API Reference

API Reference#

The public API mirrors the Rust crate layout: base (crystal structures and operation containers), dataset (symmetry analysis results), data (crystallographic classification tables), and identify (group identification primitives). The moyopy.interface adapters provide conversion helpers to/from pymatgen and ASE.

This page documents the core types and the space-group API. Layer-group and magnetic-space-group APIs live on additional pages:

Core types#

Lattice + sites, the non-magnetic operation container, and the unimodular transformation type used across all group families.

`Cell`	A crystal structure: a lattice plus fractional positions and atomic numbers.
`Operations`	A list of crystallographic symmetry operations (rotation + translation).
`UnimodularTransformation`	A unimodular transformation: an integer linear part with determinant +-1 plus an

class moyopy.Cell(basis: list[list[float]], positions: list[list[float]], numbers: list[int])#

A crystal structure: a lattice plus fractional positions and atomic numbers.

as_dict() → dict[str, Any]#: Convert this object to a dictionary.

property basis: list[list[float]]#: Row-wise basis vectors of the lattice.

classmethod deserialize_json(json_str: str) → Cell#: Deserialize an object from a JSON string.

classmethod from_dict(data: dict[str, Any]) → Cell#: Create an object from a dictionary.

property num_atoms: int#: Number of atoms in the cell.

property numbers: list[int]#: Atomic number of each site.

property positions: list[list[float]]#: Fractional coordinates of each site.

serialize_json() → str#: Serialize this object to a JSON string.

class moyopy.Operations#

A list of crystallographic symmetry operations (rotation + translation).

as_dict() → dict[str, Any]#: Convert this object to a dictionary.

classmethod deserialize_json(json_str: str) → Operations#: Deserialize an object from a JSON string.

classmethod from_dict(data: dict[str, Any]) → Operations#: Create an object from a dictionary.

property num_operations: int#: Number of symmetry operations.

property rotations: list[list[list[float]]]#: Rotation parts of the symmetry operations.

serialize_json() → str#: Serialize this object to a JSON string.

property translations: list[list[float]]#: Translation parts of the symmetry operations (fractional coordinates).

class moyopy.UnimodularTransformation#

A unimodular transformation: an integer linear part with determinant +-1 plus an origin shift.

as_dict() → dict[str, Any]#: Convert this object to a dictionary.

property linear: list[list[int]]#: Linear part (integer 3x3 matrix with determinant +-1).

property origin_shift: list[float]#: Origin shift (fractional coordinates).

serialize_json() → str#: Serialize this object to a JSON string.

Symmetry datasets#

Run a symmetry analysis on a moyopy.Cell and inspect the result.

MoyoDataset

A dataset containing symmetry information of the input crystal structure.

class moyopy.MoyoDataset(cell: moyopy._base.Cell, *, symprec: float = 0.0001, angle_tolerance: float | None = None, setting: moyopy._data.Setting | None = None, rotate_basis: bool = True)#

A dataset containing symmetry information of the input crystal structure.

property angle_tolerance: float | None#: Actually used angle_tolerance in iterative symmetry search.

as_dict() → dict[str, Any]#: Convert an object to a dictionary.

classmethod deserialize_json(json_str: str) → Self#: Deserialize an object from a JSON string.

classmethod from_dict(obj: dict[str, Any]) → Self#: Create an object from a dictionary.

property hall_number: int#: Hall symbol number.

property mapping_std_prim: list[int]#

Mapping sites in the input cell to those in the primitive standardized cell.

The i-th atom in the input cell is mapped to the mapping_to_std_prim[i]-th atom in the primitive standardized cell.

property number: int#: Space group number.

property operations: moyopy._base.Operations#: Symmetry operations in the input cell.

property orbits: list[int]#

Spglib’s crystallographic_orbits not equivalent_atoms.

The i-th atom in the input cell is equivalent to the orbits[i]-th atom in the input cell. For example, orbits=[0, 0, 2, 2, 2, 2] means the first two atoms are equivalent and the last four atoms are equivalent to each other.

property pearson_symbol: str#: Pearson symbol for standardized cell.

property prim_std_cell: moyopy._base.Cell#

Primitive standardized cell.

Same transformation convention as the standardized cell above:

prim_std_cell.basis.T = std_rotation_matrix @ cell.basis.T @ prim_std_linear
x_prim_std = np.linalg.inv(prim_std_linear) @ (x_input - prim_std_origin_shift)

property prim_std_linear: list[list[float]]#: Linear part of transformation from the input cell to the primitive standardized cell.

property prim_std_origin_shift: list[float]#: Origin shift of transformation from the input cell to the primitive standardized cell.

serialize_json() → str#: Serialize an object to a JSON string.

property site_symmetry_symbols: list[str]#

Site symmetry symbols for each site in the input cell.

The orientation of the site symmetry is w.r.t. the standardized cell.

property std_cell: moyopy._base.Cell#

Standardized cell.

The input cell is related to the standardized cell by (std_linear, std_origin_shift) and std_rotation_matrix:

Lattice:

std_cell.basis.T = std_rotation_matrix @ cell.basis.T @ std_linear

Fractional positions:

x_std = np.linalg.inv(std_linear) @ (x_input - std_origin_shift)

std_rotation_matrix is a rigid rotation (orthogonal matrix) applied only to the Cartesian lattice basis. It does not affect fractional coordinates.

property std_linear: list[list[float]]#: Linear part of transformation from the input cell to the standardized cell.

property std_origin_shift: list[float]#: Origin shift of transformation from the input cell to the standardized cell.

property std_rotation_matrix: list[list[float]]#: Rigid rotation (orthogonal matrix) applied to the lattice basis.

property symprec: float#: Actually used symprec in iterative symmetry search.

property wyckoffs: list[str]#: Wyckoff letters for each site in the input cell.

Crystallographic data#

Hall symbols, settings, centering, classification tables, and helpers to fetch operations by ITA number.

`Setting`	Preference for the setting of the space group.
`Centering`
`HallSymbolEntry`	An entry containing space-group information for a specified hall_number.
`SpaceGroupType`	Space-group type information.
`ArithmeticCrystalClass`	Arithmetic crystal class information.
`operations_from_number`(→ moyopy._base.Operations)

class moyopy.Setting#

Preference for the setting of the space group.

as_dict() → dict[str, Any]#: Convert an object to a dictionary

classmethod hall_number(hall_number: int) → Setting#: Specific Hall number from 1 to 530.

serialize_json() → str#: Serialize an object to a JSON string

classmethod spglib() → Setting#: The setting of the smallest Hall number.

classmethod standard() → Setting#: Unique axis b, cell choice 1 for monoclinic, hexagonal axes for rhombohedral, and origin choice 2 for centrosymmetric space groups.

class moyopy.Centering#

as_dict() → dict[str, Any]#: Convert an object to a dictionary

property lattice_points: list[list[float]]#: Unique lattice points.

property linear: list[list[int]]#: Transformation matrix.

property order: int#: Order of the centering.

serialize_json() → str#: Serialize an object to a JSON string

class moyopy.HallSymbolEntry(hall_number: int)#

An entry containing space-group information for a specified hall_number.

property arithmetic_number: int#: Number for arithmetic crystal classes (1 - 73).

as_dict() → dict[str, Any]#: Convert an object to a dictionary

property centering: Centering#: Centering.

property hall_number: int#: Number for Hall symbols (1 - 530).

property hall_symbol: str#: Hall symbol.

property hm_full: str#: Hermann-Mauguin symbol in full notation.

property hm_short: str#: Hermann-Mauguin symbol in short notation.

property number: int#: ITA number for space group types (1 - 230).

serialize_json() → str#: Serialize an object to a JSON string

property setting: Setting#: Setting.

class moyopy.SpaceGroupType(number: int)#

Space-group type information.

property arithmetic_number: int#: Number for arithmetic crystal classes (1 - 73).

property arithmetic_symbol: str#

Symbol for arithmetic crystal class.

See spglib/moyo for string values.

as_dict() → dict[str, Any]#: Convert an object to a dictionary

property bravais_class: str#

Bravais class.

See spglib/moyo for string values.

property crystal_family: str#

Crystal family.

See spglib/moyo for string values.

property crystal_system: str#

Crystal system.

See spglib/moyo for string values.

property geometric_crystal_class: str#

Geometric crystal class.

See spglib/moyo for string values.

property hm_full: str#: Hermann-Mauguin symbol in full notation.

property hm_short: str#: Hermann-Mauguin symbol in short notation.

property lattice_system: str#

Lattice system.

See spglib/moyo for string values.

property number: int#: ITA number for space group types (1 - 230).

serialize_json() → str#: Serialize an object to a JSON string

class moyopy.ArithmeticCrystalClass(arithmetic_number: int)#

Arithmetic crystal class information.

property arithmetic_number: int#: Number for arithmetic crystal classes (1 - 73).

property arithmetic_symbol: str#: Symbol for arithmetic crystal class.

as_dict() → dict[str, Any]#: Convert an object to a dictionary

property bravais_class: str#: Bravais class.

property geometric_crystal_class: str#: Geometric crystal class.

serialize_json() → str#: Serialize an object to a JSON string

moyopy.operations_from_number(number: int, *, setting: Setting | None = None, primitive: bool = False) → moyopy._base.Operations#

Group identification#

Identify point groups and space groups from a primitive list of symmetry operations.

`PointGroup`	Point group identified from a list of rotation matrices.
`SpaceGroup`	Space group identified from a list of primitive symmetry operations.
`integral_normalizer`(...)	Compute the integral normalizer of a space group.

class moyopy.PointGroup(prim_rotations: list[list[int]], *, basis: list[list[float]] | None = None)#

Point group identified from a list of rotation matrices.

property arithmetic_number: int#: Number for the arithmetic crystal class (1 - 73).

as_dict() → dict[str, Any]#: Convert this object to a dictionary.

property prim_trans_mat: list[list[int]]#: Transformation matrix from the input primitive basis to the standardized basis.

serialize_json() → str#: Serialize this object to a JSON string.

class moyopy.SpaceGroup(prim_rotations: list[list[int]], prim_translations: list[list[float]], *, basis: list[list[float]] | None = None, setting: moyopy._data.Setting | None = None, epsilon: float = 0.0001)#

Space group identified from a list of primitive symmetry operations.

as_dict() → dict[str, Any]#: Convert this object to a dictionary.

property hall_number: int#: Hall symbol number (1 - 530) for the chosen setting.

property linear: list[list[int]]#: Linear part of the transformation from the input primitive basis to the standardized basis.

property number: int#: ITA number for the identified space group (1 - 230).

property origin_shift: list[float]#: Origin shift of the transformation from the input primitive basis to the standardized basis.

serialize_json() → str#: Serialize this object to a JSON string.

moyopy.integral_normalizer(prim_rotations: list[list[list[int]]], prim_translations: list[list[float]], *, prim_generators: list[int] | None = None, epsilon: float = 0.0001) → list[moyopy._base.UnimodularTransformation]#

Compute the integral normalizer of a space group.

Returns the unimodular transformations that conjugate the given space group into itself.

Parameters:

prim_rotations (list[list[list[int]]]) – Rotation matrices of the symmetry operations of the primitive cell.
prim_translations (list[list[float]]) – Translation vectors of the symmetry operations of the primitive cell.
prim_generators (list[int] | None) – Optional indices of operations to use as generators. If None, a small generating set is derived automatically.
epsilon (float) – Numerical tolerance for matching translations.

Adapters#

Convert between moyopy.Cell and pymatgen Structure / ASE Atoms. Requires the optional dependencies installed via pip install moyopy[interface]. The magnetic counterpart moyopy.interface.MoyoNonCollinearMagneticAdapter lives on the Magnetic Space Group page.

MoyoAdapter

class moyopy.interface.MoyoAdapter[source]#

static from_atoms(atoms: ase.Atoms) → moyopy.Cell[source]#

static from_disordered_structure(structure: pymatgen.core.Structure) → tuple[moyopy.Cell, dict[int, pymatgen.core.Composition]][source]#

Convert a disordered pymatgen Structure to a Moyo Cell.

Parameters:

structure (Structure) – A pymatgen Structure object, which may contain disordered sites.

Returns:

cell (moyopy.Cell) – The converted Moyo Cell object.
unique_species_mapping (dict[int, Composition]) – A mapping from integer indices used in the Moyo Cell to the original pymatgen SpeciesLike objects.

static from_py_obj(struct: pymatgen.core.Structure | ase.Atoms | pymatgen.io.ase.MSONAtoms) → moyopy.Cell[source]#

Convert a Python atomic structure object to a Moyo Cell.

Parameters:: struct – Currently supports pymatgen Structure, ASE Atoms, and MSONAtoms
Returns:: The converted Moyo cell
Return type:: moyopy.Cell

static from_structure(structure: pymatgen.core.Structure) → moyopy.Cell[source]#: Convert a pymatgen Structure to a Moyo Cell.

static get_atoms(cell: moyopy.Cell) → ase.Atoms[source]#

static get_structure(cell: moyopy.Cell, *, unique_species_mapping: dict[int, pymatgen.core.Composition] | None = None) → pymatgen.core.Structure[source]#

Convert a Moyo Cell to a pymatgen Structure.

If the Cell was created from a disordered Structure, the unique_species_mapping should be provided to reconstruct the original species.

Parameters:

cell (moyopy.Cell) – The Moyo Cell to convert.
unique_species_mapping (dict[int, Composition] | None) – A mapping from integer indices used in the Moyo Cell to the original pymatgen SpeciesLike objects. If None, assumes the Cell was created from an ordered Structure.

Returns:

structure – The converted pymatgen Structure object.

Return type:

Structure

API Reference

Contents

API Reference#

Core types#

Symmetry datasets#

Crystallographic data#

Group identification#

Adapters#