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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 the readers |
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: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 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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class PeriodicSet: |
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"""A periodic set representats a crystal by putting a point in the |
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center of each atom. Mathematically it's defined by a basis (unit |
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cell) and collection of points (motif) which repeats according to |
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the basis. Periodic sets are defined for any dimension. |
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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 the 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): |
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return self.cell.shape[0] |
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def __str__(self): |
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"""Returns a string representation of the format |
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PeriodicSet(name, motif (m, d), t asym sites, |
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abcαβγ=cellpar). |
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""" |
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if self.asymmetric_unit is None: |
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n_asym_sites = len(self.motif) |
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else: |
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n_asym_sites = len(self.asymmetric_unit) |
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cellpar_str = None |
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if self.ndim == 1: |
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cellpar_str = f', cell={self.cell[0][0]}' |
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if self.ndim == 2: |
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cellpar = np.round(cell_to_cellpar_2D(self.cell), 2) |
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cellpar_str = ','.join(str(round(p, 2)) for p in cellpar) |
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cellpar_str = f', abα={cellpar_str}' |
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elif self.ndim == 3: |
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cellpar = np.round(cell_to_cellpar(self.cell), 2) |
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cellpar_str = ','.join(str(round(p, 2)) for p in cellpar) |
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cellpar_str = f', abcαβγ={cellpar_str}' |
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else: |
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cellpar_str = f'' |
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s = f'PeriodicSet(name={self.name}, ' \ |
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f'motif {self.motif.shape} ({n_asym_sites} asym sites)' \ |
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f'{cellpar_str})' |
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return s |
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def __repr__(self): |
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if self.asymmetric_unit is None: |
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n_asym_sites = len(self.motif) |
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else: |
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n_asym_sites = len(self.asymmetric_unit) |
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s = f'PeriodicSet(name={self.name}, ' \ |
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f'motif={self.motif} ({n_asym_sites} asym sites), ' \ |
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f'cell={self.cell})' |
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return s |
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def __eq__(self, other): |
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"""Used for debugging/tests. Returns True if: |
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1. The unit cells are identical (element for element within tol) |
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2. The motifs are the same shape, and when transformed into |
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fractional coordinates every point in one motif has an identical |
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(within tol) point somewhere in the other, accounting for pbc. |
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""" |
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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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fm1 = np.mod(self.motif @ np.linalg.inv(self.cell), 1) |
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fm2 = np.mod(other.motif @ np.linalg.inv(other.cell), 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((np.amin(diffs, axis=0) <= 1e-8) | (np.amin(diffs, axis=-1) <= 1e-8)): |
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return False |
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return True |
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def __ne__(self, other): |
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return not self.__eq__(other) |
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@staticmethod |
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def cubic(scale=1, dims=3): |
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"""Return a :class:`PeriodicSet` representing a cubic lattice. |
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""" |
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cell = np.identity(dims) * scale |
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return PeriodicSet(np.zeros((1, dims)), cell) |
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@staticmethod |
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def hexagonal(scale=1, dims=3): |
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"""Dimensions 2 and 3 only. Return a :class:`PeriodicSet` |
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representing a hexagonal lattice. |
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""" |
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if dims == 3: |
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cell = cellpar_to_cell(scale, scale, scale, 90, 90, 120) |
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elif dims == 2: |
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cell = cellpar_to_cell_2D(scale, scale, 60) |
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else: |
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msg = 'PeriodicSet.hexagonal() only implemented for dimensions ' \ |
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f'2 and 3 (passed {dims})' |
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raise NotImplementedError(msg) |
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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, |
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length_bounds=(1, 2), |
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angle_bounds=(60, 120), |
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dims=3 |
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): |
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"""Dimensions 2 and 3 only. Return a :class:`PeriodicSet` with a |
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chosen number of randomly placed points, in random cell with |
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edges between length_bounds and angles between angle_bounds. |
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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
