#include <SymGroup.hh>

Inheritance diagram for CASM::SymGroup:

Detailed Description

SymGroup is a collection of symmetry operations that satisfy the group property The symmetry operations are stored as their coordinate representation, as described by the SymOp class i.e., if SymOps 'A' and 'B' are in SymGroup, C=A*B is also in SymGroup if 'A' is in SymGroup, then A.inverse() is in SymGroup SymGroup always contains an identity operation.

Definition at line 42 of file SymGroup.hh.

Public Types
typedef SymOp::vector_type	vector_type

typedef SymOp::matrix_type	matrix_type

Public Member Functions
	SymGroup (PERIODICITY_TYPE init_type=PERIODIC)
	Initialize by setting periodicity mode (default mode is PERIODIC) More...

	SymGroup (std::vector< SymOp > from_array, Lattice const *lat_ptr, PERIODICITY_TYPE init_type=PERIODIC)

template<typename IterType >
	SymGroup (IterType begin, IterType end, PERIODICITY_TYPE init_type=PERIODIC)

virtual	~SymGroup ()

virtual void	push_back (const SymOp &new_op)

virtual void	clear ()

virtual void	clear_tables ()

void	set_lattice (const Lattice &new_lat)
	Lattice used for periodic comparisons (for instance, to generate multiplcation table) More...

const Lattice &	lattice () const
	Lattice used for periodic comparisons (for instance, to generate multiplcation table) More...

const MasterSymGroup &	master_group () const

std::vector< Index >	op_indices () const

std::vector< Index >	master_group_indices () const
	Return the MasterSymGroup indices of the operations in this SymGroup. More...

bool	contains_periodic (const SymOp &test_op, double tol=TOL) const
	Check to see if a SymOp is contained in in SymGroup. More...

Index	find_no_trans (const SymOp &test_op) const
	Check to see if a SymOp is contained in in SymGroup and return its index. More...

Index	find_periodic (const SymOp &test_op, double tol=TOL) const

std::vector< Index >	find_all_periodic (const std::vector< SymOp > &subgroup, double tol=TOL) const

virtual void	sort ()
	Sort SymOp in the SymGroup. More...

SymGroup	get_union (const SymGroup &other_group) const
	Adds SymOps from 'other_group' and enforces the group property. More...

SymGroup &	apply_sym (const SymOp &op)
	Calls 'apply_sym' on all SymOps in the group. More...

Index	ind_prod (Index i, Index j) const
	Get index of operation that is result of multiplication of at(i)*at(j) More...

Index	ind_inverse (Index i) const
	Get index of operation that is inverse of operation at(i) More...

Index	class_of_op (Index i) const
	Get conjugacy class index of operation at(i) More...

void	set_irrep_ID (Index i, SymGroupRepID ID) const
	set symrep ID of a particular irrep More...

SymGroupRepID	get_irrep_ID (Index i) const
	Get symrep ID of a particular irrep. More...

SymGroupRepID	coord_rep_ID () const

SymGroupRep const &	get_irrep (Index i) const
	Get symrep for a particular irrep. More...

SymGroupRepID	allocate_representation () const
	Add a new empty representation. More...

void	calc_space_group_in_cell (SymGroup &space_group, const Lattice &_cell) const

void	calc_space_group_in_range (SymGroup &space_group, const Lattice &_cell, Eigen::Vector3i min_trans, Eigen::Vector3i max_trans) const

bool	is_group (double tol=TOL) const
	Check to see if SymGroup satisfies the group property. More...

void	enforce_group (double tol=TOL, Index max_size=200)
	Enforce group property by adding products of operations to the group. More...

void	print_locations (std::ostream &stream) const
	print locations of the symmetry-generating element of each SymOp More...

void	write (std::string filename, COORD_TYPE mode) const
	Write the SymGroup to a file. More...

void	print (std::ostream &out, COORD_TYPE mode) const
	Print the SymGroup to a stream. More...

SymGroup &	operator+= (const Eigen::Ref< const SymOp::vector_type > &shift)
	Cartesian translation of SymGroup origin by vector 'shift'. More...

SymGroup &	operator-= (const Eigen::Ref< const SymOp::vector_type > &shift)

double	max_error ()
	This returns the group's max_error. More...

std::vector< std::vector< Index > >	left_cosets (const std::vector< SymOp > &subgroup, double tol=TOL) const

template<typename IterType >
std::vector< std::vector< Index > >	left_cosets (IterType const &begin, IterType const &end) const

const std::vector< std::vector< Index > > &	get_multi_table () const

const std::vector< std::vector< Index > > &	get_alt_multi_table () const

void	invalidate_multi_tables () const

const std::vector< std::vector< Index > > &	get_conjugacy_classes () const

const std::string &	get_name () const

const std::string &	get_latex_name () const

PERIODICITY_TYPE	periodicity () const

std::string	possible_space_groups () const

const std::vector< std::set< std::set< Index > > > &	subgroups () const

bool	is_irreducible () const

std::vector< SymGroup >	unique_subgroups () const

SymGroup	copy_no_trans (bool keep_repeated=false) const
	Fill up a SymGroup with *this minus the shifts. More...

SymInfo	info (Index i) const

std::vector< std::set< std::set< Index > > >	small_subgroups () const

Static Public Member Functions
static SymGroup	lattice_point_group (Lattice const &_lat)

Protected Member Functions
void	_generate_conjugacy_classes () const

void	_generate_centralizers () const

void	_generate_elem_order_table () const

void	_generate_class_names () const

bool	_generate_multi_table () const

void	_generate_alt_multi_table () const

void	_generate_subgroups () const

std::vector< std::set< std::set< Index > > >	_small_subgroups () const

Protected Attributes
Lattice const *	m_lat_ptr
	Pointer to a lattice for doing periodic comparisons. More...

PERIODICITY_TYPE	m_group_periodicity
	Specifies whether to use lattice periodicity when testing for equivalence. More...

multivector< Index >::X< 2 >	multi_table
	multi_table[i][j] gives index of operation that is result of at(i)*at(j) More...

multivector< Index >::X< 2 >	alt_multi_table

std::vector< std::vector< Index > >	conjugacy_classes

std::vector< std::string >	class_names

std::vector< Index >	index2conjugacy_class

std::vector< SymGroupRepID >	irrep_IDs

std::vector< std::set< std::set< Index > > >	m_subgroups

multivector< Index >::X< 2 >	centralizer_table

multivector< Index >::X< 2 >	elem_order_table

std::string	name

std::string	latex_name

std::string	comment

double	m_max_error

Member Typedef Documentation

◆ matrix_type

typedef SymOp::matrix_type CASM::SymGroup::matrix_type

Definition at line 45 of file SymGroup.hh.

◆ vector_type

typedef SymOp::vector_type CASM::SymGroup::vector_type

Definition at line 44 of file SymGroup.hh.

Constructor & Destructor Documentation

◆ SymGroup() [1/2]

CASM::SymGroup::SymGroup ( PERIODICITY_TYPE init_type = PERIODIC )

inline

Initialize by setting periodicity mode (default mode is PERIODIC)

Definition at line 50 of file SymGroup.hh.

◆ SymGroup() [2/2]

CASM::SymGroup::SymGroup	(	std::vector< SymOp >	from_array,
		Lattice const *	lat_ptr,
		PERIODICITY_TYPE	init_type = `PERIODIC`
	)

Definition at line 806 of file SymGroup.cc.

◆ ~SymGroup()

CASM::SymGroup::~SymGroup ( )

virtual

Definition at line 773 of file SymGroup.cc.

Member Function Documentation

◆ _generate_alt_multi_table()

void CASM::SymGroup::_generate_alt_multi_table ( ) const

protected

Definition at line 1746 of file SymGroup.cc.

◆ _generate_centralizers()

void CASM::SymGroup::_generate_centralizers ( ) const

protected

The centralizer of a subset S of a group G is the set of elements of G that commute with each element of S. The centralizer is a subgroup of G.

In our specific case, the subsets are the conjugacy classes, so we fill the centralizer_table with subgroups of G that commute with the corresponding conjugacy class.qq

Definition at line 1227 of file SymGroup.cc.

◆ _generate_class_names()

void CASM::SymGroup::_generate_class_names ( ) const

protected

This will name your conjugacy classes according to some crazy convention, which is similar, but not exactly identical to the Schoenflies notation.

We start by finding the principal axes. Often, there will only be one. However, in cases like fcc, there can be several. All rotations that are about the principal axis will be named "XCn" if they are proper and "XSn" if they are improper. Here, X is the size of their conjugacy class, and n is the foldedness of the rotation, i.e. 60 degree rotations are 6-fold, while 120 degree rotations are 3-fold.

Definition at line 972 of file SymGroup.cc.

◆ _generate_conjugacy_classes()

void CASM::SymGroup::_generate_conjugacy_classes ( ) const

protected

The number of irreducible representations is equal to the number of conjugacy classes.

The number of elements in each conjugacy class must be a divisor of the number of symmetry group operations.

Definition at line 1487 of file SymGroup.cc.

◆ _generate_elem_order_table()

void CASM::SymGroup::_generate_elem_order_table ( ) const

protected

Definition at line 1253 of file SymGroup.cc.

◆ _generate_multi_table()

bool CASM::SymGroup::_generate_multi_table ( ) const

protected

Definition at line 1702 of file SymGroup.cc.

◆ _generate_subgroups()

void CASM::SymGroup::_generate_subgroups ( ) const

protected

Definition at line 1337 of file SymGroup.cc.

◆ _small_subgroups()

std::vector< std::set< std::set< Index > > > CASM::SymGroup::_small_subgroups ( ) const

protected

Definition at line 1281 of file SymGroup.cc.

◆ allocate_representation()

SymGroupRepID CASM::SymGroup::allocate_representation ( ) const

Add a new empty representation.

Definition at line 1601 of file SymGroup.cc.

◆ apply_sym()

SymGroup & CASM::SymGroup::apply_sym ( const SymOp & op )

Calls 'apply_sym' on all SymOps in the group.

Definition at line 1867 of file SymGroup.cc.

◆ calc_space_group_in_cell()

void CASM::SymGroup::calc_space_group_in_cell	(	SymGroup &	space_group,
		const Lattice &	_cell
	)		const

Gets all the space group operations in unit cell and stores them in space_group assuming that this SymGroup contains the factor group

Definition at line 1889 of file SymGroup.cc.

◆ calc_space_group_in_range()

void CASM::SymGroup::calc_space_group_in_range	(	SymGroup &	space_group,
		const Lattice &	_cell,
		Eigen::Vector3i	min_trans,
		Eigen::Vector3i	max_trans
	)		const

gets all teh space group operations corresponding to translations in the specified range max_trans sets boundary of parillellipiped centered at origin.

Definition at line 1931 of file SymGroup.cc.

◆ class_of_op()

Index CASM::SymGroup::class_of_op ( Index i ) const

Get conjugacy class index of operation at(i)

Definition at line 1565 of file SymGroup.cc.

◆ clear()

void CASM::SymGroup::clear ( )

virtual

Reimplemented in CASM::MasterSymGroup.

Definition at line 871 of file SymGroup.cc.

◆ clear_tables()

void CASM::SymGroup::clear_tables ( )

virtual

Definition at line 826 of file SymGroup.cc.

◆ contains_periodic()

bool CASM::SymGroup::contains_periodic	(	const SymOp &	test_op,
		double	tol = `TOL`
	)		const

Check to see if a SymOp is contained in in SymGroup.

Definition at line 1861 of file SymGroup.cc.

◆ coord_rep_ID()

SymGroupRepID CASM::SymGroup::coord_rep_ID ( ) const

Get symrep ID of the representation that stores the Cartesian symop matrices

Definition at line 1589 of file SymGroup.cc.

◆ copy_no_trans()

SymGroup CASM::SymGroup::copy_no_trans ( bool keep_repeated = false ) const

Fill up a SymGroup with *this minus the shifts.

Definition at line 928 of file SymGroup.cc.

◆ enforce_group()

void CASM::SymGroup::enforce_group	(	double	tol = `TOL`,
		Index	max_size = `200`
	)

Enforce group property by adding products of operations to the group.

Definition at line 1821 of file SymGroup.cc.

◆ find_all_periodic()

std::vector< Index > CASM::SymGroup::find_all_periodic	(	const std::vector< SymOp > &	subgroup,
		double	tol = `TOL`
	)		const

Definition at line 1790 of file SymGroup.cc.

◆ find_no_trans()

Index CASM::SymGroup::find_no_trans ( const SymOp & test_op ) const

Check to see if a SymOp is contained in in SymGroup and return its index.

Check to see if a SymOp matrix ONLY is contained in SymGroup and return the index of this operation. This was originally written for pruning the factor groups of primitive structures to construct the factor groups of their superstructures to be consistent with the supercell lattice point groups.

Definition at line 1767 of file SymGroup.cc.

◆ find_periodic()

Index CASM::SymGroup::find_periodic	(	const SymOp &	test_op,
		double	tol = `TOL`
	)		const

This is meant for factor groups. It will compare the Cartesian matrix of the test_op with those of the SymOps in the group. Upon a successful matrix match, it will attempt to match the shift shift vector with min_dist.

Definition at line 1779 of file SymGroup.cc.

◆ get_alt_multi_table()

const std::vector< std::vector< Index > > & CASM::SymGroup::get_alt_multi_table ( ) const

Definition at line 1644 of file SymGroup.cc.

◆ get_conjugacy_classes()

const std::vector< std::vector< Index > > & CASM::SymGroup::get_conjugacy_classes ( ) const

Definition at line 1661 of file SymGroup.cc.

◆ get_irrep()

SymGroupRep const & CASM::SymGroup::get_irrep ( Index i ) const

Get symrep for a particular irrep.

Definition at line 1614 of file SymGroup.cc.

◆ get_irrep_ID()

SymGroupRepID CASM::SymGroup::get_irrep_ID ( Index i ) const

Get symrep ID of a particular irrep.

Definition at line 1581 of file SymGroup.cc.

◆ get_latex_name()

const std::string & CASM::SymGroup::get_latex_name ( ) const

Definition at line 1687 of file SymGroup.cc.

◆ get_multi_table()

const std::vector< std::vector< Index > > & CASM::SymGroup::get_multi_table ( ) const

Definition at line 1633 of file SymGroup.cc.

◆ get_name()

const std::string & CASM::SymGroup::get_name ( ) const

Definition at line 1668 of file SymGroup.cc.

◆ get_union()

SymGroup CASM::SymGroup::get_union ( const SymGroup & other_group ) const

Adds SymOps from 'other_group' and enforces the group property.

◆ ind_inverse()

Index CASM::SymGroup::ind_inverse ( Index i ) const

Get index of operation that is inverse of operation at(i)

Definition at line 1540 of file SymGroup.cc.

◆ ind_prod()

Index CASM::SymGroup::ind_prod	(	Index	i,
		Index	j
	)		const

Get index of operation that is result of multiplication of at(i)*at(j)

Definition at line 1550 of file SymGroup.cc.

◆ info()

SymInfo CASM::SymGroup::info ( Index i ) const

Definition at line 942 of file SymGroup.cc.

◆ invalidate_multi_tables()

void CASM::SymGroup::invalidate_multi_tables ( ) const

Definition at line 1654 of file SymGroup.cc.

◆ is_group()

bool CASM::SymGroup::is_group ( double tol = TOL ) const

Check to see if SymGroup satisfies the group property.

Definition at line 1805 of file SymGroup.cc.

◆ is_irreducible()

bool CASM::SymGroup::is_irreducible ( ) const

Definition at line 2116 of file SymGroup.cc.

◆ lattice()

const Lattice & CASM::SymGroup::lattice ( ) const

Lattice used for periodic comparisons (for instance, to generate multiplcation table)

Definition at line 950 of file SymGroup.cc.

◆ lattice_point_group()

SymGroup CASM::SymGroup::lattice_point_group ( Lattice const & _lat )

static

Definition at line 779 of file SymGroup.cc.

◆ left_cosets()

std::vector< std::vector< Index > > CASM::SymGroup::left_cosets	(	const std::vector< SymOp > &	subgroup,
		double	tol = `TOL`
	)		const

Definition at line 1625 of file SymGroup.cc.

◆ master_group()

const MasterSymGroup& CASM::SymGroup::master_group ( ) const

inline

Definition at line 73 of file SymGroup.hh.

◆ master_group_indices()

std::vector< Index > CASM::SymGroup::master_group_indices ( ) const

Return the MasterSymGroup indices of the operations in this SymGroup.

Definition at line 857 of file SymGroup.cc.

◆ max_error()

double CASM::SymGroup::max_error ( )

This returns the group's max_error.

Definition at line 946 of file SymGroup.cc.

◆ op_indices()

std::vector< Index > CASM::SymGroup::op_indices ( ) const

Return the MasterSymGroup indices of the operations in this SymGroup (equivalent to master_group_indices)

Definition at line 850 of file SymGroup.cc.

◆ operator+=()

SymGroup & CASM::SymGroup::operator+= ( const Eigen::Ref< const SymOp::vector_type > & shift )

Cartesian translation of SymGroup origin by vector 'shift'.

Translation operators for origin shift need to be defined.

Definition at line 2132 of file SymGroup.cc.

◆ operator-=()

SymGroup & CASM::SymGroup::operator-= ( const Eigen::Ref< const SymOp::vector_type > & shift )

Definition at line 2140 of file SymGroup.cc.

◆ periodicity()

PERIODICITY_TYPE CASM::SymGroup::periodicity ( ) const

inline

Definition at line 191 of file SymGroup.hh.

◆ possible_space_groups()

std::string CASM::SymGroup::possible_space_groups ( ) const

inline

Definition at line 193 of file SymGroup.hh.

◆ print()

void CASM::SymGroup::print	(	std::ostream &	out,
		COORD_TYPE	mode
	)		const

Print the SymGroup to a stream.

Definition at line 1874 of file SymGroup.cc.

◆ print_locations()

void CASM::SymGroup::print_locations ( std::ostream & stream ) const

print locations of the symmetry-generating element of each SymOp

Definition at line 1958 of file SymGroup.cc.

◆ push_back()

void CASM::SymGroup::push_back ( const SymOp & new_op )

virtual

Reimplemented in CASM::MasterSymGroup.

Definition at line 818 of file SymGroup.cc.

◆ set_irrep_ID()

void CASM::SymGroup::set_irrep_ID	(	Index	i,
		SymGroupRepID	ID
	)		const

set symrep ID of a particular irrep

Definition at line 1572 of file SymGroup.cc.

◆ set_lattice()

void CASM::SymGroup::set_lattice ( const Lattice & new_lat )

Lattice used for periodic comparisons (for instance, to generate multiplcation table)

Definition at line 814 of file SymGroup.cc.

◆ small_subgroups()

std::vector<std::set<std::set<Index> > > CASM::SymGroup::small_subgroups ( ) const

inline

Definition at line 206 of file SymGroup.hh.

◆ sort()

void CASM::SymGroup::sort ( )

virtual

Sort SymOp in the SymGroup.

If multiplication table can be generated:
- Generate conjugacy classes
- Sort SymOp in each conjugacy class
- Sort each conjugacy class by the first SymOp in the class
Else:
- Sort all SymOp

SymOp are sorted by lexicographical comparison of: (-det, -trace, angle, axis, tau)

angle is positive
axis[0] is positive

Reimplemented in CASM::MasterSymGroup.

Definition at line 2016 of file SymGroup.cc.

◆ subgroups()

const std::vector< std::set< std::set< Index > > > & CASM::SymGroup::subgroups ( ) const

Definition at line 1695 of file SymGroup.cc.

◆ unique_subgroups()

std::vector< SymGroup > CASM::SymGroup::unique_subgroups ( ) const

Definition at line 1403 of file SymGroup.cc.

◆ write()

void CASM::SymGroup::write	(	std::string	filename,
		COORD_TYPE	mode
	)		const

Write the SymGroup to a file.

Member Data Documentation

◆ alt_multi_table

multivector<Index>::X<2> CASM::SymGroup::alt_multi_table

mutableprotected

alt_multi_table[i][j] gives index of operation that is result of at(i).inverse()*at(j)

Definition at line 236 of file SymGroup.hh.

◆ centralizer_table

multivector<Index>::X<2> CASM::SymGroup::centralizer_table

mutableprotected

Definition at line 251 of file SymGroup.hh.

◆ class_names

std::vector<std::string> CASM::SymGroup::class_names

mutableprotected

Definition at line 241 of file SymGroup.hh.

◆ comment

std::string CASM::SymGroup::comment

mutableprotected

Definition at line 256 of file SymGroup.hh.

◆ conjugacy_classes

std::vector<std::vector<Index> > CASM::SymGroup::conjugacy_classes

mutableprotected

Definition at line 240 of file SymGroup.hh.

◆ elem_order_table

multivector<Index>::X<2> CASM::SymGroup::elem_order_table

mutableprotected

Definition at line 252 of file SymGroup.hh.

◆ index2conjugacy_class

std::vector<Index> CASM::SymGroup::index2conjugacy_class

mutableprotected

Definition at line 242 of file SymGroup.hh.

◆ irrep_IDs

std::vector<SymGroupRepID> CASM::SymGroup::irrep_IDs

mutableprotected

Definition at line 245 of file SymGroup.hh.

◆ latex_name

std::string CASM::SymGroup::latex_name

mutableprotected

Definition at line 255 of file SymGroup.hh.

◆ m_group_periodicity

PERIODICITY_TYPE CASM::SymGroup::m_group_periodicity

protected

Specifies whether to use lattice periodicity when testing for equivalence.

Definition at line 229 of file SymGroup.hh.

◆ m_lat_ptr

Lattice const* CASM::SymGroup::m_lat_ptr

protected

Pointer to a lattice for doing periodic comparisons.

Definition at line 226 of file SymGroup.hh.

◆ m_max_error

double CASM::SymGroup::m_max_error

mutableprotected

Definition at line 258 of file SymGroup.hh.

◆ m_subgroups

std::vector<std::set<std::set<Index> > > CASM::SymGroup::m_subgroups

mutableprotected

Definition at line 249 of file SymGroup.hh.

◆ multi_table

multivector<Index>::X<2> CASM::SymGroup::multi_table

mutableprotected

multi_table[i][j] gives index of operation that is result of at(i)*at(j)

Definition at line 232 of file SymGroup.hh.

◆ name

std::string CASM::SymGroup::name

mutableprotected

Definition at line 254 of file SymGroup.hh.

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

/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/include/casm/symmetry/SymGroup.hh
/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/src/casm/symmetry/SymGroup.cc

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Member Typedef Documentation

◆ matrix_type

◆ vector_type

Constructor & Destructor Documentation

◆ SymGroup() [1/2]

◆ SymGroup() [2/2]

◆ ~SymGroup()

Member Function Documentation

◆ _generate_alt_multi_table()

◆ _generate_centralizers()

◆ _generate_class_names()

◆ _generate_conjugacy_classes()

◆ _generate_elem_order_table()

◆ _generate_multi_table()

◆ _generate_subgroups()

◆ _small_subgroups()

◆ allocate_representation()

◆ apply_sym()

◆ calc_space_group_in_cell()

◆ calc_space_group_in_range()

◆ class_of_op()

◆ clear()

◆ clear_tables()

◆ contains_periodic()

◆ coord_rep_ID()

◆ copy_no_trans()

◆ enforce_group()

◆ find_all_periodic()

◆ find_no_trans()

◆ find_periodic()

◆ get_alt_multi_table()

◆ get_conjugacy_classes()

◆ get_irrep()

◆ get_irrep_ID()

◆ get_latex_name()

◆ get_multi_table()

◆ get_name()

◆ get_union()

◆ ind_inverse()

◆ ind_prod()

◆ info()

◆ invalidate_multi_tables()

◆ is_group()

◆ is_irreducible()

◆ lattice()

◆ lattice_point_group()

◆ left_cosets()

◆ master_group()

◆ master_group_indices()

◆ max_error()

◆ op_indices()

◆ operator+=()

◆ operator-=()

◆ periodicity()

◆ possible_space_groups()

◆ print()

◆ print_locations()

◆ push_back()

◆ set_irrep_ID()

◆ set_lattice()

◆ small_subgroups()

◆ sort()

◆ subgroups()

◆ unique_subgroups()

◆ write()

Member Data Documentation

◆ alt_multi_table

◆ centralizer_table

◆ class_names

◆ comment

◆ conjugacy_classes

◆ elem_order_table

◆ index2conjugacy_class

◆ irrep_IDs