amd._nearest_neighbours.generate_concentric_cloud() - Code Metrics - Inspection of "diameter njit, manifest.in & reconstruct fixes" - dwiddo/average-minimum-distance - Measure and Improve Code Quality continuously with Scrutinizer

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Push — master ( c02a6e...9e2dce )

by Daniel

created 2023-03-22 01:38 UTC

generate_concentric_cloud() A

↳ Parent: amd._nearest_neighbours

Complexity

Conditions

Size

Total Lines	25
Code Lines	4

Duplication

Lines	0
Ratio	0 %

Importance

Changes

Metric	Value
eloc	4
dl	0
loc	25
rs	10
c	0
b	0
f	0
cc	2
nop	2

"""Implements core function nearest_neighbours used for AMD and PDD
calculations.
"""

from typing import Tuple, Iterable
from itertools import product

import numba
import numpy as np
import numpy.typing as npt
from scipy.spatial import KDTree
from scipy.spatial.distance import cdist


def nearest_neighbours(
        motif: npt.NDArray,
        cell: npt.NDArray,
        x: npt.NDArray,
        k: int
) -> Tuple[npt.NDArray[np.float64], ...]:
    """Find the ``k`` nearest neighbours in a periodic set for points in
    ``x``.

    Given a periodic set described by ``motif`` and ``cell``, a query
    set of points ``x`` and an integer ``k``, find the ``k`` nearest
    neighbours in the periodic set for all points in ``x``. Return
    distances to neighbours in order, the point cloud generated during
    the search and the indices of which points in the cloud are the
    neighbours of points in ``x``.

    Parameters
    ----------
    motif : :class:`numpy.ndarray`
        Cartesian coordinates of the motif, shape (no points, dims).
    cell : :class:`numpy.ndarray`
        The unit cell as a square array, shape (dims, dims).
    x : :class:`numpy.ndarray`
        Array of points to query for neighbours. For AMD/PDD invariants
        this is the motif, or more commonly an asymmetric unit of it.
    k : int
        Number of nearest neighbours to find for each point in ``x``.

    Returns
    -------
    dists : numpy.ndarray
        Array shape ``(x.shape[0], k)`` of distances from points in
        ``x`` to their ``k`` nearest neighbours in the periodic set, in
        order. E.g. ``dists[m][n]`` is the distance from ``x[m]`` to its
        n-th nearest neighbour in the periodic set.
    cloud : numpy.ndarray
        Collection of points in the periodic set that was generated
        during the nearest neighbour search.
    inds : numpy.ndarray
        Array shape ``(x.shape[0], k)`` containing the indices of
        nearest neighbours in ``cloud``. E.g. the n-th nearest neighbour
        to ``x[m]`` is ``cloud[inds[m][n]]``.
    """

    # Generate an initial cloud of enough points, at least k
    int_lat_generator = _generate_integer_lattice(cell.shape[0])
    n_points = 0
    int_lat_cloud = []
    while n_points <= k:
        layer = next(int_lat_generator)
        n_points += layer.shape[0] * len(motif)
        int_lat_cloud.append(layer)

    # Add one layer from the lattice generator, on average this is faster
    int_lat_cloud.append(next(int_lat_generator))
    cloud = _int_lattice_to_cloud(motif, cell, np.concatenate(int_lat_cloud))

    # Find k neighbours for points in x
    dists_, inds = KDTree(
        cloud, leafsize=30, compact_nodes=False, balanced_tree=False
    ).query(x, k=k)

    # Generate more layers of lattice points until they are too large to
    # contain nearer neighbours than have already been found. For a lattice
    # point l, points in l + motif further away from x than |l| - max|p-p'|
    # (p in x, p' in motif), this is used to check if l is too far away.
    max_cdist = np.amax(cdist(x, motif))
    lattice_layers = []
    while True:
        lattice = _close_lattice_points(
            next(int_lat_generator), cell, dists_[:, -1], max_cdist
        )
        if lattice.size == 0:
            break
        lattice_layers.append(lattice)

    if lattice_layers:
        lattice_layers = np.concatenate(lattice_layers)
        cloud = np.vstack((
            cloud[np.unique(inds)], _lattice_to_cloud(motif, lattice_layers)
        ))
        dists_, inds = KDTree(
            cloud, leafsize=30, compact_nodes=False, balanced_tree=False
        ).query(x, k=k)

    return dists_, cloud, inds





def _generate_integer_lattice(dims: int) -> Iterable[npt.NDArray[np.float64]]:
    """Generate batches of integer lattice points. Each yield gives all
    points (that have not already been yielded) inside a sphere centered
    at the origin with radius d. d starts at 0 and increments by 1 on
    each loop.

    Parameters
    ----------
    dims : int
        The dimension of Euclidean space the lattice is in.

    Yields
    -------
    :class:`numpy.ndarray`
        Yields arrays of integer points in dims dimensional Euclidean
        space.
    """

    d = 0

    if dims == 1:
        yield np.array([[0]], dtype=np.float64)
        while True:
            d += 1
            yield np.array([[-d], [d]], dtype=np.float64)

    ymax = {}
    while True:
        positive_int_lattice = []
        while True:
            batch = []
            for xy in product(range(d + 1), repeat=dims-1):
                if xy not in ymax:
                    ymax[xy] = 0
                if _in_sphere(xy, ymax[xy], d):
                    batch.append((*xy, ymax[xy]))
                    ymax[xy] += 1
            if not batch:
                break
            positive_int_lattice.extend(batch)

        yield _reflect_positive_integer_lattice(np.array(positive_int_lattice))
        d += 1


@numba.njit(cache=True)
def _reflect_positive_integer_lattice(
        positive_int_lattice: npt.NDArray
) -> npt.NDArray[np.float64]:
    """Reflect points in the positive quadrant across all combinations
    of axes, without duplicating points that are invariant under
    reflections.
    """

    dims = positive_int_lattice.shape[-1]
    batches = []
    batches.extend(positive_int_lattice)

    for n_reflections in range(1, dims + 1):

        axes = np.arange(n_reflections)
        batches.extend(_reflect_in_axes(positive_int_lattice, axes))

        while True:
            i = n_reflections - 1
            for _ in range(n_reflections):
                if axes[i] != i + dims - n_reflections:
                    break
                i -= 1
            else:
                break
            axes[i] += 1
            for j in range(i + 1, n_reflections):
                axes[j] = axes[j-1] + 1
            batches.extend(_reflect_in_axes(positive_int_lattice, axes))

    int_lattice = np.empty(shape=(len(batches), dims), dtype=np.float64)
    for i in range(len(batches)):
        int_lattice[i] = batches[i]

    return int_lattice


@numba.njit(cache=True)
def _reflect_in_axes(
        positive_int_lattice: npt.NDArray,
        axes: npt.NDArray
) -> npt.NDArray:
    """Reflect points in `positive_int_lattice` in the axes described by
    `axes`, without including invariant points.
    """

    not_on_axes = (positive_int_lattice[:, axes] == 0).sum(axis=-1) == 0
    int_lattice = positive_int_lattice[not_on_axes]
    int_lattice[:, axes] *= -1
    return int_lattice


@numba.njit(cache=True)
def _close_lattice_points(
        int_lattice: npt.NDArray,
        cell: npt.NDArray,
        max_nn_dists: npt.NDArray,
        max_cdist: float
) -> npt.NDArray[np.float64]:
    """Given integer lattice points, a unit cell, ``max_cdist`` (max of
    cdist(x, motif)) and ``max_nn_dist`` (max of the dists to k-th
    nearest neighbours found so far), return lattice points which are
    close enough such that the corresponding motif copy could contain
    nearest neighbours.
    """

    lattice = int_lattice @ cell
    bound = np.amax(max_nn_dists) + max_cdist
    return lattice[np.sqrt(np.sum(lattice ** 2, axis=-1)) < bound]


@numba.njit(cache=True)
def _lattice_to_cloud(
        motif: npt.NDArray,
        lattice: npt.NDArray
) -> npt.NDArray[np.float64]:
    """Transform a batch of non-integer lattice points (generated by
    _generate_integer_lattice then mutliplied by the cell) into a cloud
    of points from a periodic set with the motif and cell.
    """

    m = len(motif)
    layer = np.empty((m * len(lattice), motif.shape[-1]), dtype=np.float64)
    i1 = 0
    for translation in lattice:
        i2 = i1 + m
        layer[i1:i2] = motif + translation
        i1 = i2
    return layer


@numba.njit(cache=True)
def _int_lattice_to_cloud(
        motif: npt.NDArray,
        cell: npt.NDArray,
        int_lattice: npt.NDArray
) -> npt.NDArray[np.float64]:
    """Transform a batch of integer lattice points (generated by
    _generate_integer_lattice) into a cloud of points from a periodic
    set with the motif and cell.
    """
    return _lattice_to_cloud(motif, int_lattice @ cell)


@numba.njit(cache=True)
def _in_sphere(xy: Tuple[float, float], z: float, d: float) -> bool:
    """Return True if sum(i^2 for i in xy) + z^2 <= d^2."""
    s = z ** 2
    for val in xy:
        s += val ** 2
    return s <= d ** 2


def nearest_neighbours_minval(
        motif: npt.NDArray,
        cell: npt.NDArray,
        min_val: float
) -> npt.NDArray[np.float64]:
    """Return the same ``dists``/PDD matrix as ``nearest_neighbours``,
    but with enough columns such that all values in the last column are
    at least ``min_val``. Unlike ``nearest_neighbours``, does not take a
    query array ``x`` but only finds neighbours to motif points, and
    does not return the point cloud or indices of the nearest
    neighbours. Used in ``PDD_reconstructable``.
    """
    
    max_cdist = np.amax(cdist(motif, motif))
    # generate initial cloud of points, at least k + two more layers
    int_lat_generator = _generate_integer_lattice(cell.shape[0])
    
    cloud = []
    for _ in range(3):
        cloud.append(_lattice_to_cloud(motif, next(int_lat_generator) @ cell))
    cloud = np.concatenate(cloud)

    dists_, inds = KDTree(
        cloud, leafsize=30, compact_nodes=False, balanced_tree=False
    ).query(motif, k=cloud.shape[0])
    dists = np.zeros_like(dists_, dtype=np.float64)

    # add layers & find k nearest neighbours until they don't change
    while True:
        if np.all(dists_[:, -1] >= min_val):
            col = np.argwhere(np.all(dists_ >= min_val, axis=0))[0][0] + 1
            if np.array_equal(dists[:, :col], dists_[:, :col]):
                break
        dists = dists_
        lattice = next(int_lat_generator) @ cell
        closest_dist_bound = np.linalg.norm(lattice, axis=-1) - max_cdist
        is_close = closest_dist_bound <= np.amax(dists_[:, -1])
        if not np.any(is_close):
            break
        cloud = np.vstack((cloud, _lattice_to_cloud(motif, lattice[is_close])))
        dists_, inds = KDTree(
            cloud, leafsize=30, compact_nodes=False, balanced_tree=False
        ).query(motif, k=cloud.shape[0])

    k = np.argwhere(np.all(dists >= min_val, axis=0))[0][0]
    return dists_[:, 1:k+1], cloud, inds


def generate_concentric_cloud(motif, cell):
    """
    Generates batches of points from a periodic set given by (motif,
    cell) which get successively further away from the origin.

    Each yield gives all points (that have not already been yielded)
    which lie in a unit cell whose corner lattice point was generated by
    ``generate_integer_lattice(motif.shape[1])``.

    Parameters
    ----------
    motif : :class:`numpy.ndarray`
        Cartesian representation of the motif, shape (no points, dims).
    cell : :class:`numpy.ndarray`
        Cartesian representation of the unit cell, shape (dims, dims).

    Yields
    -------
    :class:`numpy.ndarray`
        Yields arrays of points from the periodic set.
    """

    int_lat_generator = _generate_integer_lattice(cell.shape[0])
    for layer in int_lat_generator:
        yield _int_lattice_to_cloud(motif, cell, layer)


1			"""Implements core function nearest_neighbours used for AMD and PDD
2			calculations.
3			"""
4
5			from typing import Tuple, Iterable
6			from itertools import product
7
8			import numba
9			import numpy as np
10			import numpy.typing as npt
11			from scipy.spatial import KDTree
12			from scipy.spatial.distance import cdist
13
14
15			def nearest_neighbours(
16			motif: npt.NDArray,
17			cell: npt.NDArray,
18			x: npt.NDArray,
19			k: int
20			) -> Tuple[npt.NDArray[np.float64], ...]:
21			"""Find the ``k`` nearest neighbours in a periodic set for points in
22			``x``.
23
24			Given a periodic set described by ``motif`` and ``cell``, a query
25			set of points ``x`` and an integer ``k``, find the ``k`` nearest
26			neighbours in the periodic set for all points in ``x``. Return
27			distances to neighbours in order, the point cloud generated during
28			the search and the indices of which points in the cloud are the
29			neighbours of points in ``x``.
30
31			Parameters
32			----------
33			motif : :class:`numpy.ndarray`
34			Cartesian coordinates of the motif, shape (no points, dims).
35			cell : :class:`numpy.ndarray`
36			The unit cell as a square array, shape (dims, dims).
37			x : :class:`numpy.ndarray`
38			Array of points to query for neighbours. For AMD/PDD invariants
39			this is the motif, or more commonly an asymmetric unit of it.
40			k : int
41			Number of nearest neighbours to find for each point in ``x``.
42
43			Returns
44			-------
45			dists : numpy.ndarray
46			Array shape ``(x.shape[0], k)`` of distances from points in
47			``x`` to their ``k`` nearest neighbours in the periodic set, in
48			order. E.g. ``dists[m][n]`` is the distance from ``x[m]`` to its
49			n-th nearest neighbour in the periodic set.
50			cloud : numpy.ndarray
51			Collection of points in the periodic set that was generated
52			during the nearest neighbour search.
53			inds : numpy.ndarray
54			Array shape ``(x.shape[0], k)`` containing the indices of
55			nearest neighbours in ``cloud``. E.g. the n-th nearest neighbour
56			to ``x[m]`` is ``cloud[inds[m][n]]``.
57			"""
58
59			# Generate an initial cloud of enough points, at least k
60			int_lat_generator = _generate_integer_lattice(cell.shape[0])
61			n_points = 0
62			int_lat_cloud = []
63			while n_points <= k:
64			layer = next(int_lat_generator)
65			n_points += layer.shape[0] * len(motif)
66			int_lat_cloud.append(layer)
67
68			# Add one layer from the lattice generator, on average this is faster
69			int_lat_cloud.append(next(int_lat_generator))
70			cloud = _int_lattice_to_cloud(motif, cell, np.concatenate(int_lat_cloud))
71
72			# Find k neighbours for points in x
73			dists_, inds = KDTree(
74			cloud, leafsize=30, compact_nodes=False, balanced_tree=False
75			).query(x, k=k)
76
77			# Generate more layers of lattice points until they are too large to
78			# contain nearer neighbours than have already been found. For a lattice
79			# point l, points in l + motif further away from x than \|l\| - max\|p-p'\|
80			# (p in x, p' in motif), this is used to check if l is too far away.
81			max_cdist = np.amax(cdist(x, motif))
82			lattice_layers = []
83			while True:
84			lattice = _close_lattice_points(
85			next(int_lat_generator), cell, dists_[:, -1], max_cdist
86			)
87			if lattice.size == 0:
88			break
89			lattice_layers.append(lattice)
90
91			if lattice_layers:
92			lattice_layers = np.concatenate(lattice_layers)
93			cloud = np.vstack((
94			cloud[np.unique(inds)], _lattice_to_cloud(motif, lattice_layers)
95			))
96			dists_, inds = KDTree(
97			cloud, leafsize=30, compact_nodes=False, balanced_tree=False
98			).query(x, k=k)
99
100			return dists_, cloud, inds
101
102
103
104
105
106			def _generate_integer_lattice(dims: int) -> Iterable[npt.NDArray[np.float64]]:
107			"""Generate batches of integer lattice points. Each yield gives all
108			points (that have not already been yielded) inside a sphere centered
109			at the origin with radius d. d starts at 0 and increments by 1 on
110			each loop.
111
112			Parameters
113			----------
114			dims : int
115			The dimension of Euclidean space the lattice is in.
116
117			Yields
118			-------
119			:class:`numpy.ndarray`
120			Yields arrays of integer points in dims dimensional Euclidean
121			space.
122			"""
123
124			d = 0
125
126			if dims == 1:
127			yield np.array([[0]], dtype=np.float64)
128			while True:
129			d += 1
130			yield np.array([[-d], [d]], dtype=np.float64)
131
132			ymax = {}
133			while True:
134			positive_int_lattice = []
135			while True:
136			batch = []
137			for xy in product(range(d + 1), repeat=dims-1):
138			if xy not in ymax:
139			ymax[xy] = 0
140			if _in_sphere(xy, ymax[xy], d):
141			batch.append((*xy, ymax[xy]))
142			ymax[xy] += 1
143			if not batch:
144			break
145			positive_int_lattice.extend(batch)
146
147			yield _reflect_positive_integer_lattice(np.array(positive_int_lattice))
148			d += 1
149
150
151			@numba.njit(cache=True)
152			def _reflect_positive_integer_lattice(
153			positive_int_lattice: npt.NDArray
154			) -> npt.NDArray[np.float64]:
155			"""Reflect points in the positive quadrant across all combinations
156			of axes, without duplicating points that are invariant under
157			reflections.
158			"""
159
160			dims = positive_int_lattice.shape[-1]
161			batches = []
162			batches.extend(positive_int_lattice)
163
164			for n_reflections in range(1, dims + 1):
165
166			axes = np.arange(n_reflections)
167			batches.extend(_reflect_in_axes(positive_int_lattice, axes))
168
169			while True:
170			i = n_reflections - 1
171			for _ in range(n_reflections):
172			if axes[i] != i + dims - n_reflections:
173			break
174			i -= 1
175			else:
176			break
177			axes[i] += 1
178			for j in range(i + 1, n_reflections):
179			axes[j] = axes[j-1] + 1
180			batches.extend(_reflect_in_axes(positive_int_lattice, axes))
181
182			int_lattice = np.empty(shape=(len(batches), dims), dtype=np.float64)
183			for i in range(len(batches)):
184			int_lattice[i] = batches[i]
185
186			return int_lattice
187
188
189			@numba.njit(cache=True)
190			def _reflect_in_axes(
191			positive_int_lattice: npt.NDArray,
192			axes: npt.NDArray
193			) -> npt.NDArray:
194			"""Reflect points in `positive_int_lattice` in the axes described by
195			`axes`, without including invariant points.
196			"""
197
198			not_on_axes = (positive_int_lattice[:, axes] == 0).sum(axis=-1) == 0
199			int_lattice = positive_int_lattice[not_on_axes]
200			int_lattice[:, axes] *= -1
201			return int_lattice
202
203
204			@numba.njit(cache=True)
205			def _close_lattice_points(
206			int_lattice: npt.NDArray,
207			cell: npt.NDArray,
208			max_nn_dists: npt.NDArray,
209			max_cdist: float
210			) -> npt.NDArray[np.float64]:
211			"""Given integer lattice points, a unit cell, ``max_cdist`` (max of
212			cdist(x, motif)) and ``max_nn_dist`` (max of the dists to k-th
213			nearest neighbours found so far), return lattice points which are
214			close enough such that the corresponding motif copy could contain
215			nearest neighbours.
216			"""
217
218			lattice = int_lattice @ cell
219			bound = np.amax(max_nn_dists) + max_cdist
220			return lattice[np.sqrt(np.sum(lattice ** 2, axis=-1)) < bound]
221
222
223			@numba.njit(cache=True)
224			def _lattice_to_cloud(
225			motif: npt.NDArray,
226			lattice: npt.NDArray
227			) -> npt.NDArray[np.float64]:
228			"""Transform a batch of non-integer lattice points (generated by
229			_generate_integer_lattice then mutliplied by the cell) into a cloud
230			of points from a periodic set with the motif and cell.
231			"""
232
233			m = len(motif)
234			layer = np.empty((m * len(lattice), motif.shape[-1]), dtype=np.float64)
235			i1 = 0
236			for translation in lattice:
237			i2 = i1 + m
238			layer[i1:i2] = motif + translation
239			i1 = i2
240			return layer
241
242
243			@numba.njit(cache=True)
244			def _int_lattice_to_cloud(
245			motif: npt.NDArray,
246			cell: npt.NDArray,
247			int_lattice: npt.NDArray
248			) -> npt.NDArray[np.float64]:
249			"""Transform a batch of integer lattice points (generated by
250			_generate_integer_lattice) into a cloud of points from a periodic
251			set with the motif and cell.
252			"""
253			return _lattice_to_cloud(motif, int_lattice @ cell)
254
255
256			@numba.njit(cache=True)
257			def _in_sphere(xy: Tuple[float, float], z: float, d: float) -> bool:
258			"""Return True if sum(i^2 for i in xy) + z^2 <= d^2."""
259			s = z ** 2
260			for val in xy:
261			s += val ** 2
262			return s <= d ** 2
263
264
265			def nearest_neighbours_minval(
266			motif: npt.NDArray,
267			cell: npt.NDArray,
268			min_val: float
269			) -> npt.NDArray[np.float64]:
270			"""Return the same ``dists``/PDD matrix as ``nearest_neighbours``,
271			but with enough columns such that all values in the last column are
272			at least ``min_val``. Unlike ``nearest_neighbours``, does not take a
273			query array ``x`` but only finds neighbours to motif points, and
274			does not return the point cloud or indices of the nearest
275			neighbours. Used in ``PDD_reconstructable``.
276			"""
277
278			max_cdist = np.amax(cdist(motif, motif))
279			# generate initial cloud of points, at least k + two more layers
280			int_lat_generator = _generate_integer_lattice(cell.shape[0])
281
282			cloud = []
283			for _ in range(3):
284			cloud.append(_lattice_to_cloud(motif, next(int_lat_generator) @ cell))
285			cloud = np.concatenate(cloud)
286
287			dists_, inds = KDTree(
288			cloud, leafsize=30, compact_nodes=False, balanced_tree=False
289			).query(motif, k=cloud.shape[0])
290			dists = np.zeros_like(dists_, dtype=np.float64)
291
292			# add layers & find k nearest neighbours until they don't change
293			while True:
294			if np.all(dists_[:, -1] >= min_val):
295			col = np.argwhere(np.all(dists_ >= min_val, axis=0))[0][0] + 1
296			if np.array_equal(dists[:, :col], dists_[:, :col]):
297			break
298			dists = dists_
299			lattice = next(int_lat_generator) @ cell
300			closest_dist_bound = np.linalg.norm(lattice, axis=-1) - max_cdist
301			is_close = closest_dist_bound <= np.amax(dists_[:, -1])
302			if not np.any(is_close):
303			break
304			cloud = np.vstack((cloud, _lattice_to_cloud(motif, lattice[is_close])))
305			dists_, inds = KDTree(
306			cloud, leafsize=30, compact_nodes=False, balanced_tree=False
307			).query(motif, k=cloud.shape[0])
308
309			k = np.argwhere(np.all(dists >= min_val, axis=0))[0][0]
310			return dists_[:, 1:k+1], cloud, inds
311
312
313			def generate_concentric_cloud(motif, cell):
314			"""
315			Generates batches of points from a periodic set given by (motif,
316			cell) which get successively further away from the origin.
317
318			Each yield gives all points (that have not already been yielded)
319			which lie in a unit cell whose corner lattice point was generated by
320			``generate_integer_lattice(motif.shape[1])``.
321
322			Parameters
323			----------
324			motif : :class:`numpy.ndarray`
325			Cartesian representation of the motif, shape (no points, dims).
326			cell : :class:`numpy.ndarray`
327			Cartesian representation of the unit cell, shape (dims, dims).
328
329			Yields
330			-------
331			:class:`numpy.ndarray`
332			Yields arrays of points from the periodic set.
333			"""
334
335			int_lat_generator = _generate_integer_lattice(cell.shape[0])
336			for layer in int_lat_generator:
337			yield _int_lattice_to_cloud(motif, cell, layer)
338

dwiddo / average-minimum-distance

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generate_concentric_cloud() A

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