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"""Helpful utility functions, e.g. unit cell diameter, converting |
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cell parameters to Cartesian form, and an ETA class.""" |
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from typing import Tuple |
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import numpy as np |
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from scipy.spatial.distance import squareform |
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9
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10
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def diameter(cell): |
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"""Diameter of a unit cell (as a square matrix in Cartesian form) |
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in 3 or fewer dimensions.""" |
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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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d = np.amax(np.linalg.norm(np.array([cell[0] + cell[1], cell[0] - cell[1]]), 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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raise ValueError(f'diameter only implimented for dimensions <= 3 (passed {dims})') |
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return d |
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32
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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 same name. |
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3D unit cell parameters a,b,c,α,β,γ --> cell as 3x3 NumPy array. |
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""" |
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# Handle orthorhombic cells separately to avoid rounding errors |
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eps = 2 * np.spacing(90.0, dtype=np.float64) # around 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 parameters ' + \ |
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f'a={a},b={b},c={c},α={alpha},β={beta},γ={gamma}') |
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57
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return np.array([[a, 0, 0], |
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[b*cos_gamma, b*sin_gamma, 0], |
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[c*cos_beta, c*cy, c*np.sqrt(cz_sqr)]]) |
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61
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62
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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 ndarray.""" |
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65
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return np.array([[a, 0], |
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[b * np.cos(alpha * np.pi / 180.), b * np.sin(alpha * np.pi / 180.)]]) |
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68
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69
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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 item. |
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75
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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 : numpy.ndarray |
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2D distance matrix or 1D condensed distance matrix. |
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82
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Returns |
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------- |
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nn_dm, inds : Tuple[numpy.ndarray, numpy.ndarray] |
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85
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``nn_dm[i][j]`` is the distance from item ``i`` to its ``j+1`` st |
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86
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nearest neighbour, and ``inds[i][j]`` is the index of this neighbour |
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87
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(``j+1`` since index 0 is the first nearest neighbour). |
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""" |
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90
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inds = None |
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92
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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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95
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96
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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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105
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106
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else: |
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ValueError( |
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'Input must be an ndarray, either a 2D distance matrix ' |
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'or a condensed distance matrix (returned by pdist).') |
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110
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111
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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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117
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118
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119
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def lattice_cubic(scale=1, dims=3): |
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120
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"""Return a pair ``(motif, cell)`` representing a cubic lattice, passable to |
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``amd.AMD()`` or ``amd.PDD()``.""" |
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122
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123
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return (np.zeros((1, dims)), np.identity(dims) * scale) |
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124
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125
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126
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def random_cell(length_bounds=(1, 2), angle_bounds=(60, 120), dims=3): |
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127
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"""Random unit cell with uniformally chosen length and angle parameters |
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128
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between bounds.""" |
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129
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130
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if dims == 3: |
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131
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while True: |
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lengths = [np.random.uniform(low=length_bounds[0], |
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high=length_bounds[1]) |
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for _ in range(dims)] |
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angles = [np.random.uniform(low=angle_bounds[0], |
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high=length_bounds[1]) |
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for _ in range(dims)] |
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138
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139
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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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144
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145
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elif dims == 2: |
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146
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lengths = [np.random.uniform(low=length_bounds[0], |
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high=length_bounds[1]) |
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148
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for _ in range(dims)] |
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149
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alpha = np.random.uniform(low=angle_bounds[0], |
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high=length_bounds[1]) |
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151
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cell = cellpar_to_cell_2D(*lengths, alpha) |
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152
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153
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else: |
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154
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raise ValueError(f'random_cell only implimented for dimensions 2 and 3 (passed {dims})') |
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155
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156
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return cell |
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157
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dwiddo /
average-minimum-distance
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