#include <Orbit.hh>

Inheritance diagram for CASM::Orbit< _SymCompareType >:

Detailed Description

template<typename _SymCompareType>
class CASM::Orbit< _SymCompareType >

An Orbit of Element.

Provides prototype Element, orbit of equivalent elements, and equivalence map giving symmetry operations that map the prototype onto the equivalents.

Element and orbit comparison is done via a SymCompareType functor, which includes any necessary tolerance for floating point comparison. See SymCompare for how to implement the necessary methods.

The following relationships will be valid: element(i) = sym_compare.copy_apply(equivalence_map()[i][j], prototype()), for all j < equivalence_map()[i].size() equivalence_map()[i][j] = t * g; where g is a generating group element, and t is the "spatial_transform" defined by the SymCompareType for equivalent elements such that: sym_compare.representation_prepare(element(i)) == copy_apply(t, sym_compare.representation_prepare(copy_apply(g, prototype)))

Definition at line 43 of file Orbit.hh.

Public Types
using	size_type = unsigned int

using	Element = typename _SymCompareType::Element

using	InvariantsType = typename _SymCompareType::InvariantsType

using	SymCompareType = _SymCompareType

using	const_iterator = typename std::vector< Element >::const_iterator

using	const_symop_iterator = typename std::vector< SymOp >::const_iterator

typedef Base::MostDerived	MostDerived

Public Member Functions
	Orbit (Element generating_element, SymGroup const &generating_group, SymCompareType const &sym_compare)
	Construct an Orbit from a generating_element Element, using provided symmetry group. More...

const_iterator	begin () const

const_iterator	end () const

const_iterator	cbegin () const

const_iterator	cend () const

size_type	size () const

const Element &	prototype () const
	Identical to element(0) More...

const Element &	operator[] (size_type index) const
	Return Element at index, without bounds checking. More...

const Element &	element (size_type index) const
	Equivalent to operator[](size_type index) const. More...

const std::vector< Element > &	elements () const
	const Access vector of Element More...

const multivector< SymOp >::X< 2 > &	equivalence_map () const
	Return the equivalence map. More...

std::pair< const_symop_iterator, const_symop_iterator >	equivalence_map (size_type index) const
	Return the equivalence map for element[index]. More...

SymGroupRepID	canonization_rep_ID () const
	Return the canonization symmetry representation ID. More...

const_iterator	find (const Element &e) const
	Find element in Orbit. More...

bool	contains (const Element &e) const
	Check if element is in Orbit. More...

const SymGroup &	generating_group () const
	Return the generating SymGroup. More...

const SymCompareType &	sym_compare () const
	Return the SymCompare functor reference. More...

InvariantsType const &	invariants () const

Orbit &	apply_sym (const SymOp &op)
	Apply symmetry to Orbit. More...

bool	operator< (const Orbit &B) const
	Compare orbits, using SymCompareType::inter_orbit_compare. More...

bool	operator> (const MostDerived &B) const

bool	operator<= (const MostDerived &B) const

bool	operator>= (const MostDerived &B) const

bool	operator== (const MostDerived &B) const

bool	operator!= (const MostDerived &B) const

Protected Member Functions
bool	eq_impl (const MostDerived &B) const

bool	ne_impl (const MostDerived &B) const

Private Member Functions
void	_construct_canonization_rep () const

template<typename SymOpIterator >
void	_construct (Element generating_element, SymOpIterator begin, SymOpIterator end)
	Construct an Orbit from a generating_element Element, using provided symmetry rep. More...

Private Attributes
std::vector< Element >	m_element
	All symmetrically equivalent elements (excluding those that SymCompare equivalent) More...

multivector< SymOp >::X< 2 >	m_equivalence_map
	element(i) compares equivalent to prototype().copy_apply(m_equivalence_map[i][j]) for all j More...

SymGroup	m_generating_group
	Group used to generate the orbit. More...

SymGroupRepID	m_canonization_rep_ID
	ID of symmetry representation that describes the effect of each SymOp with respect to the canonical equivalent. More...

SymCompareType	m_sym_compare
	Functor used to check compare Element, including symmetry rules, and make canonical forms. More...

InvariantsType	m_invariants
	Orbit invariants. More...

Member Typedef Documentation

◆ const_iterator

template<typename _SymCompareType >

using CASM::Orbit< _SymCompareType >::const_iterator = typename std::vector<Element>::const_iterator

Definition at line 49 of file Orbit.hh.

◆ const_symop_iterator

template<typename _SymCompareType >

using CASM::Orbit< _SymCompareType >::const_symop_iterator = typename std::vector<SymOp>::const_iterator

Definition at line 50 of file Orbit.hh.

◆ Element

template<typename _SymCompareType >

using CASM::Orbit< _SymCompareType >::Element = typename _SymCompareType::Element

Definition at line 46 of file Orbit.hh.

◆ InvariantsType

template<typename _SymCompareType >

using CASM::Orbit< _SymCompareType >::InvariantsType = typename _SymCompareType::InvariantsType

Definition at line 47 of file Orbit.hh.

◆ MostDerived

template<typename Base >

typedef Base::MostDerived notstd::Comparisons< Base >::MostDerived

inherited

Definition at line 27 of file Comparisons.hh.

◆ size_type

template<typename _SymCompareType >

using CASM::Orbit< _SymCompareType >::size_type = unsigned int

Definition at line 45 of file Orbit.hh.

◆ SymCompareType

template<typename _SymCompareType >

using CASM::Orbit< _SymCompareType >::SymCompareType = _SymCompareType

Definition at line 48 of file Orbit.hh.

Constructor & Destructor Documentation

◆ Orbit()

template<typename _SymCompareType >

CASM::Orbit< _SymCompareType >::Orbit	(	Element	generating_element,
		SymGroup const &	generating_group,
		SymCompareType const &	sym_compare
	)

Construct an Orbit from a generating_element Element, using provided symmetry group.

Construct an Orbit from a generating_element Element, using provided Group.

Parameters

generating_element	The element used to generate equivalents
generating_group	The group used for generating the orbit
sym_compare	Binary functor that implements symmetry properties

find the best equivalence map out of all possible (lowest lexicographical sorting columnwise) ties are resolved by virtue of fact that 'tmp_element' is already sorted by m_sym_compare.compare

copy results

Definition at line 91 of file Orbit_impl.hh.

Member Function Documentation

◆ _construct()

template<typename _SymCompareType >

template<typename SymOpIterator >

void CASM::Orbit< _SymCompareType >::_construct	(	Element	generating_element,
		SymOpIterator	begin,
		SymOpIterator	end
	)

private

Construct an Orbit from a generating_element Element, using provided symmetry rep.

◆ _construct_canonization_rep()

template<typename _SymCompareType >

void CASM::Orbit< _SymCompareType >::_construct_canonization_rep

private

Definition at line 252 of file Orbit_impl.hh.

◆ apply_sym()

template<typename _SymCompareType >

Orbit< _SymCompareType > & CASM::Orbit< _SymCompareType >::apply_sym ( const SymOp & op )

Apply symmetry to Orbit.

Definition at line 224 of file Orbit_impl.hh.

◆ begin()

template<typename _SymCompareType >

const_iterator CASM::Orbit< _SymCompareType >::begin ( ) const

inline

Definition at line 57 of file Orbit.hh.

◆ canonization_rep_ID()

template<typename _SymCompareType >

SymGroupRepID CASM::Orbit< _SymCompareType >::canonization_rep_ID ( ) const

inline

Return the canonization symmetry representation ID.

Definition at line 105 of file Orbit.hh.

◆ cbegin()

template<typename _SymCompareType >

const_iterator CASM::Orbit< _SymCompareType >::cbegin ( ) const

inline

Definition at line 61 of file Orbit.hh.

◆ cend()

template<typename _SymCompareType >

const_iterator CASM::Orbit< _SymCompareType >::cend ( ) const

inline

Definition at line 63 of file Orbit.hh.

◆ contains()

template<typename _SymCompareType >

bool CASM::Orbit< _SymCompareType >::contains ( const Element & e ) const

inline

Check if element is in Orbit.

Assumes 'e' is 'prepared', uses SymCompare<Element>::intra_orbit_equal to check equivalence

Definition at line 124 of file Orbit.hh.

◆ element()

template<typename _SymCompareType >

const Element& CASM::Orbit< _SymCompareType >::element ( size_type index ) const

inline

Equivalent to operator[](size_type index) const.

May not be prepared

Definition at line 78 of file Orbit.hh.

◆ elements()

template<typename _SymCompareType >

const std::vector<Element>& CASM::Orbit< _SymCompareType >::elements ( ) const

inline

const Access vector of Element

May not be prepared

Definition at line 83 of file Orbit.hh.

◆ end()

template<typename _SymCompareType >

const_iterator CASM::Orbit< _SymCompareType >::end ( ) const

inline

Definition at line 59 of file Orbit.hh.

◆ eq_impl()

template<typename Base >

bool notstd::Comparisons< Base >::eq_impl ( const MostDerived & B ) const

inlineprotectedinherited

Definition at line 40 of file Comparisons.hh.

◆ equivalence_map() [1/2]

template<typename _SymCompareType >

const multivector<SymOp>::X<2>& CASM::Orbit< _SymCompareType >::equivalence_map ( ) const

inline

Return the equivalence map.

Returns: element(i) compares equivalent to prototype().copy_apply(equivalence_map[i][j]) for all j

Definition at line 90 of file Orbit.hh.

◆ equivalence_map() [2/2]

template<typename _SymCompareType >

std::pair<const_symop_iterator, const_symop_iterator> CASM::Orbit< _SymCompareType >::equivalence_map ( size_type index ) const

inline

Return the equivalence map for element[index].

Returns: a pair of const_iterators, begin and end, over SymOp such that element(index) compares equivalent to prototype().copy_apply(op)

Definition at line 98 of file Orbit.hh.

◆ find()

template<typename _SymCompareType >

const_iterator CASM::Orbit< _SymCompareType >::find ( const Element & e ) const

inline

Find element in Orbit.

Assumes 'e' is 'prepared', uses SymCompare<Element>::intra_orbit_equal to check equivalence

Definition at line 114 of file Orbit.hh.

◆ generating_group()

template<typename _SymCompareType >

Definition at line 73 of file Orbit.hh.

◆ prototype()

template<typename _SymCompareType >

const Element& CASM::Orbit< _SymCompareType >::prototype ( ) const

inline

Identical to element(0)

Definition at line 68 of file Orbit.hh.

◆ size()

template<typename _SymCompareType >

size_type CASM::Orbit< _SymCompareType >::size ( ) const

inline

Definition at line 65 of file Orbit.hh.

◆ sym_compare()

template<typename _SymCompareType >

const SymCompareType& CASM::Orbit< _SymCompareType >::sym_compare ( ) const

inline

Return the SymCompare functor reference.

implements symmetry properties of this orbit

Functor used to check compare Element, including symmetry rules, and make canonical forms.

Definition at line 169 of file Orbit.hh.

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

/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/include/casm/symmetry/Orbit.hh
/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/include/casm/symmetry/Orbit_impl.hh

Detailed Description

template<typename _SymCompareType> class CASM::Orbit< _SymCompareType >

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Member Typedef Documentation

◆ const_iterator

◆ const_symop_iterator

◆ Element

◆ InvariantsType

◆ MostDerived

◆ size_type

◆ SymCompareType

Constructor & Destructor Documentation

◆ Orbit()

Member Function Documentation

◆ _construct()

◆ _construct_canonization_rep()

◆ apply_sym()

◆ begin()

◆ canonization_rep_ID()

◆ cbegin()

◆ cend()

◆ contains()

◆ element()

◆ elements()

◆ end()

◆ eq_impl()

◆ equivalence_map() [1/2]

◆ equivalence_map() [2/2]

◆ find()

◆ generating_group()

◆ invariants()

◆ ne_impl()

◆ operator!=()

◆ operator<()

◆ operator<=()

◆ operator==()

◆ operator>()

◆ operator>=()

◆ operator[]()

◆ prototype()

◆ size()

◆ sym_compare()

Member Data Documentation

◆ m_canonization_rep_ID

◆ m_element

◆ m_equivalence_map

◆ m_generating_group

◆ m_invariants

◆ m_sym_compare

template<typename _SymCompareType>
class CASM::Orbit< _SymCompareType >