# -*- coding: utf-8 -*-
"""Copyright 2019 DScribe developers
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""
import numpy as np
import scipy.sparse
from scipy.spatial.distance import cdist
from ase import Atoms
[docs]def get_adjacency_matrix(radius, pos1, pos2=None, output_type="coo_matrix"):
"""Calculates a sparse adjacency matrix by only considering distances
within a certain cutoff. Uses a k-d tree to reach O(n log(N)) time
complexity.
Args:
radius(float): The cutoff radius within which distances are
calculated. Distances outside this radius are not included.
pos1(np.ndarray): A list of N-dimensional positions.
pos2(np.ndarray): A list of N-dimensional positions. If not provided,
is assumed to be the same as pos1.
output_type(str): Which container to use for output data. Options:
"dok_matrix", "coo_matrix", "dict", or "ndarray". Default:
"dok_matrix".
Returns:
dok_matrix | np.array | coo_matrix | dict: Symmetric sparse 2D
matrix containing the pairwise distances.
"""
tree1 = scipy.spatial.cKDTree(
pos1,
leafsize=16,
compact_nodes=True,
copy_data=False,
balanced_tree=True,
boxsize=None
)
if pos2 is None:
pos2 = pos1
tree2 = scipy.spatial.cKDTree(
pos2,
leafsize=16,
compact_nodes=True,
copy_data=False,
balanced_tree=True,
boxsize=None
)
dmat = tree1.sparse_distance_matrix(tree2, radius, output_type=output_type)
return dmat
[docs]def get_adjacency_list(adjacency_matrix):
"""Used to transform an adjacency matrix into an adjacency list. The
adjacency list provides much faster access to the neighbours of a node.
Args:
adjacency_matrix(scipy.sparse.spmatrix): The adjacency matrix from
which the adjacency list is constructed from. Any of the scipy
sparse matrix classes.
Returns:
list: A list of neighbouring indices. The list of neighbouring indices
for atom at index i is given by accessing the ith element of this list.
"""
# Ensure that we have a coo-matrix
if type(adjacency_matrix) != scipy.sparse.coo_matrix:
adjacency_matrix = adjacency_matrix.tocoo()
# Build adjacency list
adjacency_list = [[] for i in range(adjacency_matrix.shape[0])]
for i, j in zip(adjacency_matrix.row, adjacency_matrix.col):
adjacency_list[i].append(j)
return adjacency_list
[docs]def get_extended_system(system, radial_cutoff, centers=None, return_cell_indices=False):
"""Used to create a periodically extended system. If centers are not
specified, simply takes returns the original system multiplied by an
integer amount of times in each direction to cover the radial cutoff. If
centers are provided, returns the exact atoms that are within the given
radial cutoff from the given centers.
Args:
original_system (ase.Atoms): The original periodic system to duplicate.
radial_cutoff (float): The radial cutoff to use in constructing the
extended system.
centers (np.ndarray): Array of xyz-coordinates from which the distance
is calculated. If provided, these centers are used to calculate the
exact distance and only atoms within the radial cutoff from these
centers are returned.
return_cell_indices (boolean): Whether to return an array of cell
indices for each atom in the extended system.
Returns:
ase.Atoms | tuple: If return_cell_indices is False, returns the new
extended system. Else returns a tuple containing the new extended
system as the first entry and the index of the periodically repeated
cell for each atom as the second entry.
"""
# Determine the upper limit of how many copies we need in each cell vector
# direction. We take as many copies as needed to reach the radial cutoff.
# Notice that we need to use vectors that are perpendicular to the cell
# vectors to ensure that the correct atoms are included for non-cubic cells.
cell = np.array(system.get_cell())
a1, a2, a3 = cell[0], cell[1], cell[2]
b1 = np.cross(a2, a3, axis=0)
b2 = np.cross(a3, a1, axis=0)
b3 = np.cross(a1, a2, axis=0)
p1 = np.dot(a1, b1) / np.dot(b1, b1) * b1 # Projections onto perpendicular vectors
p2 = np.dot(a2, b2) / np.dot(b2, b2) * b2
p3 = np.dot(a3, b3) / np.dot(b3, b3) * b3
xyz_arr = np.linalg.norm(np.array([p1, p2, p3]), axis=1)
cell_images = np.ceil(radial_cutoff/xyz_arr)
nx = int(cell_images[0])
ny = int(cell_images[1])
nz = int(cell_images[2])
n_copies_axis = np.array([nx, ny, nz], dtype=int)
# If no centers are given, and the cell indices are not requested, simply
# return the multiplied system. This is much faster.
if centers is None and not return_cell_indices:
n_atoms = len(system)
n_rep = np.product(2*n_copies_axis+1) # Number of repeated copies
ext_pos = np.tile(system.get_positions(), (n_rep, 1))
# Calculate the extended system positions so that the original cell
# stays in place: both in space and in index
i_curr = 0
for m0 in np.append(np.arange(0, nx+1), np.arange(-nx, 0)):
for m1 in np.append(np.arange(0, ny+1), np.arange(-ny, 0)):
for m2 in np.append(np.arange(0, nz+1), np.arange(-nz, 0)):
ext_pos[i_curr:i_curr+n_atoms] += np.dot((m0, m1, m2), cell)
i_curr += n_atoms
ext_symbols = np.tile(system.get_atomic_numbers(), n_rep)
extended_system = Atoms(
positions=ext_pos,
symbols=ext_symbols,
)
return extended_system
# If centers are given and/or cell indices are needed, the process is done
# one cell at a time to keep track of the cell inded and the distances.
# This is a bit slower.
else:
# We need to specify that the relative positions should not be wrapped.
# Otherwise the repeated systems may overlap with the positions taken
# with get_positions()
relative_pos = np.array(system.get_scaled_positions(wrap=False))
numbers = np.array(system.numbers)
cartesian_pos = np.array(system.get_positions())
# Create copies of the cell but keep track of the atoms in the
# original cell
num_extended = []
pos_extended = []
num_extended.append(numbers)
pos_extended.append(cartesian_pos)
a = np.array([1, 0, 0])
b = np.array([0, 1, 0])
c = np.array([0, 0, 1])
cell_indices = [np.zeros((len(system), 3), dtype=int)]
for i in range(-n_copies_axis[0], n_copies_axis[0]+1):
for j in range(-n_copies_axis[1], n_copies_axis[1]+1):
for k in range(-n_copies_axis[2], n_copies_axis[2]+1):
if i == 0 and j == 0 and k == 0:
continue
# Calculate the positions of the copied atoms and filter
# out the atoms that are farther away than the given
# cutoff.
num_copy = np.array(numbers)
pos_copy = np.array(relative_pos)
pos_shifted = pos_copy-i*a-j*b-k*c
pos_copy_cartesian = np.dot(pos_shifted, cell)
# Only distances to the atoms within the interaction limit
# are considered.
distances = cdist(pos_copy_cartesian, centers)
weight_mask = distances < radial_cutoff
# Create a boolean mask that says if the atom is within the
# range from at least one atom in the original cell
valids_mask = np.any(weight_mask, axis=1)
if np.any(valids_mask):
valid_pos = pos_copy_cartesian[valids_mask]
valid_num = num_copy[valids_mask]
valid_ind = np.tile(np.array([i, j, k], dtype=int), (len(valid_num), 1))
pos_extended.append(valid_pos)
num_extended.append(valid_num)
cell_indices.append(valid_ind)
pos_extended = np.concatenate(pos_extended)
num_extended = np.concatenate(num_extended)
cell_indices = np.vstack(cell_indices)
extended_system = Atoms(
positions=pos_extended,
numbers=num_extended,
cell=cell,
pbc=False
)
return extended_system, cell_indices