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
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
|
# Copyright 2017 by Peter Cock. All rights reserved.
# This file is part of the Biopython distribution and governed by your
# choice of the "Biopython License Agreement" or the "BSD 3-Clause License".
# Please see the LICENSE file that should have been included as part of this
# package.
"""Tests for the vector code in Bio.PDB."""
import unittest
try:
import numpy
from numpy.random import random
except ImportError:
from Bio import MissingPythonDependencyError
raise MissingPythonDependencyError(
"Install NumPy if you want to use Bio.PDB."
) from None
from Bio.PDB.vectors import Vector
from Bio.PDB import rotmat, refmat, calc_angle, calc_dihedral, rotaxis, m2rotaxis
from Bio.PDB.vectors import get_spherical_coordinates, coord_space, homog_trans_mtx
class VectorTests(unittest.TestCase):
"""Tests for the Vector class."""
def test_division(self):
"""Confirm division works."""
v = Vector(1, 1, 1) / 2
self.assertEqual(repr(v), "<Vector 0.50, 0.50, 0.50>")
def test_Vector(self):
"""Test Vector object."""
v1 = Vector(0, 0, 1)
v2 = Vector(0, 0, 0)
v3 = Vector(0, 1, 0)
v4 = Vector(1, 1, 0)
self.assertEqual(calc_angle(v1, v2, v3), 1.5707963267948966)
self.assertEqual(calc_dihedral(v1, v2, v3, v4), 1.5707963267948966)
self.assertTrue(
numpy.array_equal((v1 - v2).get_array(), numpy.array([0.0, 0.0, 1.0]))
)
self.assertTrue(
numpy.array_equal((v1 - 1).get_array(), numpy.array([-1.0, -1.0, 0.0]))
)
self.assertTrue(
numpy.array_equal(
(v1 - (1, 2, 3)).get_array(), numpy.array([-1.0, -2.0, -2.0])
)
)
self.assertTrue(
numpy.array_equal((v1 + v2).get_array(), numpy.array([0.0, 0.0, 1.0]))
)
self.assertTrue(
numpy.array_equal((v1 + 3).get_array(), numpy.array([3.0, 3.0, 4.0]))
)
self.assertTrue(
numpy.array_equal(
(v1 + (1, 2, 3)).get_array(), numpy.array([1.0, 2.0, 4.0])
)
)
self.assertTrue(numpy.array_equal(v1.get_array() / 2, numpy.array([0, 0, 0.5])))
self.assertTrue(numpy.array_equal(v1.get_array() / 2, numpy.array([0, 0, 0.5])))
self.assertEqual(v1 * v2, 0.0)
self.assertTrue(
numpy.array_equal((v1 ** v2).get_array(), numpy.array([0.0, -0.0, 0.0]))
)
self.assertTrue(
numpy.array_equal((v1 ** 2).get_array(), numpy.array([0.0, 0.0, 2.0]))
)
self.assertTrue(
numpy.array_equal(
(v1 ** (1, 2, 3)).get_array(), numpy.array([0.0, 0.0, 3.0])
)
)
self.assertEqual(v1.norm(), 1.0)
self.assertEqual(v1.normsq(), 1.0)
v1[2] = 10
self.assertEqual(v1.__getitem__(2), 10)
def test_normalization(self):
"""Test Vector normalization."""
v1 = Vector([2, 0, 0])
self.assertTrue(
numpy.array_equal(v1.normalized().get_array(), numpy.array([1, 0, 0]))
)
# State of v1 should not be affected by `normalized`
self.assertTrue(numpy.array_equal(v1.get_array(), numpy.array([2, 0, 0])))
v1.normalize()
# State of v1 should be affected by `normalize`
self.assertTrue(numpy.array_equal(v1.get_array(), numpy.array([1, 0, 0])))
def test_refmat(self):
v1 = Vector(0, 0, 1)
v2 = Vector(0, 1, 0)
ref = refmat(v1, v2)
self.assertTrue(numpy.allclose(ref[0], [1.0, 0.0, 0.0]))
self.assertTrue(numpy.allclose(ref[1], [0.0, 0.0, 1.0]))
self.assertTrue(numpy.allclose(ref[2], [0.0, 1.0, 0.0]))
self.assertTrue(
numpy.allclose(v1.left_multiply(ref).get_array(), [0.0, 1.0, 0.0])
)
def test_rotmat_90(self):
"""Test regular 90 deg rotation."""
v1 = Vector(0, 0, 1)
v2 = Vector(0, 1, 0)
rot = rotmat(v1, v2)
self.assertTrue(numpy.allclose(rot[0], numpy.array([1.0, 0.0, 0.0])))
self.assertTrue(numpy.allclose(rot[1], numpy.array([0.0, 0.0, 1.0])))
self.assertTrue(numpy.allclose(rot[2], numpy.array([0.0, -1.0, 0.0])))
self.assertTrue(
numpy.allclose(v1.left_multiply(rot).get_array(), [0.0, 1.0, 0.0])
)
self.assertTrue(
numpy.allclose(
v1.right_multiply(numpy.transpose(rot)).get_array(), [0.0, 1.0, 0.0]
)
)
def test_rotmat_180(self):
"""Test rotmat when the rotation is 180 deg (singularity)."""
v1 = Vector([1.0, 0.8, 0])
v2 = Vector([-1.0, -0.8, 0])
rot = rotmat(v1, v2)
v3 = v1.left_multiply(rot)
self.assertTrue(numpy.allclose(v2.get_array(), v3.get_array()))
def test_rotmat_0(self):
"""Test rotmat when the rotation is 0 deg (singularity)."""
v1 = Vector([1.0, 0.8, 0])
v2 = Vector([1.0, 0.8, 0])
rot = rotmat(v1, v2)
v3 = v1.left_multiply(rot)
self.assertTrue(numpy.allclose(v1.get_array(), v3.get_array()))
def test_m2rotaxis_90(self):
"""Test 90 deg rotation."""
v1 = Vector(0, 0, 1)
v2 = Vector(0, 1, 0)
rot = rotmat(v1, v2)
angle, axis = m2rotaxis(rot)
self.assertTrue(numpy.allclose(axis.get_array(), [-1.0, 0.0, 0.0]))
self.assertTrue(abs(angle - numpy.pi / 2) < 1e-5)
def test_m2rotaxis_180(self):
"""Test 180 deg rotation."""
v1 = Vector([1.0, 0.8, 0])
v2 = Vector([-1.0, -0.8, 0])
rot = rotmat(v1, v2)
angle, axis = m2rotaxis(rot)
self.assertTrue(abs(axis * v1) < 1e-5) # axis orthogonal to v1
self.assertTrue(abs(angle - numpy.pi) < 1e-5)
def test_m2rotaxis_0(self):
"""Test 0 deg rotation. Axis must be [1, 0, 0] as per Vector documentation."""
v1 = Vector([1.0, 0.8, 0])
v2 = Vector([1.0, 0.8, 0])
rot = rotmat(v1, v2)
angle, axis = m2rotaxis(rot)
self.assertTrue(numpy.allclose(axis.get_array(), [1, 0, 0]))
self.assertTrue(abs(angle) < 1e-5)
def test_Vector_angles(self):
"""Test Vector angles."""
angle = random() * numpy.pi
axis = Vector(random(3) - random(3))
axis.normalize()
m = rotaxis(angle, axis)
cangle, caxis = m2rotaxis(m)
self.assertAlmostEqual(angle, cangle, places=3)
self.assertTrue(
numpy.allclose(list(map(int, (axis - caxis).get_array())), [0, 0, 0]),
"Want %r and %r to be almost equal" % (axis.get_array(), caxis.get_array()),
)
def test_get_spherical_coordinates(self):
"""Test spherical coordinates."""
srt22 = numpy.sqrt(2.0) / 2
r45 = numpy.radians(45)
r90 = numpy.radians(90)
r135 = numpy.radians(135)
for i in range(2):
for j in range(2):
for k in range(2):
sc = get_spherical_coordinates(
[
(0.5 if i else -0.5),
0.5 if j else -0.5,
(1 if k else -1) * srt22,
]
)
# print(sc[0], numpy.degrees(sc[1]), numpy.degrees(sc[2]))
self.assertEqual(1.0, sc[0]) # r
self.assertEqual(
(1 if j else -1) * (r45 if i else r135), sc[1]
) # azimuth
self.assertEqual((r45 if k else r135), sc[2]) # polar angle
def test_coord_space(self):
# start with 3 points already aligned to axes
point_set = (
numpy.array([[2.0], [0.0], [2.0], [1.0]]),
numpy.array([[0.0], [0.0], [0.0], [1.0]]),
numpy.array([[0.0], [0.0], [2.0], [1.0]]),
)
# confirm get id matrix to transform to/from coord space
homog_id = numpy.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
mtxs = coord_space(point_set[0], point_set[1], point_set[2], True)
for i in range(2):
self.assertTrue(numpy.array_equal(mtxs[i], homog_id))
# test in every quadrant
for i in range(2):
for j in range(2):
for k in range(2):
# translate point_set arbitrary amount in each axis
tm = homog_trans_mtx(
(3 if i else -3), (3 if j else -3), (3 if k else -3)
)
ps2 = [1, 2, 3]
for i in range(3):
ps2[i] = tm.dot(point_set[i])
# confirm coord_space puts points back to axis alignment
mtxs = coord_space(ps2[0], ps2[1], ps2[2], True)
rslt = [1, 2, 3]
for i in range(3):
rslt[i] = mtxs[0].dot(ps2[i])
self.assertTrue(numpy.array_equal(rslt, point_set))
# confirm reverse transform returns translated points
for i in range(3):
rslt[i] = mtxs[1].dot(rslt[i])
self.assertTrue(numpy.array_equal(rslt, ps2))
if __name__ == "__main__":
runner = unittest.TextTestRunner(verbosity=2)
unittest.main(testRunner=runner)
|
