amd.utils.lattice_cubic() - Code Metrics - Inspection of "1.3.3a1 - io update" - dwiddo/average-minimum-distance - Measure and Improve Code Quality continuously with Scrutinizer

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by Daniel

created 2022-10-20 16:42 UTC

amd.utils.lattice_cubic() A

↳ Parent: amd.utils.neighbours_from_distance_matrix()

Complexity

Conditions

Size

Total Lines	5
Code Lines	2

Duplication

Lines	0
Ratio	0 %

Importance

Changes

Metric	Value
eloc	2
dl	0
loc	5
rs	10
c	0
b	0
f	0
cc	1
nop	2

"""General utility functions."""

from typing import Tuple

import numpy as np
import numba
from scipy.spatial.distance import squareform


def diameter(cell):
    """Diameter of a unit cell (as a square matrix in Cartesian/Orthogonal form)
    in 3 or fewer dimensions."""

    dims = cell.shape[0]
    if dims == 1:
        return cell[0][0]
    if dims == 2:
        d = np.amax(np.linalg.norm(np.array([cell[0] + cell[1], cell[0] - cell[1]]), axis=-1))
    elif dims == 3:
        diams = np.array([
              cell[0] + cell[1] + cell[2],

              cell[0] + cell[1] - cell[2],

              cell[0] - cell[1] + cell[2],

            - cell[0] + cell[1] + cell[2]
        ])
        d =  np.amax(np.linalg.norm(diams, axis=-1))

    else:
        raise ValueError(f'diameter only implimented for dimensions <= 3.')

    return d


@numba.njit()
def cellpar_to_cell(a, b, c, alpha, beta, gamma):

    """Simplified version of function from :mod:`ase.geometry` of the same name.
    3D unit cell parameters a,b,c,α,β,γ --> cell as 3x3 NumPy array.
    """

    eps = 2 * np.spacing(90.0)  # ~1.4e-14

    cos_alpha = 0. if abs(abs(alpha) - 90.) < eps else np.cos(alpha * np.pi / 180.)
    cos_beta = 0. if abs(abs(beta) - 90.) < eps else np.cos(beta * np.pi / 180.)
    cos_gamma = 0. if abs(abs(gamma) - 90.) < eps else np.cos(gamma * np.pi / 180.)

    if abs(gamma - 90) < eps:
        sin_gamma = 1.
    elif abs(gamma + 90) < eps:
        sin_gamma = -1.
    else:
        sin_gamma = np.sin(gamma * np.pi / 180.)

    cy = (cos_alpha - cos_beta * cos_gamma) / sin_gamma
    cz_sqr = 1. - cos_beta ** 2 - cy ** 2
    if cz_sqr < 0:
        raise RuntimeError('Could not create unit cell from given parameters.')

    cell = np.zeros((3, 3))
    cell[0, 0] = a
    cell[1, 0] = b * cos_gamma
    cell[1, 1] = b * sin_gamma
    cell[2, 0] = c * cos_beta
    cell[2, 1] = c * cy
    cell[2, 2] = c * np.sqrt(cz_sqr)

    return cell


@numba.njit()
def cellpar_to_cell_2D(a, b, alpha):
    """2D unit cell parameters a,b,α --> cell as 2x2 ndarray."""

    cell = np.zeros((2, 2))
    cell[0, 0] = a
    cell[1, 0] = b * np.cos(alpha * np.pi / 180.)
    cell[1, 1] = b * np.sin(alpha * np.pi / 180.)

    return cell


def cell_to_cellpar(cell):
    """Unit cell as a 3x3 NumPy array -> list of 6 lengths + angles."""
    lengths = np.linalg.norm(cell, axis=-1)
    angles = []
    for i, j in [(1, 2), (0, 2), (0, 1)]:
        ang_rad = np.arccos(np.dot(cell[i], cell[j]) / (lengths[i] * lengths[j]))
        angles.append(np.rad2deg(ang_rad))
    return np.concatenate((lengths, np.array(angles)))


def cell_to_cellpar_2D(cell):
    """Unit cell as a 2x2 NumPy array -> list of 2 lengths and an angle."""
    cellpar = np.zeros((3, ))
    lengths = np.linalg.norm(cell, axis=-1)
    ang_rad = np.arccos(np.dot(cell[0], cell[1]) / (lengths[0] * lengths[1]))
    cellpar[0] = lengths[0]
    cellpar[1] = lengths[1]
    cellpar[2] = np.rad2deg(ang_rad)
    return cellpar


def neighbours_from_distance_matrix(
        n: int,
        dm: np.ndarray
) -> Tuple[np.ndarray, np.ndarray]:
    """Given a distance matrix, find the n nearest neighbours of each item.

    Parameters
    ----------
    n : int
        Number of nearest neighbours to find for each item.
    dm : numpy.ndarray
        2D distance matrix or 1D condensed distance matrix.

    Returns
    -------
    nn_dm, inds : Tuple[numpy.ndarray, numpy.ndarray] 

        ``nn_dm[i][j]`` is the distance from item ``i`` to its ``j+1`` st
        nearest neighbour, and ``inds[i][j]`` is the index of this neighbour 

        (``j+1`` since index 0 is the first nearest neighbour).
    """

    inds = None

    # 2D distance matrix
    if len(dm.shape) == 2:
        inds = np.array([np.argpartition(row, n)[:n] for row in dm])

    # 1D condensed distance vector
    elif len(dm.shape) == 1:
        dm = squareform(dm)
        inds = []
        for i, row in enumerate(dm):
            inds_row = np.argpartition(row, n+1)[:n+1]
            inds_row = inds_row[inds_row != i][:n]
            inds.append(inds_row)
        inds = np.array(inds)

    else:
        ValueError(
            'Input must be an ndarray, either a 2D distance matrix '
            'or a condensed distance matrix (returned by pdist).')

    # inds are the indexes of nns: inds[i,j] is the j-th nn to point i
    nn_dm = np.take_along_axis(dm, inds, axis=-1)
    sorted_inds = np.argsort(nn_dm, axis=-1)
    inds = np.take_along_axis(inds, sorted_inds, axis=-1)
    nn_dm = np.take_along_axis(nn_dm, sorted_inds, axis=-1)
    return nn_dm, inds


def random_cell(length_bounds=(1, 2), angle_bounds=(60, 120), dims=3):
    """Dimensions 2 and 3 only. Random unit cell with uniformally chosen length and 

    angle parameters between bounds."""

    if dims == 3:
        while True:
            lengths = [np.random.uniform(low=length_bounds[0],
                                         high=length_bounds[1])
                       for _ in range(dims)]
            angles = [np.random.uniform(low=angle_bounds[0],
                                        high=length_bounds[1])
                      for _ in range(dims)]

            try:
                cell = cellpar_to_cell(*lengths, *angles)
                break
            except RuntimeError:
                continue

    elif dims == 2:
        lengths = [np.random.uniform(low=length_bounds[0],
                                     high=length_bounds[1])
                       for _ in range(dims)]

        alpha = np.random.uniform(low=angle_bounds[0],
                                  high=length_bounds[1])
        cell = cellpar_to_cell_2D(*lengths, alpha)

    else:
        raise ValueError(f'random_cell only implimented for dimensions 2 and 3 (passed {dims})')

    return cell


1			"""General utility functions."""
2
3			from typing import Tuple
4
5			import numpy as np
6			import numba
7			from scipy.spatial.distance import squareform
8
9
10			def diameter(cell):
11			"""Diameter of a unit cell (as a square matrix in Cartesian/Orthogonal form)
12			in 3 or fewer dimensions."""
13
14			dims = cell.shape[0]
15			if dims == 1:
16			return cell[0][0]
17			if dims == 2:
18			d = np.amax(np.linalg.norm(np.array([cell[0] + cell[1], cell[0] - cell[1]]), axis=-1))
19			elif dims == 3:
20			diams = np.array([
21			cell[0] + cell[1] + cell[2],
			0 ignored issues – show Coding Style introduced 2022-10-20 16:49 UTC by Report Bug Copy Issue Report Wrong hanging indentation (remove 2 spaces). Loading history...
22			cell[0] + cell[1] - cell[2],
			0 ignored issues – show Coding Style introduced 2022-10-20 16:49 UTC by Report Bug Copy Issue Report Wrong hanging indentation (remove 2 spaces). Loading history...
23			cell[0] - cell[1] + cell[2],
			0 ignored issues – show Coding Style introduced 2022-10-20 16:49 UTC by Report Bug Copy Issue Report Wrong hanging indentation (remove 2 spaces). Loading history...
24			- cell[0] + cell[1] + cell[2]
25			])
26			d = np.amax(np.linalg.norm(diams, axis=-1))
			0 ignored issues – show Coding Style introduced 2022-05-22 17:42 UTC by Report Bug Copy Issue Report Exactly one space required after assignment Loading history...
27			else:
28			raise ValueError(f'diameter only implimented for dimensions <= 3.')
			0 ignored issues – show introduced 2022-08-08 10:48 UTC by Report Bug Copy Issue Report Using an f-string that does not have any interpolated variables Loading history...
29			return d
30
31
32			@numba.njit()
33			def cellpar_to_cell(a, b, c, alpha, beta, gamma):
			0 ignored issues – show best-practice introduced 2022-04-14 08:53 UTC by Report Bug Copy Issue Report Too many arguments (6/5) Loading history...
34			"""Simplified version of function from :mod:`ase.geometry` of the same name.
35			3D unit cell parameters a,b,c,α,β,γ --> cell as 3x3 NumPy array.
36			"""
37
38			eps = 2 * np.spacing(90.0) # ~1.4e-14
39
40			cos_alpha = 0. if abs(abs(alpha) - 90.) < eps else np.cos(alpha * np.pi / 180.)
41			cos_beta = 0. if abs(abs(beta) - 90.) < eps else np.cos(beta * np.pi / 180.)
42			cos_gamma = 0. if abs(abs(gamma) - 90.) < eps else np.cos(gamma * np.pi / 180.)
43
44			if abs(gamma - 90) < eps:
45			sin_gamma = 1.
46			elif abs(gamma + 90) < eps:
47			sin_gamma = -1.
48			else:
49			sin_gamma = np.sin(gamma * np.pi / 180.)
50
51			cy = (cos_alpha - cos_beta * cos_gamma) / sin_gamma
52			cz_sqr = 1. - cos_beta 2 - cy 2
53			if cz_sqr < 0:
54			raise RuntimeError('Could not create unit cell from given parameters.')
55
56			cell = np.zeros((3, 3))
57			cell[0, 0] = a
58			cell[1, 0] = b * cos_gamma
59			cell[1, 1] = b * sin_gamma
60			cell[2, 0] = c * cos_beta
61			cell[2, 1] = c * cy
62			cell[2, 2] = c * np.sqrt(cz_sqr)
63
64			return cell
65
66
67			@numba.njit()
68			def cellpar_to_cell_2D(a, b, alpha):
69			"""2D unit cell parameters a,b,α --> cell as 2x2 ndarray."""
70
71			cell = np.zeros((2, 2))
72			cell[0, 0] = a
73			cell[1, 0] = b * np.cos(alpha * np.pi / 180.)
74			cell[1, 1] = b * np.sin(alpha * np.pi / 180.)
75
76			return cell
77
78
79			def cell_to_cellpar(cell):
80			"""Unit cell as a 3x3 NumPy array -> list of 6 lengths + angles."""
81			lengths = np.linalg.norm(cell, axis=-1)
82			angles = []
83			for i, j in [(1, 2), (0, 2), (0, 1)]:
84			ang_rad = np.arccos(np.dot(cell[i], cell[j]) / (lengths[i] * lengths[j]))
85			angles.append(np.rad2deg(ang_rad))
86			return np.concatenate((lengths, np.array(angles)))
87
88
89			def cell_to_cellpar_2D(cell):
90			"""Unit cell as a 2x2 NumPy array -> list of 2 lengths and an angle."""
91			cellpar = np.zeros((3, ))
92			lengths = np.linalg.norm(cell, axis=-1)
93			ang_rad = np.arccos(np.dot(cell[0], cell[1]) / (lengths[0] * lengths[1]))
94			cellpar[0] = lengths[0]
95			cellpar[1] = lengths[1]
96			cellpar[2] = np.rad2deg(ang_rad)
97			return cellpar
98
99
100			def neighbours_from_distance_matrix(
101			n: int,
102			dm: np.ndarray
103			) -> Tuple[np.ndarray, np.ndarray]:
104			"""Given a distance matrix, find the n nearest neighbours of each item.
105
106			Parameters
107			----------
108			n : int
109			Number of nearest neighbours to find for each item.
110			dm : numpy.ndarray
111			2D distance matrix or 1D condensed distance matrix.
112
113			Returns
114			-------
115			nn_dm, inds : Tuple[numpy.ndarray, numpy.ndarray]
			0 ignored issues – show Coding Style introduced 2022-05-22 17:42 UTC by Report Bug Copy Issue Report Trailing whitespace Loading history...
116			``nn_dm[i][j]`` is the distance from item ``i`` to its ``j+1`` st
117			nearest neighbour, and ``inds[i][j]`` is the index of this neighbour
			0 ignored issues – show Coding Style introduced 2022-08-08 10:48 UTC by Report Bug Copy Issue Report Trailing whitespace Loading history...
118			(``j+1`` since index 0 is the first nearest neighbour).
119			"""
120
121			inds = None
122
123			# 2D distance matrix
124			if len(dm.shape) == 2:
125			inds = np.array([np.argpartition(row, n)[:n] for row in dm])
126
127			# 1D condensed distance vector
128			elif len(dm.shape) == 1:
129			dm = squareform(dm)
130			inds = []
131			for i, row in enumerate(dm):
132			inds_row = np.argpartition(row, n+1)[:n+1]
133			inds_row = inds_row[inds_row != i][:n]
134			inds.append(inds_row)
135			inds = np.array(inds)
136
137			else:
138			ValueError(
139			'Input must be an ndarray, either a 2D distance matrix '
140			'or a condensed distance matrix (returned by pdist).')
141
142			# inds are the indexes of nns: inds[i,j] is the j-th nn to point i
143			nn_dm = np.take_along_axis(dm, inds, axis=-1)
144			sorted_inds = np.argsort(nn_dm, axis=-1)
145			inds = np.take_along_axis(inds, sorted_inds, axis=-1)
146			nn_dm = np.take_along_axis(nn_dm, sorted_inds, axis=-1)
147			return nn_dm, inds
148
149
150			def random_cell(length_bounds=(1, 2), angle_bounds=(60, 120), dims=3):
151			"""Dimensions 2 and 3 only. Random unit cell with uniformally chosen length and
			0 ignored issues – show Coding Style introduced 2022-08-08 10:48 UTC by Report Bug Copy Issue Report Trailing whitespace Loading history...
152			angle parameters between bounds."""
153
154			if dims == 3:
155			while True:
156			lengths = [np.random.uniform(low=length_bounds[0],
157			high=length_bounds[1])
158			for _ in range(dims)]
159			angles = [np.random.uniform(low=angle_bounds[0],
160			high=length_bounds[1])
161			for _ in range(dims)]
162
163			try:
164			cell = cellpar_to_cell(lengths, angles)
165			break
166			except RuntimeError:
167			continue
168
169			elif dims == 2:
170			lengths = [np.random.uniform(low=length_bounds[0],
171			high=length_bounds[1])
172			for _ in range(dims)]
			0 ignored issues – show Coding Style introduced 2022-05-22 17:42 UTC by Report Bug Copy Issue Report Wrong continued indentation (remove 4 spaces). Loading history...
173			alpha = np.random.uniform(low=angle_bounds[0],
174			high=length_bounds[1])
175			cell = cellpar_to_cell_2D(*lengths, alpha)
176
177			else:
178			raise ValueError(f'random_cell only implimented for dimensions 2 and 3 (passed {dims})')
179
180			return cell
181

dwiddo / average-minimum-distance

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amd.utils.lattice_cubic() A

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