# 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]

Returns the symmetries which are compatible with the given structure.

Parameters
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).