CASM::SymRepTools Namespace Reference

Classes
struct	IrrepInfo
struct	IrrepWedge
	An irreducible wedge in an irreducible vector space. More...
class	SubWedge
	SubWedge is a vector of IrrepWedge, one from each irreducible subspace Together, the IrrepWedges that comprise the Subwedge span the entire space However, it is likely that the orbit of equivalent SubWedges does not fill the entire space. More...

Typedefs
using	Symmetrizer = std::pair< Eigen::MatrixXcd, multivector< Eigen::VectorXcd >::X< 2 > >
using	SymmetrizerFunction = std::function< Symmetrizer(Eigen::Ref< const Eigen::MatrixXcd > const &f_subspace)>

Functions
std::vector< IrrepWedge >	irrep_wedges (SymGroup const &head_group, SymGroupRepID id, Eigen::Ref< const Eigen::MatrixXd > const &_subspace)
std::vector< IrrepWedge >	irrep_wedges (SymGroupRep const &_rep, SymGroup const &head_group, Eigen::Ref< const Eigen::MatrixXd > const &_subspace)
std::vector< SubWedge >	symrep_subwedges (SymGroup const &_group, SymGroupRepID id)
std::vector< SubWedge >	symrep_subwedges (SymGroup const &_group, SymGroupRepID id, Eigen::Ref< const Eigen::MatrixXd > const &_subspace)
std::vector< SubWedge >	symrep_subwedges (SymGroupRep const &_rep, SymGroup const &head_group)
std::vector< SubWedge >	symrep_subwedges (SymGroupRep const &_rep, SymGroup const &head_group, Eigen::Ref< const Eigen::MatrixXd > const &_subspace)

Typedef Documentation

Symmetrizer

using CASM::SymRepTools::Symmetrizer = typedef std::pair<Eigen::MatrixXcd, multivector<Eigen::VectorXcd>::X<2> >

A Symmetrizer comprises a MatrixXcd, which defines a rotation of a generically-oriented irreducible subspace that aligns its components along high-symmetry directions, and a vector of orbits of high-symmetry directions

Definition at line 20 of file SymRepTools.hh.

SymmetrizerFunction

using CASM::SymRepTools::SymmetrizerFunction = typedef std::function<Symmetrizer( Eigen::Ref<const Eigen::MatrixXcd> const &f_subspace)>

A SymmetrizerFunction takes a matrix whose columns specify an irreducible subspace, and returns a Symmetrizer for symmetrizing that subspace

Definition at line 25 of file SymRepTools.hh.

Function Documentation

irrep_wedges() [1/2]

std::vector< IrrepWedge > CASM::SymRepTools::irrep_wedges	(	SymGroup const &	head_group,
		SymGroupRepID	id,
		Eigen::Ref< const Eigen::MatrixXd > const &	_subspace
	)

Find IrrepWedges for a group-represented vector space, knowing only the group and the representation ID

Parameters

_subspace

matrix whose columns span a subspace of the full vector space (pass Identity matrix to decompose full space)

Definition at line 1312 of file SymRepTools.cc.

irrep_wedges() [2/2]

std::vector< IrrepWedge > CASM::SymRepTools::irrep_wedges	(	SymGroupRep const &	_rep,
		SymGroup const &	head_group,
		Eigen::Ref< const Eigen::MatrixXd > const &	_subspace
	)

Find IrrepWedges for a group-represented vector space, knowing only the group and representation

Parameters

_subspace

matrix whose columns span a subspace of the full vector space (pass Identity matrix to decompose full space)

Definition at line 1321 of file SymRepTools.cc.

symrep_subwedges() [1/4]

std::vector< SubWedge > CASM::SymRepTools::symrep_subwedges	(	SymGroup const &	_group,
		SymGroupRepID	id
	)

Find full irreducible wedge of a group-represented vector space, as a vector of SubWedges, knowing only the SymGroup and representation ID

Definition at line 1382 of file SymRepTools.cc.

symrep_subwedges() [2/4]

std::vector< SubWedge > CASM::SymRepTools::symrep_subwedges	(	SymGroup const &	_group,
		SymGroupRepID	id,
		Eigen::Ref< const Eigen::MatrixXd > const &	_subspace
	)

Find full irreducible wedge of a group-represented vector space, as a vector of SubWedges, knowing only the SymGroup and representation ID

Parameters

_subspace

matrix whose columns span a subspace of the full vector space

Definition at line 1390 of file SymRepTools.cc.

symrep_subwedges() [3/4]

std::vector< SubWedge > CASM::SymRepTools::symrep_subwedges	(	SymGroupRep const &	_rep,
		SymGroup const &	head_group
	)

Find full irreducible wedge of a group-represented vector space, as a vector of SubWedges, knowing only the SymGroup and representation

Definition at line 1399 of file SymRepTools.cc.

symrep_subwedges() [4/4]

std::vector< SubWedge > CASM::SymRepTools::symrep_subwedges	(	SymGroupRep const &	_rep,
		SymGroup const &	head_group,
		Eigen::Ref< const Eigen::MatrixXd > const &	_subspace
	)

Find full irreducible wedge of a group-represented vector space, as a vector of SubWedges, knowing only the SymGroup and representation

Parameters

_subspace

matrix whose columns span a subspace of the full vector space

Definition at line 1406 of file SymRepTools.cc.