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"""Implements the :class:`PeriodicSet` class representing a periodic |
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set, defined by a motif and unit cell. This models a crystal with a |
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point at the center of each atom. |
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This is the type yielded by :class:`amd.CifReader <.io.CifReader>` and |
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:class:`amd.CSDReader <.io.CSDReader>`. A :class:`PeriodicSet` can be |
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passed as the first argument to :func:`amd.AMD() <.calculate.AMD>` or |
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:func:`amd.PDD() <.calculate.PDD>` to calculate its invariants. |
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""" |
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from __future__ import annotations |
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from typing import Optional |
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import numpy as np |
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from .utils import ( |
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cellpar_to_cell, |
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cellpar_to_cell_2D, |
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cell_to_cellpar, |
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cell_to_cellpar_2D, |
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random_cell, |
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) |
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__all__ = ['PeriodicSet'] |
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class PeriodicSet: |
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"""A periodic set is a collection of points (motif) which |
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periodically repeats according to a lattice (unit cell), often |
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representing a crystal. |
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:class:`PeriodicSet` s are returned by the readers in the |
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:mod:`.io` module. They can be passed to |
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:func:`amd.AMD() <.calculate.AMD>` or |
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:func:`amd.PDD() <.calculate.PDD>` to calculate their invariants. |
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Parameters |
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---------- |
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motif : :class:`numpy.ndarray` |
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Cartesian (orthogonal) coordinates of the motif, shape (no |
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points, dims). |
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cell : :class:`numpy.ndarray` |
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Cartesian (orthogonal) square array representing the unit cell, |
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shape (dims, dims). Use |
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:func:`amd.cellpar_to_cell <.utils.cellpar_to_cell>` to convert |
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6 cell parameters to an orthogonal square matrix. |
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name : str, optional |
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Name of the periodic set. |
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asymmetric_unit : :class:`numpy.ndarray`, optional |
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Indices for the asymmetric unit, pointing to the motif. Useful |
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in invariant calculations. |
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wyckoff_multiplicities : :class:`numpy.ndarray`, optional |
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Wyckoff multiplicities of each atom in the asymmetric unit |
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(number of unique sites generated under all symmetries). Useful |
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in invariant calculations. |
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types : :class:`numpy.ndarray`, optional |
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Array of atomic numbers of motif points. |
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""" |
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def __init__( |
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self, |
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motif: np.ndarray, |
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cell: np.ndarray, |
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name: Optional[str] = None, |
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asymmetric_unit: Optional[np.ndarray] = None, |
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wyckoff_multiplicities: Optional[np.ndarray] = None, |
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types: Optional[np.ndarray] = None |
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): |
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self.motif = motif |
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self.cell = cell |
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self.name = name |
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self.asymmetric_unit = asymmetric_unit |
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self.wyckoff_multiplicities = wyckoff_multiplicities |
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self.types = types |
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@property |
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def ndim(self) -> int: |
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return self.cell.shape[0] |
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def __str__(self): |
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def format_cellpar(par): |
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return f'{par:.2f}'.rstrip('0').rstrip('.') |
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m, n = self.motif.shape |
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m_pl = '' if m == 1 else 's' |
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n_pl = '' if n == 1 else 's' |
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if self.ndim == 1: |
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cellpar_str = f', cell={format_cellpar(self.cell[0][0])}' |
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elif self.ndim == 2: |
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cellpar = cell_to_cellpar_2D(self.cell) |
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cellpar_str = ','.join(map(format_cellpar, cellpar)) |
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cellpar_str = f', abα={cellpar_str}' |
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elif self.ndim == 3: |
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cellpar = cell_to_cellpar(self.cell) |
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cellpar_str = ','.join(map(format_cellpar, cellpar)) |
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cellpar_str = f', abcαβγ={cellpar_str}' |
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else: |
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cellpar_str = '' |
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return ( |
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f'PeriodicSet(name={self.name}: {m} point{m_pl} in {n} dim{n_pl}' |
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f'{cellpar_str})' |
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) |
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def __repr__(self): |
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name_str = f'name={self.name}, ' if self.name is not None else '' |
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optional_attrs = [] |
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for attr_str in ('asymmetric_unit', 'wyckoff_multiplicities', 'types'): |
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attr = getattr(self, attr_str) |
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if attr is not None: |
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optional_attrs.append(f'{attr_str}={attr}') |
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optional_attrs_str = ', ' if optional_attrs else '' |
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optional_attrs_str += ', '.join(optional_attrs) |
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return ( |
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f'PeriodicSet({name_str}motif={self.motif}, cell={self.cell}' |
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f'{optional_attrs_str})' |
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) |
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def _equal_cell_and_motif(self, other): |
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"""Used for debugging/tests. True if both 1. the unit cells are |
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(close to) identical, and 2. the motifs are the same shape, and |
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every point in one motif has a (close to) identical point |
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somewhere in the other, accounting for pbc. |
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""" |
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tol = 1e-8 |
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if self.cell.shape != other.cell.shape or \ |
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self.motif.shape != other.motif.shape or \ |
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not np.allclose(self.cell, other.cell): |
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return False |
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cell_inv = np.linalg.inv(self.cell) |
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fm1 = np.mod(self.motif @ cell_inv, 1) |
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fm2 = np.mod(other.motif @ cell_inv, 1) |
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d1 = np.abs(fm2[:, None] - fm1) |
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d2 = np.abs(d1 - 1) |
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diffs = np.amax(np.minimum(d1, d2), axis=-1) |
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if not np.all( |
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(np.amin(diffs, axis=0) <= tol) | (np.amin(diffs, axis=-1) <= tol) |
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): |
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return False |
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return True |
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@staticmethod |
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def cubic(scale: float = 1.0, dims: int = 3) -> PeriodicSet: |
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"""Returns a :class:`PeriodicSet` representing a cubic lattice. |
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""" |
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return PeriodicSet(np.zeros((1, dims)), np.identity(dims) * scale) |
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@staticmethod |
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def hexagonal(scale: float = 1.0, dims: int = 3) -> PeriodicSet: |
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""" Return a :class:`PeriodicSet` representing a hexagonal |
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lattice. Dimensions 2 and 3 only. |
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""" |
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if dims == 3: |
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cellpar = np.array([scale, scale, scale, 90.0, 90.0, 120.0]) |
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cell = cellpar_to_cell(cellpar) |
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elif dims == 2: |
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cell = cellpar_to_cell_2D(np.array([scale, scale, 60.0])) |
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else: |
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raise NotImplementedError( |
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'amd.PeriodicSet.hexagonal() only implemented for dimensions ' |
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f'2 and 3, passed {dims}' |
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) |
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return PeriodicSet(np.zeros((1, dims)), cell) |
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@staticmethod |
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def _random( |
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n_points: int, |
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length_bounds: tuple = (1.0, 2.0), |
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angle_bounds: tuple = (60.0, 120.0), |
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dims: int = 3 |
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) -> PeriodicSet: |
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"""Return a :class:`PeriodicSet` with a chosen number of |
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randomly placed points, in a random cell with edges between |
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``length_bounds`` and angles between ``angle_bounds``. |
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Dimensions 2 and 3 only. |
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""" |
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cell = random_cell( |
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length_bounds=length_bounds, |
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angle_bounds=angle_bounds, |
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dims=dims |
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) |
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frac_motif = np.random.uniform(size=(n_points, dims)) |
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return PeriodicSet(frac_motif @ cell, cell) |
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dwiddo /
average-minimum-distance
