Reference¶

Library¶

A tool for describing symmetry operations and their representations.

class symmetry_representation.SymmetryGroup(symmetries, full_group=False)[source]¶

Describes a symmetry group.

Parameters

symmetries (List[SymmetryOperation]) – Elements of the symmetry group.
full_group (bool) – Flag which determines whether the symmetry elements describe the full group or just a generating subset.

symmetries¶

Elements of the symmetry group.

Type: List[SymmetryOperation]

full_group¶

Flag which determines whether the symmetry elements describe the full group or just a generating subset.

Type: bool

classmethod from_hdf5(hdf5_handle)¶: Deserializes the object stored in HDF5 format.

class symmetry_representation.SymmetryOperation(*, rotation_matrix, translation_vector=None, repr_matrix, repr_has_cc=False, numeric=None)[source]¶

Describes a symmetry operation.

Parameters

rotation_matrix (array) – Real-space rotation matrix of the symmetry (in reduced coordinates).
translation_vector (array) – Real-space displacement vector of the symmetry (in reduced coordinates).
repr_matrix (array) – Matrix of the representation corresponding to the symmetry operation.
repr_has_cc (bool) – Specifies whether the representation contains a complex conjugation.
numeric (bool) – Specifies whether the symmetry operation contains a numeric or analytic values. By default, this is determined by the type of the rotation matrix.

real_space_operator¶

Real-space operator of the symmetry.

Type: RealSpaceOperator

repr¶

Symmetry representation.

Type: Representation

classmethod from_hdf5(hdf5_handle)[source]¶: Deserializes the object stored in HDF5 format.

classmethod from_orbitals(*, orbitals, real_space_operator, rotation_matrix_cartesian, numeric, **kwargs)[source]¶

Construct a (unitary) symmetry operation from the basis orbitals, real space operator and cartesian rotation matrix. The automatic construction of the representation matrix is used.

Parameters

orbitals (Iterable[Orbital]) – The basis of orbitals with respect to which the represenation matrix is constructed.
real_space_operator (RealSpaceOperator) – The real space operator of the matrix.
rotation_matrix_cartesian (array) – The rotation matrix of the symmetry, in cartesian coordinates.
numeric (bool) – Determines whether a numeric (numpy) or analytic (sympy) representation matrix is constructed.

get_order(max_order=20)[source]¶: Get the order of a symmetry, i.e. the lowest power to which the symmetry is identity.

class symmetry_representation.RealSpaceOperator(rotation_matrix, translation_vector=None, numeric=None)[source]¶

Describes the real-space operator of a symmetry operation.

Parameters

rotation_matrix (array) – Describes the rotation matrix of the symmetry, in reduced coordinates
translation_vector (array) – The translation vector of the symmetry.
numeric (bool) – Specifies whether the symmetry operation contains a numeric or analytic values. By default, this is determined by the type of the rotation matrix.

apply(r)[source]¶: Apply symmetry operation to a vector in reduced real-space coordinates.

classmethod from_hdf5(hdf5_handle)¶: Deserializes the object stored in HDF5 format.

property is_lattice_translation¶: Checks if the operation is a lattice translation, i.e. a pure translation where the translation vector is a lattice vector.

property is_pure_translation¶: Checks whether the operation is a pure translation, without rotation or reflection part.

class symmetry_representation.Representation(matrix, has_cc=False, numeric=None)[source]¶

Describes an (anti-)unitary representation of a symmetry operation. For unitary symmetry, the representation is given as a unitary matrix \(U_g\). For anti-unitary symmetries, it is given as \(U_g \hat{K}\), where \(\hat{K}\) is the complex conjugation operator.

Parameters

matrix (array) – The unitary matrix of the representation.
has_cc (bool) – Determines whether the representation contains complex conjugation (that is, whether it is anti-unitary).
numeric (bool) – Determines if the representation matrix is numeric or analytic. By default this is determined from the type of the passed matrix.

classmethod from_hdf5(hdf5_handle)¶: Deserializes the object stored in HDF5 format.

property is_identity¶: Checks if a representation is the identity.

symmetry_representation.is_compatible(*, structure, symmetry)[source]¶

Checks whether a given symmetry’s real space action (rotation + translation vector) is consistent with a given structure.

Parameters

structure (pymatgen.Structure) – The crystal structure.
symmetry (SymmetryOperation) – The symmetry operation that is checked for compatibility.

symmetry_representation.filter_compatible(symmetries, *, structure)[source]¶

symmetry_representation.filter_compatible(symmetries: collections.abc.Iterable, *, structure)

symmetry_representation.filter_compatible(symmetry: symmetry_representation._sym_op.SymmetryOperation, *, structure)

symmetry_representation.filter_compatible(symmetry_group: symmetry_representation._sym_op.SymmetryGroup, *, structure)

Returns the symmetries which are compatible with the given structure.

Parameters

symmetries (SymmetryGroup, Iterable) – The symmetries which should be checked for compatibility. If a SymmetryGroup is given, the result is also given as a SymmetryGroup.
structure (pymatgen.Structure) – The crystal structure.

class symmetry_representation.Orbital(*, position, function_string, spin=None)[source]¶

Defines a basis orbital.

position¶

Position of the orbital, in reduced coordinates.

Type: array

function_string¶

String describing the function of the orbital.

Type: str

spin¶

Spin component of the orbital.

Type: Spin

classmethod from_hdf5(hdf5_handle)¶: Deserializes the object stored in HDF5 format.

class symmetry_representation.Spin[source]¶

Describes the spin component of an orbital.

total¶

The total spin.

Type: Fraction

z_component¶

The component of spin in z direction.

Type: Fraction

classmethod from_hdf5(hdf5_handle)¶: Deserializes the object stored in HDF5 format.

symmetry_representation.get_time_reversal(*, orbitals, numeric)[source]¶

Create the symmetry operation for time-reversal.

Parameters

orbitals (List(Orbital)) – Basis orbitals with respect to which the representation should be created.
numeric (bool) – Flag to determine whether numeric (numpy) or symbolic (sympy) computation should be used.

symmetry_representation.get_repr_matrix(*, orbitals, real_space_operator, rotation_matrix_cartesian, numeric, position_tolerance=0.0001)[source]¶

Create the representation matrix for a unitary operator. If analytic values are used (numeric=False), the rotation_matrix_cartesian must be an exact value.

Parameters

orbitals (List(Orbital)) – Basis orbitals with respect to which the representation should be created.
real_space_operator (RealSpaceOperator) – Real-space operator of the symmetry operation.
rotation_matrix_cartesian (np.array or sp.Matrix) – Rotation matrix of the symmetry operation in cartesian coordinates.
numeric (bool) – Flag to determine whether numeric (numpy) or symbolic (sympy) computation should be used.
position_tolerance (float) – Absolute distance between positions (in reciprocal units) for which they are still considered to be the same position.

Command Line Interface¶

symmetry-repr¶

symmetry-repr [OPTIONS] COMMAND [ARGS]...

filter-symmetries¶

Selects symmetries which are compatible with the given lattice.

symmetry-repr filter-symmetries [OPTIONS]

Options

-s, --symmetries <symmetries>¶: File containing the symmetries (in HDF5 format).

-l, --lattice <lattice>¶: File containing the lattice structure.

-o, --output <output>¶: File where the filtered symmetries are written (in HDF5 format).