at line 381 of file permutation.h.

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◆ is_in_domain()

template<typename Integer , typename std::enable_if< std::is_integral< Integer >::value >::type * = nullptr>

bool TiledArray::symmetry::Permutation::is_in_domain ( Integer i ) const

inline

Test if an index is in the domain of this permutation.

Template Parameters

Integer an integer type

Parameters

i	an index whose presence in domain is tested

Returns: true , if i is in the domain, false otherwise

Definition at line 303 of file permutation.h.

◆ mult()

Permutation TiledArray::symmetry::Permutation::mult ( const Permutation & other ) const

inline

Product of this permutation by other.

Parameters

other a Permutation

Returns: other * this, i.e. this applied first, then other

Definition at line 360 of file permutation.h.

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◆ operator=() [1/2]

Permutation& TiledArray::symmetry::Permutation::operator= ( const Permutation & )

default

◆ operator=() [2/2]

Permutation& TiledArray::symmetry::Permutation::operator= ( Permutation && other )

default

◆ operator[]()

index_type TiledArray::symmetry::Permutation::operator[] ( index_type e ) const

inline

Computes image of an element under this permutation.

Parameters

e	input index

Returns: the image of element e; if e is in the domain of this permutation, returns its image, otherwise returns e

Definition at line 273 of file permutation.h.

◆ pow()

Permutation TiledArray::symmetry::Permutation::pow ( int n ) const

inline

Raise this permutation to the n-th power.

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

Parameters

n	Exponent value

Returns: This permutation raised to the n-th power

Definition at line 397 of file permutation.h.

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◆ serialize()

template<typename Archive >

void TiledArray::symmetry::Permutation::serialize ( Archive & ar )

inline

Serialize permutation.

MADNESS compatible serialization function

Template Parameters

Archive The serialization archive type

Parameters

[in,out] ar The serialization archive

Definition at line 438 of file permutation.h.

Friends And Related Function Documentation

◆ operator<<

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

friend

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 481 of file permutation.h.

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

TiledArray/symm/permutation.h

Search Results

Documentation

Public Types

Public Member Functions

Friends

Member Typedef Documentation

◆ const_iterator

◆ index_type

◆ Map

◆ Permutation_

◆ vector

Constructor & Destructor Documentation

◆ Permutation() [1/7]

◆ Permutation() [2/7]

◆ Permutation() [3/7]

◆ ~Permutation()

◆ Permutation() [4/7]

◆ Permutation() [5/7]

◆ Permutation() [6/7]

◆ Permutation() [7/7]

Member Function Documentation

◆ begin()

◆ cbegin()

◆ cend()

◆ cycles()

◆ data()

◆ domain()

◆ domain_size()

◆ end()

◆ identity()

◆ inv()

◆ is_in_domain()

◆ mult()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator[]()

◆ pow()

◆ serialize()

Friends And Related Function Documentation

◆ operator<<