# Copyright (c) 2022, mushroomfire in Beijing Institute of Technology
# This file is from the mdapy project, released under the BSD 3-Clause License.
import taichi as ti
import numpy as np
try:
from neigh._neigh import (
_build_cell_rec,
_build_cell_rec_with_jishu,
_build_cell_tri,
_build_cell_tri_with_jishu,
)
except Exception:
from _neigh import (
_build_cell_rec,
_build_cell_rec_with_jishu,
_build_cell_tri,
_build_cell_tri_with_jishu,
)
import warnings
warnings.simplefilter("ignore", category=DeprecationWarning)
[docs]
@ti.data_oriented
class Neighbor:
"""This module is used to cerate neighbor of atoms within a given cutoff distance.
Using linked-cell list method makes fast neighbor finding possible.
Args:
pos (np.ndarray): (:math:`N_p, 3`) particles positions.
box (np.ndarray): (:math:`4, 3`) system box, must be rectangle.
rc (float): cutoff distance.
boundary (list, optional): boundary conditions, 1 is periodic and 0 is free boundary. Defaults to [1, 1, 1].
max_neigh (int, optional): maximum neighbor number. If not given, will estimate atomatically. Default to None.
Outputs:
- **verlet_list** (np.ndarray) - (:math:`N_p, max\_neigh`) verlet_list[i, j] means j atom is a neighbor of i atom if j > -1.
- **distance_list** (np.ndarray) - (:math:`N_p, max\_neigh`) distance_list[i, j] means distance between i and j atom.
- **neighbor_number** (np.ndarray) - (:math:`N_p`) neighbor atoms number.
Examples:
>>> import mdapy as mp
>>> mp.init()
>>> import numpy as np
>>> FCC = mp.LatticeMaker(3.615, 'FCC', 10, 10, 10) # Create a FCC structure
>>> FCC.compute() # Get atom positions
>>> neigh = mp.Neighbor(FCC.pos, FCC.box,
5.) # Initialize Neighbor class.
>>> neigh.compute() # Calculate particle neighbor information.
>>> neigh.verlet_list # Check the neighbor index.
>>> neigh.distance_list # Check the neighbor distance.
>>> neigh.neighbor_number # Check the neighbor atom number.
"""
def __init__(self, pos, box, rc, boundary=[1, 1, 1], max_neigh=None):
if pos.dtype != np.float64:
pos = pos.astype(np.float64)
self.pos = pos
if box.dtype != np.float64:
box = box.astype(np.float64)
if box.shape == (3, 2):
self.box = np.zeros((4, 3), dtype=box.dtype)
self.box[0, 0], self.box[1, 1], self.box[2, 2] = box[:, 1] - box[:, 0]
self.box[-1] = box[:, 0]
elif box.shape == (4, 3):
self.box = box
assert self.box[0, 1] == 0
assert self.box[0, 2] == 0
assert self.box[1, 2] == 0
self.rc = rc
self.boundary = ti.Vector([int(boundary[i]) for i in range(3)])
self.bin_length = self.rc + 0.01
self.max_neigh = max_neigh
self.box_length = ti.Vector([np.linalg.norm(box[i]) for i in range(3)])
self.N = self.pos.shape[0]
for i, direc in zip(range(3), ["x", "y", "z"]):
if self.boundary[i] == 1:
assert (
self.box_length[i] / 2 > self.bin_length
), f"box length along {direc} direction with periodic boundary should be two times larger than rc."
self.ncel = ti.Vector(
[
max(int(np.floor(np.linalg.norm(box[i]) / self.bin_length)), 3)
for i in range(3)
]
)
self.if_computed = False
self.rec = True
if self.box[1, 0] != 0 or self.box[2, 0] != 0 or self.box[2, 1] != 0:
self.rec = False
@ti.func
def _pbc_rec(self, rij):
for m in ti.static(range(3)):
if self.boundary[m] == 1:
dx = rij[m]
x_size = self.box_length[m]
h_x_size = x_size * 0.5
if dx > h_x_size:
dx = dx - x_size
if dx <= -h_x_size:
dx = dx + x_size
rij[m] = dx
return rij
@ti.func
def _pbc(self, rij, box: ti.types.ndarray(dtype=ti.math.vec3)) -> ti.math.vec3:
nz = rij[2] / box[2][2]
ny = (rij[1] - nz * box[2][1]) / box[1][1]
nx = (rij[0] - ny * box[1][0] - nz * box[2][0]) / box[0][0]
n = ti.Vector([nx, ny, nz])
for i in ti.static(range(3)):
if self.boundary[i] == 1:
if n[i] > 0.5:
n[i] -= 1
elif n[i] < -0.5:
n[i] += 1
return n[0] * box[0] + n[1] * box[1] + n[2] * box[2]
@ti.kernel
def _build_verlet_list(
self,
pos: ti.types.ndarray(dtype=ti.math.vec3),
atom_cell_list: ti.types.ndarray(),
cell_id_list: ti.types.ndarray(),
verlet_list: ti.types.ndarray(),
distance_list: ti.types.ndarray(),
neighbor_number: ti.types.ndarray(),
box: ti.types.ndarray(dtype=ti.math.vec3),
):
rcsq = self.rc * self.rc
icel, jcel, kcel, rij = (
0,
0,
0,
ti.Vector([ti.f64(0.0), ti.f64(0.0), ti.f64(0.0)]),
)
for i in range(pos.shape[0]):
nindex = 0
if ti.static(self.rec):
icel, jcel, kcel = ti.floor(
(pos[i] - box[3]) / self.bin_length, dtype=ti.i32
)
else:
r = pos[i] - box[3]
nz = r[2] / box[2][2]
ny = (r[1] - nz * box[2][1]) / box[1][1]
nx = (r[0] - ny * box[1][0] - nz * box[2][0]) / box[0][0]
icel = ti.floor((nx * box[0]).norm() / self.bin_length, int)
jcel = ti.floor((ny * box[1]).norm() / self.bin_length, int)
kcel = ti.floor((nz * box[2]).norm() / self.bin_length, int)
iicel, jjcel, kkcel = icel, jcel, kcel # make sure correct cell
if icel < 0:
iicel = 0
elif icel > self.ncel[0] - 1:
iicel = self.ncel[0] - 1
if jcel < 0:
jjcel = 0
elif jcel > self.ncel[1] - 1:
jjcel = self.ncel[1] - 1
if kcel < 0:
kkcel = 0
elif kcel > self.ncel[2] - 1:
kkcel = self.ncel[2] - 1
for iiicel in range(iicel - 1, iicel + 2):
for jjjcel in range(jjcel - 1, jjcel + 2):
for kkkcel in range(kkcel - 1, kkcel + 2):
iiiicel = iiicel
jjjjcel = jjjcel
kkkkcel = kkkcel
if iiicel < 0:
iiiicel += self.ncel[0]
elif iiicel > self.ncel[0] - 1:
iiiicel -= self.ncel[0]
if jjjcel < 0:
jjjjcel += self.ncel[1]
elif jjjcel > self.ncel[1] - 1:
jjjjcel -= self.ncel[1]
if kkkcel < 0:
kkkkcel += self.ncel[2]
elif kkkcel > self.ncel[2] - 1:
kkkkcel -= self.ncel[2]
j = cell_id_list[iiiicel, jjjjcel, kkkkcel]
while j > -1:
if ti.static(self.rec):
rij = self._pbc_rec(pos[j] - pos[i])
else:
rij = self._pbc(pos[j] - pos[i], box)
rijdis_sq = rij[0] ** 2 + rij[1] ** 2 + rij[2] ** 2
if rijdis_sq <= rcsq and j != i:
verlet_list[i, nindex] = j
distance_list[i, nindex] = ti.sqrt(rijdis_sq)
nindex += 1
j = atom_cell_list[j]
neighbor_number[i] = nindex
[docs]
def compute(self):
"""Do the real neighbor calculation."""
atom_cell_list = np.zeros(self.N, dtype=np.int32)
cell_id_list = (
np.zeros((self.ncel[0], self.ncel[1], self.ncel[2]), dtype=np.int32)
) - 1
need_check = True
if self.max_neigh is None:
max_neigh_list = np.zeros_like(cell_id_list)
if self.rec:
_build_cell_rec_with_jishu(
self.pos,
atom_cell_list,
cell_id_list,
np.ascontiguousarray(self.box[-1]),
np.array([i for i in self.ncel]),
self.bin_length,
max_neigh_list,
)
else:
_build_cell_tri_with_jishu(
self.pos,
atom_cell_list,
cell_id_list,
self.box,
np.array([i for i in self.ncel]),
self.bin_length,
max_neigh_list,
)
self.max_neigh = np.partition(max_neigh_list.flatten(), -4)[-4:].sum()
need_check = False
else:
if self.rec:
_build_cell_rec(
self.pos,
atom_cell_list,
cell_id_list,
np.ascontiguousarray(self.box[-1]),
np.array([i for i in self.ncel]),
self.bin_length,
)
else:
_build_cell_tri(
self.pos,
atom_cell_list,
cell_id_list,
self.box,
np.array([i for i in self.ncel]),
self.bin_length,
)
self.verlet_list = np.zeros((self.N, self.max_neigh), dtype=int) - 1
self.distance_list = (
np.zeros((self.N, self.max_neigh), dtype=self.pos.dtype) + self.rc + 1.0
)
self.neighbor_number = np.zeros(self.N, dtype=int)
self._build_verlet_list(
self.pos,
atom_cell_list,
cell_id_list,
self.verlet_list,
self.distance_list,
self.neighbor_number,
self.box,
)
if need_check:
max_neigh_number = self.neighbor_number.max()
assert (
max_neigh_number <= self.max_neigh
), f"Increase the max_neigh larger than {max_neigh_number}."
self._if_computed = True
@ti.kernel
def _partition_select_sort(
self, indices: ti.types.ndarray(), keys: ti.types.ndarray(), N: int
):
"""This function sorts N-th minimal value in keys.
Args:
indices (ti.types.ndarray): indices.
keys (ti.types.ndarray): values to be sorted.
N (int): number of sorted values.
"""
for i in range(indices.shape[0]):
for j in range(N):
minIndex = j
for k in range(j + 1, indices.shape[1]):
if keys[i, k] < keys[i, minIndex]:
minIndex = k
if minIndex != j:
keys[i, minIndex], keys[i, j] = keys[i, j], keys[i, minIndex]
indices[i, minIndex], indices[i, j] = (
indices[i, j],
indices[i, minIndex],
)
[docs]
def sort_verlet_by_distance(self, N: int):
"""This function sorts the first N-th verlet_list by distance_list.
Args:
N (int): number of sorted values
"""
if not self._if_computed:
self.compute()
self._partition_select_sort(self.verlet_list, self.distance_list, N)
if __name__ == "__main__":
from lattice_maker import LatticeMaker
from time import time
# ti.init(ti.gpu, device_memory_GB=4.0)
ti.init(ti.cpu)
start = time()
lattice_constant = 3.615
x, y, z = 100, 100, 50
FCC = LatticeMaker(lattice_constant, "FCC", x, y, z)
FCC.compute()
end = time()
print(f"Build {FCC.pos.shape[0]} atoms FCC time: {end-start} s.")
start = time()
neigh = Neighbor(FCC.pos, FCC.box, 5.0, max_neigh=None)
neigh.compute()
end = time()
print(neigh.ncel)
print(f"Build neighbor time: {end-start} s.")
print(neigh.verlet_list[0])
print(neigh.distance_list[0])
# print(neigh.verlet_list.shape[1])
# print(neigh.neighbor_number.max())
# print(neigh.neighbor_number.min())
# neigh.sort_verlet_by_distance(12)
# print(neigh.verlet_list[0])
# print(neigh.distance_list[0])