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"""General utility functions. |
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""" |
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from typing import Tuple |
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import numpy as np |
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import numba |
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from scipy.spatial.distance import squareform |
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def diameter(cell): |
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"""Diameter of a unit cell (as a square matrix in |
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Cartesian/Orthogonal form) in 3 or fewer dimensions. |
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""" |
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dims = cell.shape[0] |
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if dims == 1: |
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return cell[0][0] |
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if dims == 2: |
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diagonals = np.array([cell[0] + cell[1], cell[0] - cell[1]]) |
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d = np.amax(np.linalg.norm(diagonals, axis=-1)) |
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elif dims == 3: |
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diams = np.array([ |
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cell[0] + cell[1] + cell[2], |
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cell[0] + cell[1] - cell[2], |
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cell[0] - cell[1] + cell[2], |
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- cell[0] + cell[1] + cell[2] |
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]) |
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d = np.amax(np.linalg.norm(diams, axis=-1)) |
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else: |
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msg = 'diameter() not implemented for dims > 3 (passed cell shape ' \ |
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f'{cell.shape}).' |
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raise NotImplementedError(msg) |
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return d |
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@numba.njit() |
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def cellpar_to_cell(a, b, c, alpha, beta, gamma): |
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"""Simplified version of function from :mod:`ase.geometry` of the |
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same name. 3D unit cell parameters a,b,c,α,β,γ --> cell as 3x3 |
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:class:`numpy.ndarray`. |
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""" |
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eps = 2 * np.spacing(90) # ~1.4e-14 |
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cos_alpha = 0 if abs(abs(alpha) - 90) < eps else np.cos(alpha * np.pi / 180) |
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cos_beta = 0 if abs(abs(beta) - 90) < eps else np.cos(beta * np.pi / 180) |
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cos_gamma = 0 if abs(abs(gamma) - 90) < eps else np.cos(gamma * np.pi / 180) |
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if abs(gamma - 90) < eps: |
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sin_gamma = 1 |
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elif abs(gamma + 90) < eps: |
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sin_gamma = -1 |
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else: |
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sin_gamma = np.sin(gamma * np.pi / 180.) |
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cy = (cos_alpha - cos_beta * cos_gamma) / sin_gamma |
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cz_sqr = 1 - cos_beta ** 2 - cy ** 2 |
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if cz_sqr < 0: |
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raise RuntimeError('Could not create unit cell from given parameters.') |
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cell = np.zeros((3, 3)) |
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cell[0, 0] = a |
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cell[1, 0] = b * cos_gamma |
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cell[1, 1] = b * sin_gamma |
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cell[2, 0] = c * cos_beta |
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cell[2, 1] = c * cy |
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cell[2, 2] = c * np.sqrt(cz_sqr) |
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return cell |
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@numba.njit() |
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def cellpar_to_cell_2D(a, b, alpha): |
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"""2D unit cell parameters a,b,α --> cell as 2x2 |
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:class:`numpy.ndarray`. |
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""" |
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cell = np.zeros((2, 2)) |
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ang = alpha * np.pi / 180. |
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cell[0, 0] = a |
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cell[1, 0] = b * np.cos(ang) |
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cell[1, 1] = b * np.sin(ang) |
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return cell |
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def cell_to_cellpar(cell): |
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"""Unit cell as a 3x3 :class:`numpy.ndarray` --> list of 6 lengths + |
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angles. |
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""" |
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lengths = np.linalg.norm(cell, axis=-1) |
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angles = [] |
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for i, j in [(1, 2), (0, 2), (0, 1)]: |
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ang_rad = np.arccos(np.dot(cell[i], cell[j]) / (lengths[i] * lengths[j])) |
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angles.append(np.rad2deg(ang_rad)) |
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return np.concatenate((lengths, np.array(angles))) |
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def cell_to_cellpar_2D(cell): |
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"""Unit cell as a 2x2 :class:`numpy.ndarray` --> list of 2 lengths |
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and an angle. |
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""" |
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cellpar = np.zeros((3, )) |
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lengths = np.linalg.norm(cell, axis=-1) |
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ang_rad = np.arccos(np.dot(cell[0], cell[1]) / (lengths[0] * lengths[1])) |
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cellpar[0] = lengths[0] |
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cellpar[1] = lengths[1] |
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cellpar[2] = np.rad2deg(ang_rad) |
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return cellpar |
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def neighbours_from_distance_matrix( |
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n: int, |
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dm: np.ndarray |
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) -> Tuple[np.ndarray, np.ndarray]: |
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"""Given a distance matrix, find the n nearest neighbours of each |
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item. |
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Parameters |
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---------- |
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n : int |
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Number of nearest neighbours to find for each item. |
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dm : :class:`numpy.ndarray` |
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2D distance matrix or 1D condensed distance matrix. |
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Returns |
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------- |
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(nn_dm, inds) : Tuple[:class:`numpy.ndarray`, :class:`numpy.ndarray`] |
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``nn_dm[i][j]`` is the distance from item :math:`i` to its |
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:math:`j+1` st nearest neighbour, and ``inds[i][j]`` is the |
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index of this neighbour (:math:`j+1` since index 0 is the first |
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nearest neighbour). |
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""" |
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inds = None |
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# 2D distance matrix |
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if len(dm.shape) == 2: |
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inds = np.array([np.argpartition(row, n)[:n] for row in dm]) |
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# 1D condensed distance vector |
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elif len(dm.shape) == 1: |
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dm = squareform(dm) |
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inds = [] |
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for i, row in enumerate(dm): |
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inds_row = np.argpartition(row, n+1)[:n+1] |
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inds_row = inds_row[inds_row != i][:n] |
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inds.append(inds_row) |
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inds = np.array(inds) |
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else: |
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msg = "Input must be a NumPy ndarray, either a 2D distance matrix " \ |
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"or a condensed distance matrix (returned by SciPy's pdist)." |
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ValueError(msg) |
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# inds are the indexes of nns: inds[i,j] is the j-th nn to point i |
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nn_dm = np.take_along_axis(dm, inds, axis=-1) |
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sorted_inds = np.argsort(nn_dm, axis=-1) |
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inds = np.take_along_axis(inds, sorted_inds, axis=-1) |
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nn_dm = np.take_along_axis(nn_dm, sorted_inds, axis=-1) |
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return nn_dm, inds |
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166
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167
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def random_cell(length_bounds=(1, 2), angle_bounds=(60, 120), dims=3): |
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"""Dimensions 2 and 3 only. Random unit cell with uniformally chosen |
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length and angle parameters between bounds. |
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""" |
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ll, lu = length_bounds |
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al, au = angle_bounds |
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if dims == 3: |
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while True: |
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lengths = [np.random.uniform(low=ll, high=lu) for _ in range(dims)] |
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angles = [np.random.uniform(low=al, high=au) for _ in range(dims)] |
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180
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try: |
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cell = cellpar_to_cell(*lengths, *angles) |
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break |
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except RuntimeError: |
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continue |
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elif dims == 2: |
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lengths = [np.random.uniform(low=ll, high=lu) for _ in range(dims)] |
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alpha = np.random.uniform(low=al, high=au) |
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cell = cellpar_to_cell_2D(*lengths, alpha) |
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else: |
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msg = 'random_cell only implimented for dimensions 2 and 3 (passed ' \ |
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'f{dims})' |
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raise NotImplementedError(msg) |
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return cell |
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dwiddo /
average-minimum-distance
