#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 33 of file SymGroup.hh.

Public Types
typedef SymOp::vector_type	vector_type

typedef SymOp::matrix_type	matrix_type

typedef Array< SymOp >	X1

typedef Array< X1 >	X2

typedef Array< X2 >	X3

typedef Array< X3 >	X4

typedef Array< X4 >	X5

typedef Array< X5 >	X6

typedef Array< X6 >	X7

typedef Array< X7 >	X8

typedef Array< X8 >	X9

typedef SymOp	value_type

typedef Index	size_type

typedef SymOp *	iterator

typedef const SymOp *	const_iterator

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

	SymGroup (const Array< SymOp > &from_array, PERIODICITY_TYPE init_type=PERIODIC)

virtual void	push_back (const SymOp &new_op)

virtual void	clear ()

virtual void	clear_tables ()

void	set_lattice (const Lattice &new_lat)

const Lattice &	lattice () const

const MasterSymGroup &	master_group () const

ReturnArray< Index >	op_indices () const

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

ReturnArray< Index >	find_all_periodic (const Array< 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
	Get symrep ID of the representation that stores the Cartesian symop matrices. More...

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

SymGroupRepID	add_empty_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...

ReturnArray< Array< Index > >	left_cosets (const Array< SymOp > &subgroup, double tol=TOL) const

ReturnArray< Array< Index > >	left_cosets (const Array< Index > &subgroup_inds) const

const Array< Index >::X2 &	get_multi_table () const

const Array< Index >::X2 &	get_alt_multi_table () const

void	invalidate_multi_tables () const

const Array< Index >::X2 &	get_conjugacy_classes () const

const Array< std::complex < double > >::X2 &	character_table () const

const Array< bool > &	get_complex_irrep_list () 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 Array< Index >::X3 &	subgroups () const

void	print_character_table (std::ostream &stream)

ReturnArray< Index >	get_irrep_decomposition () const

bool	is_irreducible () const

std::vector< SymGroup >	unique_subgroups () const

void	get_rotation_groups () const
	Space group (added by Donghee );. More...

void	get_point_group_type () const

void	print_space_group_info (std::ostream &out) const

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

jsonParser &	to_json (jsonParser &json) const

void	from_json (const jsonParser &json)

SymInfo	info (Index i) const

Index	size () const

void	swap (Array< SymOp > &RHS)

SymOp &	at (Index ind)

const SymOp &	at (Index ind) const

const SymOp &	operator[] (Index ind) const

SymOp &	operator[] (Index ind)

SymOp &	back ()

const SymOp &	back () const

SymOpconst *	begin () const

SymOp *	begin ()

SymOpconst *	cbegin () const

SymOpconst *	end () const

SymOp *	end ()

SymOpconst *	cend () const

void	pop_back ()

void	remove (Index ind)

void	resize (Index new_N)

void	resize (Index new_N, const SymOp &fill_val)

void	reserve (Index new_max)

void	sort (const CompareType &comp)

void	sort (Array< Index > &ind_order)

Array &	append (const Array &new_tail)

Array &	append_unique (const Array &new_tail)

void	swap_elem (Index i, Index j)

Array &	permute (const Array< Index > &perm_array)

Array &	ipermute (const Array< Index > &perm_array)

bool	next_permute ()

ReturnArray< Index >	as_perm_inverse () const

ReturnArray< Index >	as_perm_transform_by (const Array< Index > &trans_perm) const

const SymOp &	max () const

const SymOp &	min () const

ReturnArray< SymOp >	sub_array (Index ind_begin, Index ind_end) const

SymOp	sum () const

bool	is_ascending () const

bool	is_descending () const

bool	is_constant () const

bool	is_permute () const

bool	has_fixed_points () const
	Checks whether any values are equal to their index – only valid for Array<Index> More...

bool	operator== (const Array< SymOp > &RHS) const

bool	operator!= (const Array< SymOp > &RHS) const

bool	operator< (const Array< SymOp > &RHS) const

bool	operator> (const Array< SymOp > &RHS) const

bool	operator<= (const Array< SymOp > &RHS) const

bool	operator>= (const Array< SymOp > &RHS) const

bool	all_in (const Array &superset) const

Index	coincidence (const Array &superset) const

Index	incidences (const SymOp &test_elem) const

Index	find (const SymOp &test_elem) const

Index	reverse_find (const SymOp &test_elem) const
	Same as find, but starts from the last element of the Array. More...

Index	almost_find (const SymOp &test_elem, double tol_val=TOL) const

Index	almost_reverse_find (const SymOp &test_elem, double tol_val=TOL) const
	Same as almost_find, but start from the last element of the Array. More...

bool	contains (const SymOp &test_elem) const

bool	almost_contains (const SymOp &test_elem, double tol_val=TOL) const

void	print_column (std::ostream &stream, const std::string &indent="") const

Static Public Member Functions
static ReturnArray< SymOp >	sequence (const SymOp &initial, const SymOp &final)
	Returns an array with the sequence (initial, ++initial, ..., final), inclusive. More...

static ReturnArray< SymOp >	sequence (const SymOp &initial, const SymOp &increment, const SymOp &final)

Protected Member Functions
void	_generate_conjugacy_classes () const

void	_generate_character_table () const

void	_generate_centralizers () const

void	_generate_elem_order_table () const

void	_generate_class_names () const

void	_generate_irrep_names () const

bool	_generate_multi_table () const

void	_generate_alt_multi_table () const

void	_generate_subgroups () const

Array< Index >::X3	_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...

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

Array< Array< Index > >	alt_multi_table
	alt_multi_table[i][j] gives index of operation that is result of at(i).inverse()*at(j) More...

Array< Array< Index > >	conjugacy_classes

Array< std::string >	class_names

Array< Index >	index2conjugacy_class

Array< Array< std::complex < double > > >	m_character_table

Array< SymGroupRepID >	irrep_IDs

Array< bool >	complex_irrep

Array< std::string >	irrep_names

Array< Array< Array< Index > > >	m_subgroups

Array< Array< Index > >	centralizer_table

Array< Array< Index > >	elem_order_table

std::string	name

std::string	latex_name

std::string	comment

double	m_max_error

Array< Array< SymOp > >	rotation_groups
	Space group (added by Donghee );. More...

std::string	crystal_system

bool	centric

Array< int >	group_number

Array< std::string >	group_name

Member Typedef Documentation

typedef const SymOp * CASM::Array< SymOp >::const_iterator

inherited

Definition at line 76 of file Array.hh.

typedef SymOp * CASM::Array< SymOp >::iterator

inherited

Definition at line 75 of file Array.hh.

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

Definition at line 36 of file SymGroup.hh.

typedef Index CASM::Array< SymOp >::size_type

inherited

Definition at line 74 of file Array.hh.

typedef SymOp CASM::Array< SymOp >::value_type

inherited

Definition at line 73 of file Array.hh.

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

Definition at line 35 of file SymGroup.hh.

typedef Array<SymOp > CASM::Array< SymOp >::X1

inherited

Definition at line 63 of file Array.hh.

typedef Array<X1> CASM::Array< SymOp >::X2

inherited

Definition at line 64 of file Array.hh.

typedef Array<X2> CASM::Array< SymOp >::X3

inherited

Definition at line 65 of file Array.hh.

typedef Array<X3> CASM::Array< SymOp >::X4

inherited

Definition at line 66 of file Array.hh.

typedef Array<X4> CASM::Array< SymOp >::X5

inherited

Definition at line 67 of file Array.hh.

typedef Array<X5> CASM::Array< SymOp >::X6

inherited

Definition at line 68 of file Array.hh.

typedef Array<X6> CASM::Array< SymOp >::X7

inherited

Definition at line 69 of file Array.hh.

typedef Array<X7> CASM::Array< SymOp >::X8

inherited

Definition at line 70 of file Array.hh.

typedef Array<X8> CASM::Array< SymOp >::X9

inherited

Definition at line 71 of file Array.hh.

Constructor & Destructor Documentation

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

inline

Initialize by setting periodicity mode (default mode is PERIODIC)

Definition at line 38 of file SymGroup.hh.

CASM::SymGroup::SymGroup	(	const Array< SymOp > &	from_array,
		PERIODICITY_TYPE	init_type = `PERIODIC`
	)

Definition at line 425 of file SymGroup.cc.

Member Function Documentation

void CASM::SymGroup::_generate_alt_multi_table ( ) const

protected

Definition at line 3286 of file SymGroup.cc.

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 1861 of file SymGroup.cc.

void CASM::SymGroup::_generate_character_table ( ) const

protected

We need to figure out the dimensionality of each irreducible representation. We know that the total number of irreducible representations is the same as the total number of conjugacy classes, which we are calling nc. Also, we know that the sum of the squares of the dimensionalities of all of theirreducible representations must be equal to the size of the group, h.

If you're in this block, you have finished your character table using only real +/- 1 characters because all of your representations are dimension 1. Life is good. Also, your group is Abelian.

The group you are dealing with is one of the following: C1, C2, C2v, C1h (S1), C2h, S2 (Ci), D2, D2h.

This group is one of the following... If nc = 1: C1 If nc = 2: C2, C1h, S2. If nc = 4: C2v, C2h, D2 If nc = 8: D2h

If you're in this loop, then you're not done yet because you either have complex dimension 1 characters or higher dimension real characters still to look for. In this case, we need to check our group for inversion and mirror symmetries to determine if it can be broken up into subgroups in a convenient way that will help us construct the rest of the character table.

This part will handle groups that do not have special symmetries (sigma_h mirror planes or inversion). We then need to know if the group is Abelian. We can check this by looking at the number of conjugacy classes and comparing to the number of dimension 1 representations we are supposed to find. So if d1 = nc, the group must be Abelian. If this is not the case, the group must have higher dimension representations, which will be dealt with separately.

Then the group is cyclic & Abelian. This means that we can proceed by determining the smallest rotation angle in the group, which will give us omega because omega is just 2*pi*i/3 for 120 degree rotations, 2*pi*i/4 for 90 degree rotations, or 2*pi*i/6 for 60 degree rotations. We then "guess" powers of omega for our one of the complex characters if our representation and determine the rest of the characters in that representation by enforcing the cycle (which is equivalent to enforcing the multiplication table).

The possibilities here are: If nc = 3: C3 If nc = 4: C4 If nc = 6: C6

We need to keep in mind that the angle returned by get_rotation_angle() is real and is given in degrees. We need to convert it to complex radian form, which we will do using Euler's formula: e^(ix) = cos(x) + i*sin(x).

For every complex representation in the character table, there is also a complex conjugate representation, so once we have found a full set of complex characters, we can conjugate them to get another row in the table.

If we are in this loop, then our group has mirror or inversion symmetry, which means that we can determine its character table by breaking it up into subgroups and computing their character tables first. It turns out that all groups containing i or sigma_h symmetry can be broken up into the product of some other group and C1h or S2 group, for which the character table is really simple.

We can find this subgroup by looking at the sign representation, or equivalently, the determinants of our SymOp matrices. If we collect all SymOps that have positive determinant matrices, we will have found the large subgroup we are looking for.

Yes, this part is going to be recursive and therefore scary. But don't worry, we thought this through. Any subgroup that is created by only including group elements with positive determinant matrices cannot have either inversion or sigma_h symmetry. Thus, we can never end up in this loop more than once...

This next part is a little tricky. We're effectively going to paste our sub-character-table into our big character table four times. We have to be careful because we need to make sure that the columns or conjugacy classes that we are copying correspond correctly to the columns we are copying them into. Luckily, we know which SymOps the columns correspond do, we know a little bit about the order that they appear in, and we can check the weird ones by just hiting the normal ones with inversion or sigma_h. We're going to use the inversion symmetry whenever it is possible. There is at least one case where we are forced to use mirror symmetry, but this will become obvious.

At this point, we gave up on elegance entirely and decided to tabulate the three remaining character tables that would be stupidly impractical to attempt to calculate. So here they are. Point groups: Td, T, O

Definition at line 1888 of file SymGroup.cc.

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 1308 of file SymGroup.cc.

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 2995 of file SymGroup.cc.

void CASM::SymGroup::_generate_elem_order_table ( ) const

protected

Definition at line 2744 of file SymGroup.cc.

void CASM::SymGroup::_generate_irrep_names ( ) const

protected

Definition at line 947 of file SymGroup.cc.

bool CASM::SymGroup::_generate_multi_table ( ) const

protected

Definition at line 3251 of file SymGroup.cc.

void CASM::SymGroup::_generate_subgroups ( ) const

protected

Definition at line 2836 of file SymGroup.cc.

Array< Index >::X3 CASM::SymGroup::_small_subgroups ( ) const

protected

Definition at line 2776 of file SymGroup.cc.

SymGroupRepID CASM::SymGroup::add_empty_representation ( ) const

Add a new empty representation.

Definition at line 3109 of file SymGroup.cc.

bool CASM::Array< SymOp >::all_in ( const Array< SymOp > & superset ) const

inherited

bool CASM::Array< SymOp >::almost_contains	(	const SymOp &	test_elem,
		double	tol_val = `TOL`
	)		const

inlineinherited

Definition at line 284 of file Array.hh.

Index CASM::Array< SymOp >::almost_find	(	const SymOp &	test_elem,
		double	tol_val = `TOL`
	)		const

inherited

Index CASM::Array< SymOp >::almost_reverse_find	(	const SymOp &	test_elem,
		double	tol_val = `TOL`
	)		const

inherited

Same as almost_find, but start from the last element of the Array.

Array& CASM::Array< SymOp >::append ( const Array< SymOp > & new_tail )

inherited

Array& CASM::Array< SymOp >::append_unique ( const Array< SymOp > & new_tail )

inherited

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

Calls 'apply_sym' on all SymOps in the group.

Definition at line 3413 of file SymGroup.cc.

ReturnArray<Index> CASM::Array< SymOp >::as_perm_inverse ( ) const

inherited

Construct permutation that undoes the permutation performed by 'this' Inverse operation is calculated the same, regardless of permutation convention

ReturnArray<Index> CASM::Array< SymOp >::as_perm_transform_by ( const Array< Index > & trans_perm ) const

inherited

Given N distinct objects labeled from 0 to N-1, a permutation 'P_permute' that physically permutes the objects (with labels) in terms of their labels, and a permutation 'L_permute' that permutes their labels only, rewrite 'P_permute' in terms of the relabeling induced by 'L_permute' Rearrange 'this' permutation to form an equivalent permutation for any list that has already been permuted by trans_perm. Does not (nearly certain of this) depend on permutation convention

SymOp & CASM::Array< SymOp >::at ( Index ind )

inlineinherited

Definition at line 157 of file Array.hh.

const SymOp & CASM::Array< SymOp >::at ( Index ind ) const

inlineinherited

Definition at line 162 of file Array.hh.

SymOp & CASM::Array< SymOp >::back ( )

inlineinherited

Definition at line 177 of file Array.hh.

const SymOp & CASM::Array< SymOp >::back ( ) const

inlineinherited

Definition at line 180 of file Array.hh.

SymOp const* CASM::Array< SymOp >::begin ( ) const

inlineinherited

Definition at line 185 of file Array.hh.

SymOp * CASM::Array< SymOp >::begin ( )

inlineinherited

Definition at line 192 of file Array.hh.

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 3447 of file SymGroup.cc.

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 3489 of file SymGroup.cc.

SymOp const* CASM::Array< SymOp >::cbegin ( ) const

inlineinherited

Definition at line 189 of file Array.hh.

SymOp const* CASM::Array< SymOp >::cend ( ) const

inlineinherited

Definition at line 201 of file Array.hh.

const Array< std::complex< double > >::X2 & CASM::SymGroup::character_table ( ) const

Definition at line 3212 of file SymGroup.cc.

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

Get conjugacy class index of operation at(i)

Definition at line 3071 of file SymGroup.cc.

void CASM::SymGroup::clear ( )

virtual

Reimplemented in CASM::MasterSymGroup.

Definition at line 490 of file SymGroup.cc.

void CASM::SymGroup::clear_tables ( )

virtual

Definition at line 450 of file SymGroup.cc.

Index CASM::Array< SymOp >::coincidence ( const Array< SymOp > & superset ) const

inherited

bool CASM::Array< SymOp >::contains ( const SymOp & test_elem ) const

inlineinherited

Definition at line 281 of file Array.hh.

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 3407 of file SymGroup.cc.

SymGroupRepID CASM::SymGroup::coord_rep_ID ( ) const

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

Definition at line 3098 of file SymGroup.cc.

void CASM::SymGroup::copy_no_trans	(	SymGroup &	shiftless,
		bool	keep_repeated = `false`
	)		const

Fill up a SymGroup with *this minus the shifts.

Definition at line 907 of file SymGroup.cc.

SymOp const* CASM::Array< SymOp >::end ( ) const

inlineinherited

Definition at line 197 of file Array.hh.

SymOp * CASM::Array< SymOp >::end ( )

inlineinherited

Definition at line 204 of file Array.hh.

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 3365 of file SymGroup.cc.

Index CASM::Array< SymOp >::find ( const SymOp & test_elem ) const

inherited

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

Definition at line 3332 of file SymGroup.cc.

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 3309 of file SymGroup.cc.

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 3321 of file SymGroup.cc.

void CASM::SymGroup::from_json ( const jsonParser & json )

re-throw exceptions

Definition at line 3832 of file SymGroup.cc.

const Array< Index >::X2 & CASM::SymGroup::get_alt_multi_table ( ) const

Definition at line 3180 of file SymGroup.cc.

const Array< bool > & CASM::SymGroup::get_complex_irrep_list ( ) const

Definition at line 3204 of file SymGroup.cc.

const Array< Index >::X2 & CASM::SymGroup::get_conjugacy_classes ( ) const

Definition at line 3197 of file SymGroup.cc.

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

Get symrep for a particular irrep.

Definition at line 3121 of file SymGroup.cc.

ReturnArray< Index > CASM::SymGroup::get_irrep_decomposition ( ) const

Definition at line 3707 of file SymGroup.cc.

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

Get symrep ID of a particular irrep.

Definition at line 3088 of file SymGroup.cc.

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

Definition at line 3236 of file SymGroup.cc.

const Array< Index >::X2 & CASM::SymGroup::get_multi_table ( ) const

Definition at line 3170 of file SymGroup.cc.

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

Definition at line 3220 of file SymGroup.cc.

void CASM::SymGroup::get_point_group_type ( ) const

Definition at line 565 of file SymGroup.cc.

void CASM::SymGroup::get_rotation_groups ( ) const

Space group (added by Donghee );.

Definition at line 509 of file SymGroup.cc.

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

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

bool CASM::Array< SymOp >::has_fixed_points ( ) const

inherited

Checks whether any values are equal to their index – only valid for Array<Index>

Index CASM::Array< SymOp >::incidences ( const SymOp & test_elem ) const

inherited

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

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

Definition at line 3046 of file SymGroup.cc.

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 3055 of file SymGroup.cc.

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

Definition at line 927 of file SymGroup.cc.

void CASM::SymGroup::invalidate_multi_tables ( ) const

Definition at line 3189 of file SymGroup.cc.

Array& CASM::Array< SymOp >::ipermute ( const Array< Index > & perm_array )

inherited

bool CASM::Array< SymOp >::is_ascending ( ) const

inherited

bool CASM::Array< SymOp >::is_constant ( ) const

inherited

bool CASM::Array< SymOp >::is_descending ( ) const

inherited

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

Check to see if SymGroup satisfies the group property.

Definition at line 3346 of file SymGroup.cc.

bool CASM::SymGroup::is_irreducible ( ) const

Definition at line 3674 of file SymGroup.cc.

bool CASM::Array< SymOp >::is_permute ( ) const

inherited

Checks that Array contains values from 0 to perm_array.size()-1 and that no value is repeated does not depend on definition of permutation convention

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

Definition at line 940 of file SymGroup.cc.

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

Definition at line 3131 of file SymGroup.cc.

ReturnArray< Array< Index > > CASM::SymGroup::left_cosets ( const Array< Index > & subgroup_inds ) const

Definition at line 3139 of file SymGroup.cc.

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

inline

Definition at line 56 of file SymGroup.hh.

const SymOp & CASM::Array< SymOp >::max ( ) const

inherited

double CASM::SymGroup::max_error ( )

This returns the group's max_error.

Definition at line 933 of file SymGroup.cc.

const SymOp & CASM::Array< SymOp >::min ( ) const

inherited

bool CASM::Array< SymOp >::next_permute ( )

inherited

ReturnArray< Index > CASM::SymGroup::op_indices ( ) const

Definition at line 474 of file SymGroup.cc.

bool CASM::Array< SymOp >::operator!= ( const Array< SymOp > & RHS ) const

inlineinherited

Definition at line 260 of file Array.hh.

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 3691 of file SymGroup.cc.

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

Definition at line 3699 of file SymGroup.cc.

bool CASM::Array< SymOp >::operator< ( const Array< SymOp > & RHS ) const

inherited

bool CASM::Array< SymOp >::operator<= ( const Array< SymOp > & RHS ) const

inlineinherited

Definition at line 265 of file Array.hh.

bool CASM::Array< SymOp >::operator== ( const Array< SymOp > & RHS ) const

inherited

bool CASM::Array< SymOp >::operator> ( const Array< SymOp > & RHS ) const

inherited

bool CASM::Array< SymOp >::operator>= ( const Array< SymOp > & RHS ) const

inlineinherited

Definition at line 268 of file Array.hh.

const SymOp & CASM::Array< SymOp >::operator[] ( Index ind ) const

inlineinherited

Definition at line 167 of file Array.hh.

SymOp & CASM::Array< SymOp >::operator[] ( Index ind )

inlineinherited

Definition at line 172 of file Array.hh.

PERIODICITY_TYPE CASM::SymGroup::periodicity ( ) const

inline

Definition at line 160 of file SymGroup.hh.

Array& CASM::Array< SymOp >::permute ( const Array< Index > & perm_array )

inherited

void CASM::Array< SymOp >::pop_back ( )

inlineinherited

Definition at line 212 of file Array.hh.

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

inline

Definition at line 164 of file SymGroup.hh.

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

Print the SymGroup to a stream.

Definition at line 3431 of file SymGroup.cc.

void CASM::SymGroup::print_character_table ( std::ostream & stream )

Definition at line 1545 of file SymGroup.cc.

void CASM::Array< SymOp >::print_column	(	std::ostream &	stream,
		const std::string &	indent = `""`
	)		const

inherited

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

print locations of the symmetry-generating element of each SymOp

Definition at line 3518 of file SymGroup.cc.

void CASM::SymGroup::print_space_group_info ( std::ostream & out ) const

Definition at line 883 of file SymGroup.cc.

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

virtual

Reimplemented in CASM::MasterSymGroup.

Definition at line 441 of file SymGroup.cc.

void CASM::Array< SymOp >::remove ( Index ind )

inherited

void CASM::Array< SymOp >::reserve ( Index new_max )

inherited

void CASM::Array< SymOp >::resize ( Index new_N )

inherited

void CASM::Array< SymOp >::resize	(	Index	new_N,
		const SymOp &	fill_val
	)

inherited

Index CASM::Array< SymOp >::reverse_find ( const SymOp & test_elem ) const

inherited

Same as find, but starts from the last element of the Array.

static ReturnArray<SymOp > CASM::Array< SymOp >::sequence	(	const SymOp &	initial,
		const SymOp &	final
	)

staticinherited

Returns an array with the sequence (initial, ++initial, ..., final), inclusive.

Returns an array with the sequence (initial, ++initial, ..., final), inclusive requires that operator<() and operator++() are defined on type T

static ReturnArray<SymOp > CASM::Array< SymOp >::sequence	(	const SymOp &	initial,
		const SymOp &	increment,
		const SymOp &	final
	)

staticinherited

Returns an array with the sequence (initial, initial+increment, ..., final?), inclusive if final is in the sequence requires that operator<() and operator+=() are defined on type T

Returns an array with the sequence (initial, initial+increment, ..., final?), inclusive if final is in the sequence

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

set symrep ID of a particular irrep

Definition at line 3079 of file SymGroup.cc.

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

Definition at line 435 of file SymGroup.cc.

Index CASM::Array< SymOp >::size ( ) const

inlineinherited

Definition at line 145 of file Array.hh.

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 3574 of file SymGroup.cc.

void CASM::Array< SymOp >::sort ( const CompareType & comp )

inherited

void CASM::Array< SymOp >::sort ( Array< Index > & ind_order )

inherited

ReturnArray<SymOp > CASM::Array< SymOp >::sub_array	(	Index	ind_begin,
		Index	ind_end
	)		const

inherited

const Array< Index >::X3 & CASM::SymGroup::subgroups ( ) const

Definition at line 3243 of file SymGroup.cc.

SymOp CASM::Array< SymOp >::sum ( ) const

inherited

void CASM::Array< SymOp >::swap ( Array< SymOp > & RHS )

inherited

void CASM::Array< SymOp >::swap_elem	(	Index	i,
		Index	j
	)

inlineinherited

Definition at line 231 of file Array.hh.

jsonParser & CASM::SymGroup::to_json ( jsonParser & json ) const

Definition at line 3740 of file SymGroup.cc.

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

Definition at line 2913 of file SymGroup.cc.

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

Write the SymGroup to a file.

Definition at line 3421 of file SymGroup.cc.

Member Data Documentation

Array<Array<Index> > 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 218 of file SymGroup.hh.

Array<Array<Index> > CASM::SymGroup::centralizer_table

mutableprotected

Definition at line 238 of file SymGroup.hh.

bool CASM::SymGroup::centric

mutableprotected

Definition at line 250 of file SymGroup.hh.

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

mutableprotected

Definition at line 223 of file SymGroup.hh.

std::string CASM::SymGroup::comment

mutableprotected

Definition at line 243 of file SymGroup.hh.

Array<bool> CASM::SymGroup::complex_irrep

mutableprotected

Definition at line 230 of file SymGroup.hh.

Array<Array<Index> > CASM::SymGroup::conjugacy_classes

mutableprotected

Definition at line 222 of file SymGroup.hh.

std::string CASM::SymGroup::crystal_system

mutableprotected

Definition at line 249 of file SymGroup.hh.

Array<Array<Index> > CASM::SymGroup::elem_order_table

mutableprotected

Definition at line 239 of file SymGroup.hh.

Array<std::string> CASM::SymGroup::group_name

mutableprotected

Definition at line 252 of file SymGroup.hh.

Array<int> CASM::SymGroup::group_number

mutableprotected

Definition at line 251 of file SymGroup.hh.

Array<Index> CASM::SymGroup::index2conjugacy_class

mutableprotected

Definition at line 224 of file SymGroup.hh.

Array<SymGroupRepID> CASM::SymGroup::irrep_IDs

mutableprotected

Definition at line 229 of file SymGroup.hh.

Array<std::string> CASM::SymGroup::irrep_names

mutableprotected

Definition at line 231 of file SymGroup.hh.

std::string CASM::SymGroup::latex_name

mutableprotected

Definition at line 242 of file SymGroup.hh.

Array<Array<std::complex<double> > > CASM::SymGroup::m_character_table

mutableprotected

Definition at line 228 of file SymGroup.hh.

PERIODICITY_TYPE CASM::SymGroup::m_group_periodicity

protected

Specifies whether to use lattice periodicity when testing for equivalence.

Definition at line 212 of file SymGroup.hh.

Lattice const* CASM::SymGroup::m_lat_ptr

protected

Pointer to a lattice for doing periodic comparisons.

Definition at line 209 of file SymGroup.hh.

double CASM::SymGroup::m_max_error

mutableprotected

Definition at line 245 of file SymGroup.hh.

Array<Array<Array<Index> > > CASM::SymGroup::m_subgroups

mutableprotected

Definition at line 235 of file SymGroup.hh.

Array<Array<Index> > CASM::SymGroup::multi_table

mutableprotected

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

Definition at line 215 of file SymGroup.hh.

std::string CASM::SymGroup::name

mutableprotected

Definition at line 241 of file SymGroup.hh.

Array<Array<SymOp> > CASM::SymGroup::rotation_groups

mutableprotected

Space group (added by Donghee );.

Definition at line 248 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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation