1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
|
# fmt: off
import numpy as np
import pytest
from ase.geometry import (
get_angles,
get_angles_derivatives,
get_dihedrals,
get_dihedrals_derivatives,
get_distances_derivatives,
)
def get_numerical_derivatives(positions, mode, epsilon):
if mode == 'distance':
mode_n = 0 # get derivative for bond 0-1
elif mode == 'angle':
mode_n = 1 # get derivative for angle 0-1-2
elif mode == 'dihedral':
mode_n = 2 # get derivative for dihedral 0-1-2-3
derivs = np.zeros((2 + mode_n, 3))
for i in range(2 + mode_n):
for j in range(3):
pos = positions.copy()
pos[i, j] -= epsilon
if mode == 'distance':
minus = np.linalg.norm(pos[1] - pos[0])
elif mode == 'angle':
minus = get_angles(
[pos[0] - pos[1]],
[pos[2] - pos[1]],
)[0] # size-1 array -> scalar
elif mode == 'dihedral':
minus = get_dihedrals(
[pos[1] - pos[0]],
[pos[2] - pos[1]],
[pos[3] - pos[2]],
)[0] # size-1 array -> scalar
pos[i, j] += 2 * epsilon
if mode == 'distance':
plus = np.linalg.norm(pos[1] - pos[0])
elif mode == 'angle':
plus = get_angles(
[pos[0] - pos[1]],
[pos[2] - pos[1]],
)[0] # size-1 array -> scalar
elif mode == 'dihedral':
plus = get_dihedrals(
[pos[1] - pos[0]],
[pos[2] - pos[1]],
[pos[3] - pos[2]],
)[0] # size-1 array -> scalar
derivs[i, j] = (plus - minus) / (2 * epsilon)
return derivs
def _get_positions():
# example: positions for H2O2 molecule
return np.asarray([
[0.840, 0.881, 0.237], # H
[0., 0.734, -0.237], # O
[0., -0.734, -0.237], # O
[-0.840, -0.881, 0.237], # H
])
def test_atoms_angle():
pos = _get_positions()
# analytical derivatives in Angstrom/Angstrom, i.e. degrees/Angstrom
distances_derivs = get_distances_derivatives([pos[1] - pos[0]])[0]
angles_derivs = get_angles_derivatives([pos[0] - pos[1]],
[pos[2] - pos[1]])[0]
dihedrals_derivs = get_dihedrals_derivatives([pos[1] - pos[0]],
[pos[2] - pos[1]],
[pos[3] - pos[2]])[0]
# numerical approximations to derivatives using finite differences
epsilon = 1e-5
num_distances_derivs = get_numerical_derivatives(pos, mode='distance',
epsilon=epsilon)
num_angles_derivs = get_numerical_derivatives(pos, mode='angle',
epsilon=epsilon)
num_dihedrals_derivs = get_numerical_derivatives(pos, mode='dihedral',
epsilon=epsilon)
# print(distances_derivs - num_distances_derivs)
# print(angles_derivs - num_angles_derivs)
# print(dihedrals_derivs - num_dihedrals_derivs)
# finite differences versus analytical results
assert num_distances_derivs == pytest.approx(distances_derivs, abs=1e-8)
assert num_angles_derivs == pytest.approx(angles_derivs, abs=1e-8)
assert num_dihedrals_derivs == pytest.approx(dihedrals_derivs, abs=1e-8)
# derivatives of multiple internal coordinates at once
assert (distances_derivs ==
get_distances_derivatives([pos[1] - pos[0],
pos[1] - pos[0]])[0]).all()
assert (angles_derivs ==
get_angles_derivatives([pos[0] - pos[1], pos[0] - pos[1]],
[pos[2] - pos[1],
pos[2] - pos[1]])[0]).all()
assert (dihedrals_derivs ==
get_dihedrals_derivatives([pos[1] - pos[0], pos[1] - pos[0]],
[pos[2] - pos[1], pos[2] - pos[1]],
[pos[3] - pos[2],
pos[3] - pos[2]])[0]).all()
class TestNondestructive:
"""Test that plural derivative functions do not mutate inputs (#1560)."""
@staticmethod
def test_distances_derivatives():
"""Test `get_distances_derivatives`."""
pos = _get_positions()
v01s = np.atleast_2d(pos[1] - pos[0])
v01s_ref = v01s.copy()
get_distances_derivatives(v01s)
np.testing.assert_array_equal(v01s, v01s_ref)
@staticmethod
def test_angles_derivatives():
"""Test `get_angles_derivatives`."""
pos = _get_positions()
v10s = np.atleast_2d(pos[0] - pos[1])
v12s = np.atleast_2d(pos[2] - pos[1])
v10s_ref = v10s.copy()
v12s_ref = v12s.copy()
get_angles_derivatives(v10s, v12s)
np.testing.assert_array_equal(v10s, v10s_ref)
np.testing.assert_array_equal(v12s, v12s_ref)
@staticmethod
def test_dihedrals_derivatives():
"""Test `get_dihedrals_derivatives`."""
pos = _get_positions()
v01s = np.atleast_2d(pos[1] - pos[0])
v12s = np.atleast_2d(pos[2] - pos[1])
v23s = np.atleast_2d(pos[3] - pos[2])
v01s_ref = v01s.copy()
v12s_ref = v12s.copy()
v23s_ref = v23s.copy()
get_dihedrals_derivatives(v01s, v12s, v23s)
np.testing.assert_array_equal(v01s, v01s_ref)
np.testing.assert_array_equal(v12s, v12s_ref)
np.testing.assert_array_equal(v23s, v23s_ref)
|
