#include <VectorSymCompare.hh>

Inheritance diagram for CASM::SubspaceSymCompare< Element, SymApply >:

Detailed Description

template<typename Element, typename SymApply>
class CASM::SubspaceSymCompare< Element, SymApply >

Definition at line 187 of file VectorSymCompare.hh.

Public Types
using	Base = EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > >> >

using	MostDerived = typename Base::MostDerived

using	Element = typename traits< MostDerived >::Element

using	SymApply = typename traits< MostDerived >::SymApply

using	InvariantsType = typename traits< MostDerived >::InvariantsType
	type `InvariantsType` is used to screen elements for equivalence and sort orbits More...

Public Member Functions
template<typename... Args>
	SubspaceSymCompare (Args &&... args)
	Constructor. More...

double	tol () const
	Return tolerance. More...

Element	copy_apply (SymOp const &op, Element obj) const
	Applies SymOp to Element. More...

Element	spatial_prepare (Element obj) const
	Prepare an element for comparison via an isometric affine transformation. More...

Element	representation_prepare (Element obj) const
	Prepare an element for comparison via transformation of its internal representation. More...

Element	prepare (Element obj) const
	Prepare an element for comparison via representation_prepare(), followed by spatial_prepare() More...

bool	compare (const Element &A, const Element &B) const
	Orders 'prepared' elements. More...

bool	equal (const Element &A, const Element &B) const
	Check equivalence of 'prepared' elements. More...

InvariantsType	make_invariants (const Element &element) const
	Make orbit invariants from one element in the orbit. More...

bool	invariants_compare (const InvariantsType &A, const InvariantsType &B) const
	Defines an order for orbits that have different invariants. More...

bool	invariants_equal (const InvariantsType &A, const InvariantsType &B) const
	Check equivalence of invariants. More...

bool	inter_orbit_compare (const Element &A, const InvariantsType &A_invariants, const Element &B, const InvariantsType &B_invariants) const
	Orders orbit prototypes, breaking invariants_compare ties. More...

bool	inter_orbit_equal (const Element &A, const InvariantsType &A_invariants, const Element &B, const InvariantsType &B_invariants) const
	Check equivalence of prototypes in different orbit. More...

std::unique_ptr< SymOpRepresentation >	canonical_transform (Element const &obj) const
	Access transform that took cluster from unprepared to prepared state. More...

SymOp const &	spatial_transform () const
	Access spatial transform that was used during most recent spatial preparation of an element. More...

Protected Member Functions
Element	representation_prepare_impl (Element obj) const
	Prepare an element for comparison by rotating, sorting, and changing sign of column vectors. More...

InvariantsType	make_invariants_impl (Element const &obj) const
	Make orbit invariants from one element in the orbit. More...

bool	invariants_compare_impl (InvariantsType const &A_invariants, InvariantsType const &B_invariants) const
	Orders 'prepared' elements in the same orbit. More...

bool	compare_impl (const Element &A, const Element &B) const
	Compares 'prepared' elements. More...

std::unique_ptr< SymOpRepresentation >	canonical_transform_impl (Element const &obj) const
	Returns transformation that takes 'obj' to its prepared (canonical) form. More...

Element	copy_apply_impl (SymOp const &op, Element obj) const

Element	spatial_prepare_impl (Element obj) const
	Spatial prepare does not apply – element is returned unchanged. More...

SymOp const &	spatial_transform_impl () const
	Spatial prepare does not apply – transform is always identity. More...

bool	inter_orbit_compare_impl (const Element &A, const InvariantsType &A_invariants, const Element &B, const InvariantsType &B_invariants) const
	Orders orbit prototypes, breaking invariants_compare ties. More...

Protected Attributes
friend	_Base

Private Attributes
double	m_tol

SymApply	m_apply

SymOp	m_spatial_transform

Friends
class	EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >

class	SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > >

Member Typedef Documentation

◆ Base

template<typename Element , typename SymApply >

using CASM::SubspaceSymCompare< Element, SymApply >::Base = EigenSymCompare< SymCompare<CRTPBase<SubspaceSymCompare<Element, SymApply> >> >

Definition at line 191 of file VectorSymCompare.hh.

◆ Element

using CASM::EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >::Element = typename traits<MostDerived>::Element

inherited

Definition at line 94 of file VectorSymCompare.hh.

◆ InvariantsType

template<typename Base >

using CASM::SymCompare< Base >::InvariantsType = typename traits<MostDerived>::InvariantsType

inherited

type InvariantsType is used to screen elements for equivalence and sort orbits

Definition at line 82 of file SymCompare.hh.

◆ MostDerived

using CASM::EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >::MostDerived = typename Base::MostDerived

inherited

Definition at line 93 of file VectorSymCompare.hh.

◆ SymApply

using CASM::EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >::SymApply = typename traits<MostDerived>::SymApply

inherited

Definition at line 95 of file VectorSymCompare.hh.

Constructor & Destructor Documentation

◆ SubspaceSymCompare()

template<typename Element , typename SymApply >

template<typename... Args>

CASM::SubspaceSymCompare< Element, SymApply >::SubspaceSymCompare ( Args &&... args )

inline

Constructor.

Parameters

tol	Tolerance for invariants_compare of site-to-site distances

Definition at line 199 of file VectorSymCompare.hh.

Member Function Documentation

◆ canonical_transform()

template<typename Base >

std::unique_ptr< SymOpRepresentation > CASM::SymCompare< Base >::canonical_transform ( Element const & obj ) const

inherited

Access transform that took cluster from unprepared to prepared state.

Definition at line 244 of file SymCompare.hh.

◆ canonical_transform_impl()

std::unique_ptr< SymOpRepresentation > CASM::EigenSymCompare< Base >::canonical_transform_impl ( Element const & obj ) const

protectedinherited

Returns transformation that takes 'obj' to its prepared (canonical) form.

For now returns pointer to SymPermutation object that encodes permutation due to sorting elements

Definition at line 126 of file VectorSymCompare_impl.hh.

◆ compare()

template<typename Base >

bool CASM::SymCompare< Base >::compare	(	const Element &	A,
		const Element &	B
	)		const

inherited

Orders 'prepared' elements.

Returns 'true' to indicate A < B
Assumes elements are 'prepared' before being compared

Definition at line 173 of file SymCompare.hh.

◆ compare_impl()

bool CASM::EigenSymCompare< Base >::compare_impl	(	const Element &	A,
		const Element &	B
	)		const

protectedinherited

Compares 'prepared' elements.

Returns 'true' to indicate B < A
Equivalence is indicated by
!compare(A,B) && !compare(B,A)

CASM::SymCompare::compare
bool compare(const Element &A, const Element &B) const
Orders 'prepared' elements.
Definition: SymCompare.hh:173
Assumes elements are 'prepared' before being compared

Definition at line 121 of file VectorSymCompare_impl.hh.

◆ copy_apply()

template<typename Base >

SymCompare< Base >::Element CASM::SymCompare< Base >::copy_apply	(	SymOp const &	op,
		Element	obj
	)		const

inherited

Applies SymOp to Element.

Applies SymOp to Element. Default performs standalone copy_apply.

Definition at line 123 of file SymCompare.hh.

◆ copy_apply_impl()

Element CASM::EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >::copy_apply_impl	(	SymOp const &	op,
		Element	obj
	)		const

inlineprotectedinherited

Definition at line 129 of file VectorSymCompare.hh.

◆ equal()

template<typename Base >

bool CASM::SymCompare< Base >::equal	(	const Element &	A,
		const Element &	B
	)		const

inherited

Check equivalence of 'prepared' elements.

Returns: !compare(A,B) && !compare(B,A)

Assumes elements are 'prepared' before being compared

Definition at line 183 of file SymCompare.hh.

◆ inter_orbit_compare()

template<typename Base >

bool CASM::SymCompare< Base >::inter_orbit_compare	(	const Element &	A,
		const InvariantsType &	A_invariants,
		const Element &	B,
		const InvariantsType &	B_invariants
	)		const

inherited

Orders orbit prototypes, breaking invariants_compare ties.

Returns 'true' to indicate A < B
Equivalence is indicated by
!inter_orbit_compare(A,B) &&

!inter_orbit_compare(B,A)

CASM::SymCompare::inter_orbit_compare
bool inter_orbit_compare(const Element &A, const InvariantsType &A_invariants, const Element &B, const InvariantsType &B_invariants) const
Orders orbit prototypes, breaking invariants_compare ties.
Definition: SymCompare.hh:222
Assumes elements are in canonical form

Definition at line 222 of file SymCompare.hh.

◆ inter_orbit_compare_impl()

template<typename Base >

bool CASM::SymCompare< Base >::inter_orbit_compare_impl	(	const Element &	A,
		const InvariantsType &	A_invariants,
		const Element &	B,
		const InvariantsType &	B_invariants
	)		const

protectedinherited

Orders orbit prototypes, breaking invariants_compare ties.

Returns 'true' to indicate A < B
Equivalence is indicated by
!compare(A,B) && !compare(B,A)

Implementation:

First, check invariants_compare
Break ties with, compare(A, B)

Definition at line 265 of file SymCompare.hh.

◆ inter_orbit_equal()

template<typename Base >

bool CASM::SymCompare< Base >::inter_orbit_equal	(	const Element &	A,
		const InvariantsType &	A_invariants,
		const Element &	B,
		const InvariantsType &	B_invariants
	)		const

inherited

Check equivalence of prototypes in different orbit.

Returns: !inter_orbit_compare(A,B) && !inter_orbit_compare(B,A)

Assumes elements are in canonical form

Definition at line 235 of file SymCompare.hh.

◆ invariants_compare()

template<typename Base >

bool CASM::SymCompare< Base >::invariants_compare	(	const InvariantsType &	A,
		const InvariantsType &	B
	)		const

inherited

Defines an order for orbits that have different invariants.

Defines an order for elements that have different invariants.

Returns 'true' to indicate A < B
Equivalence is indicated by
!invariants_compare(A,B) &&

!invariants_compare(B,A)

CASM::SymCompare::invariants_compare
bool invariants_compare(const InvariantsType &A, const InvariantsType &B) const
Defines an order for orbits that have different invariants.
Definition: SymCompare.hh:201
Assumes elements are 'prepared' before being compared

Definition at line 201 of file SymCompare.hh.

◆ invariants_compare_impl()

bool CASM::EigenSymCompare< Base >::invariants_compare_impl	(	InvariantsType const &	A_invariants,
		InvariantsType const &	B_invariants
	)		const

protectedinherited

Orders 'prepared' elements in the same orbit.

Returns 'true' to indicate A < B
Equivalence is indicated by
!compare(A,B) && !compare(B,A)
Assumes elements are 'prepared' before being compared Implementation:
First compares by number of sites in cluster
Then compare all displacements, from longest to shortest

Definition at line 117 of file VectorSymCompare_impl.hh.

◆ invariants_equal()

template<typename Base >

bool CASM::SymCompare< Base >::invariants_equal	(	const InvariantsType &	A,
		const InvariantsType &	B
	)		const

inherited

Check equivalence of invariants.

Returns: !invariants_compare(A,B) && !invariants_compare(B,A)

Definition at line 210 of file SymCompare.hh.

◆ make_invariants()

template<typename Base >

SymCompare< Base >::InvariantsType CASM::SymCompare< Base >::make_invariants ( const Element & element ) const

inherited

Make orbit invariants from one element in the orbit.

Get orbit invariants from one element in the orbit.

Definition at line 189 of file SymCompare.hh.

◆ make_invariants_impl()

EigenSymCompare< Base >::InvariantsType CASM::EigenSymCompare< Base >::make_invariants_impl ( Element const & obj ) const

protectedinherited

Make orbit invariants from one element in the orbit.

Definition at line 114 of file VectorSymCompare_impl.hh.

◆ prepare()

template<typename Base >

SymCompare< Base >::Element CASM::SymCompare< Base >::prepare ( Element obj ) const

inherited

Prepare an element for comparison via representation_prepare(), followed by spatial_prepare()

Definition at line 163 of file SymCompare.hh.

◆ representation_prepare()

template<typename Base >

SymCompare< Base >::Element CASM::SymCompare< Base >::representation_prepare ( Element obj ) const

inherited

Prepare an element for comparison via transformation of its internal representation.

For instance, sort sites of a cluster so comparison may be performed more efficiently

Definition at line 154 of file SymCompare.hh.

◆ representation_prepare_impl()

template<typename Element , typename SymApply >

Element CASM::SubspaceSymCompare< Element, SymApply >::representation_prepare_impl ( Element obj ) const

protected

Prepare an element for comparison by rotating, sorting, and changing sign of column vectors.

Prepare an element for comparison.

Attempts to find a sparse set of spanning vectors, and sort them so that subspace matrix is nearly upper triangular (if possible)
Also enures that first nonzero element of each row (if there is one) is positive

Definition at line 117 of file VectorSymCompare_impl.hh.

◆ spatial_prepare()

template<typename Base >

SymCompare< Base >::Element CASM::SymCompare< Base >::spatial_prepare ( Element obj ) const

inherited

Prepare an element for comparison via an isometric affine transformation.

For instance, translate a cluster so comparison may be performed more efficiently.
The transformation that is applied is stored and available as spatial_transform
The spatial_transform is also included in the symmetry operations stored in the Orbit equivalence_map (i.e. equivalence_map_element = spatial_transform * generating_group_op)
Returns pair such that pair.first = apply_sym(pair.second, obj)

Definition at line 142 of file SymCompare.hh.

◆ spatial_prepare_impl()

EigenSymCompare< Base >::Element CASM::EigenSymCompare< Base >::spatial_prepare_impl ( Element obj ) const

protectedinherited

Spatial prepare does not apply – element is returned unchanged.

Definition at line 134 of file VectorSymCompare_impl.hh.

◆ spatial_transform()

template<typename Base >

SymOp const & CASM::SymCompare< Base >::spatial_transform

inherited

Access spatial transform that was used during most recent spatial preparation of an element.

Definition at line 252 of file SymCompare.hh.

◆ spatial_transform_impl()

SymOp const & CASM::EigenSymCompare< Base >::spatial_transform_impl

protectedinherited

Spatial prepare does not apply – transform is always identity.

Spatial prepare does not apply – always identity.

Definition at line 137 of file VectorSymCompare_impl.hh.

◆ tol()

double CASM::EigenSymCompare< Base >::tol

inherited

Return tolerance.

Definition at line 100 of file VectorSymCompare_impl.hh.

Friends And Related Function Documentation

◆ EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >

template<typename Element , typename SymApply >

friend class EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >

friend

Definition at line 199 of file VectorSymCompare.hh.

◆ SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > >

template<typename Element , typename SymApply >

friend class SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > >

friend

Definition at line 199 of file VectorSymCompare.hh.

Member Data Documentation

◆ _Base

friend CASM::EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >::SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > >

protectedinherited

Definition at line 103 of file VectorSymCompare.hh.

◆ m_apply

SymApply CASM::EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >::m_apply

privateinherited

Definition at line 142 of file VectorSymCompare.hh.

◆ m_spatial_transform

SymOp CASM::EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >::m_spatial_transform

privateinherited

Not applicable to VectorSymCompare – always identity

Default SymOp constructor initializes to identity

Definition at line 146 of file VectorSymCompare.hh.

◆ m_tol

double CASM::EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >::m_tol

privateinherited

Definition at line 140 of file VectorSymCompare.hh.

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

/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/include/casm/symmetry/VectorSymCompare.hh
/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/include/casm/symmetry/VectorSymCompare_impl.hh

Detailed Description

template<typename Element, typename SymApply> class CASM::SubspaceSymCompare< Element, SymApply >

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Friends

Member Typedef Documentation

◆ Base

◆ Element

◆ InvariantsType

◆ MostDerived

◆ SymApply

Constructor & Destructor Documentation

◆ SubspaceSymCompare()

Member Function Documentation

◆ canonical_transform()

◆ canonical_transform_impl()

◆ compare()

◆ compare_impl()

◆ copy_apply()

◆ copy_apply_impl()

◆ equal()

◆ inter_orbit_compare()

◆ inter_orbit_compare_impl()

◆ inter_orbit_equal()

◆ invariants_compare()

◆ invariants_compare_impl()

◆ invariants_equal()

◆ make_invariants()

◆ make_invariants_impl()

◆ prepare()

◆ representation_prepare()

◆ representation_prepare_impl()

◆ spatial_prepare()

◆ spatial_prepare_impl()

◆ spatial_transform()

◆ spatial_transform_impl()

◆ tol()

Friends And Related Function Documentation

◆ EigenSymCompare< SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > > >

◆ SymCompare< CRTPBase< SubspaceSymCompare< Element, SymApply > > >

Member Data Documentation

◆ _Base

◆ m_apply

◆ m_spatial_transform

◆ m_tol

template<typename Element, typename SymApply>
class CASM::SubspaceSymCompare< Element, SymApply >