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
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
|
#!/usr/bin/env python
#
# test_dihedral.py
#
# Tests the dihedral module.
#
"""Provides tests for functions in the file dihedral.py
"""
__author__ = "Kristian Rother"
__copyright__ = "Copyright 2007-2009 2008, The Cogent Project"
__contributors__ = ["Kristian Rother", "Sandra Smit"]
__credits__ = ["Janusz Bujnicki", "Nils Goldmann"]
__license__ = "GPL"
__version__ = "1.4.1"
__maintainer__ = "Kristian Rother"
__email__ = "krother@rubor.de"
__status__ = "Production"
from cogent.util.unit_test import main, TestCase
from cogent.struct.dihedral import dihedral, scalar, angle, \
DihedralGeometryError, AngleGeometryError
from random import random
from numpy import array
from math import pi, cos, sin
class DihedralTests(TestCase):
def get_random_array(self):
"""
Returns a one-dimensional numpy array with three random floats
in the range between -5.0 and +5.0.
"""
return array([(random()-0.5)*10,(random()-0.5)*10,(random()-0.5)*10])
def assertAlmostEqualAngle(self, is_value, should_value, digits=7):
"""
Checks two angles in degrees whether they are the same within
the given number of digits. This has been implemented to make sure
that 359.9999991 == 0.0
"""
maxv = 359.0
for i in range(digits):
maxv += 0.9 * 0.1**i
while is_value < 0.0: is_value += 360
while is_value > maxv: is_value -= 360
while should_value < 0.0: should_value += 360
while should_value > maxv: should_value -= 360
self.assertAlmostEqual(is_value,should_value, digits)
def test_scalar(self):
"""Tests the scalar product function for one-dimensional arrays."""
# test one-dimensional arrays
self.assertEqual(scalar(array([0]),array([0])),0.0)
self.assertEqual(scalar(array([2]),array([3])),6.0)
self.assertEqual(scalar(array([0,0]),array([0,0])),0.0)
self.assertEqual(scalar(array([-1,-4]),array([1,4])),-17.0)
self.assertEqual(scalar(array([1,2]),array([3,4])),11.0)
self.assertEqual(scalar(array([-1,-4]),array([-1,4])),-15.0)
self.assertEqual(scalar(array([0,0,0]),array([0,0,0])),0.0)
self.assertEqual(scalar(array([2.5,0,-1]),array([2.5,0,-1])),7.25)
self.assertEqual(scalar(array([1,2,3]),array([0,0,0])),0.0)
self.assertEqual(scalar(array([1,2,3]),array([1,2,3])),14.0)
self.assertEqual(scalar(array([1,2,3]),array([4,5,6])),32.0)
# test two-dimensional arrays (should not be a feature)
self.assertNotEqual(scalar(array([[0,0],[0,0]]),\
array([[0,0],[0,0]])),0.0)
def test_angle_simple(self):
"""Tests the angle function for one- and two-dimensional vectors."""
# test two-dimensional vectors (not arrays!)
self.assertEqual(angle(array([0,1]),array([1,0])),0.5*pi)
self.assertEqual(angle(array([5,0]),array([13,0])),0.0)
self.assertEqual(angle(array([2,3]),array([26,39])),0.0)
self.assertEqual(angle(array([2,3]),array([-3,2])),0.5*pi)
self.assertEqual(angle(array([-5,0]),array([13,0])),pi)
# test three-dimensional vectors (not arrays!)
self.assertEqual(angle(array([0,0,-1]),array([0,0,1])),pi)
self.assertEqual(angle(array([0,15,-1]),array([0,-15,1])),pi)
self.assertEqual(angle(array([0,0,7]),array([14,14,0])),0.5*pi)
self.assertEqual(angle(array([0,7,7]),array([0,14,14])),0.0)
self.assertAlmostEqual(angle(array([100000000.0,0,1]),\
array([1,0,0])),0.0)
## def make_scipy_angles(self):
## """Generates the test data given below. Was commented out
## for getting rid of the library dependency"""
## from Scientific.Geometry import Vector
## for i in range(20):
## v1 = self.get_random_array()
## v2 = self.get_random_array()
## vec1 = Vector(v1[0],v1[1],v1[2])
## vec2 = Vector(v2[0],v2[1],v2[2])
## scipy_angle = vec1.angle(vec2)
## out = [(vec1[0],vec1[1],vec1[2]),\
## (vec2[0],vec2[1],vec2[2]),scipy_angle]
## print out,","
def test_angle_scipy(self):
"""
Asserts that dihedral and ScientificPython calculate the same angles.
"""
for v1,v2,scipy_angle in SCIPY_ANGLES:
ang = angle(array(v1),array(v2))
self.assertAlmostEqual(ang, scipy_angle)
def test_angle_fail(self):
"""The angle function should fail for zero length vectors."""
# should not work for zero length vectors
self.assertRaises(AngleGeometryError,angle,\
array([0,0]),array([0,0]))
self.assertRaises(AngleGeometryError,angle,\
array([0,0,0]),array([0,0,0]))
def test_dihedral_eight_basic_directions(self):
"""Checks dihedrals in all 45 degree intervals."""
# using vectors with integer positions.
self.assertAlmostEqualAngle(\
dihedral([-2,-1,0], [-1,0,0], [1,0,0], [2,-1, 0]), 0.0)
self.assertAlmostEqualAngle(\
dihedral([-2,-1,0], [-1,0,0], [1,0,0], [2,-1,-1]), 45.0)
self.assertAlmostEqualAngle(\
dihedral([-2,-1,0], [-1,0,0], [1,0,0], [2, 0,-1]), 90.0)
self.assertAlmostEqualAngle(\
dihedral([-2,-1,0], [-1,0,0], [1,0,0], [2, 1,-1]),135.0)
self.assertAlmostEqualAngle(\
dihedral([-2,-1,0], [-1,0,0], [1,0,0], [2, 1, 0]),180.0)
self.assertAlmostEqualAngle(\
dihedral([-2,-1,0], [-1,0,0], [1,0,0], [2, 1, 1]),225.0)
self.assertAlmostEqualAngle(\
dihedral([-2,-1,0], [-1,0,0], [1,0,0], [2, 0, 1]),270.0)
self.assertAlmostEqualAngle(\
dihedral([-2,-1,0], [-1,0,0], [1,0,0], [2,-1, 1]),315.0)
def test_dihedral_rotation(self):
"""Checks all angles in 0.2 degree intervals."""
# constructs vectors using sin/cos and then calculates dihedrals
precision = 5.0 # the higher the better
v1 = array([1,0,1])
v2 = array([0,0,1])
v3 = array([0,0,2])
for i in range(int(360*precision)):
degrees = i/precision
radians = pi*degrees/180.0
opp_degrees = 360-degrees
if opp_degrees == 360.0: opp_degrees = 0.0
# construct circular motion of vector
v4 = array([cos(radians), sin(radians),2])
self.assertAlmostEqualAngle(dihedral(v4,v3,v2,v1), degrees, 5)
# check rotation in the opposite direction
self.assertAlmostEqualAngle(dihedral(v1,v2,v3,v4), degrees, 5)
def test_dihedral_samples(self):
"""Checks values measured manually from atoms in PyMOL."""
coordinates = [
[(-1.225,4.621,42.070),(-1.407,4.455,43.516),\
(-2.495,4.892,44.221),(-3.587,5.523,43.715)],
[(-2.495,4.892,44.221),(1.513,0.381,40.711),\
(-3.091,4.715,47.723),(-0.567,3.892,44.433)],
[(-0.349,5.577,39.446),(-1.559,3.400,41.427),\
(-4.304,5.563,45.998),(-2.495,4.892,44.221)],
[(-45.819,84.315,19.372),(-31.124,72.286,14.035),\
(-27.975,58.688,7.025),(-16.238,78.659,23.731)],
[(-29.346,66.973,24.152),(-29.977,69.635,24.580),\
(-30.875,68.788,24.663),(-30.668,67.495,24.449)],
[(-34.586,84.884,14.064),(-23.351,69.756,11.028),\
(-40.924,69.442,24.630),(-30.875,68.788,24.663)]
]
angles = [1.201, 304.621, 295.672, 195.184, 358.699, 246.603]
for i in range(len(coordinates)):
v1,v2,v3,v4 = coordinates[i]
self.assertAlmostEqualAngle(dihedral(v1,v2,v3,v4), angles[i],3)
def test_dihedral_linear(self):
"""The dihedral function should fail for collinear vectors."""
v1 = [1,0,0]
v2 = [2,0,0]
v3 = [3,0,0]
v4 = [4,0,0]
# print dihedral(v1,v2,v3,v4)
for i in range(100):
offset = array([int((random()-0.5)*10),\
int((random()-0.5)*10),\
int((random()-0.5)*10)])
v1 = array([int((random()-0.5)*100),\
int((random()-0.5)*100),\
int((random()-0.5)*100)])
v2 = v1 * int((random()-0.5)*100) + offset
v3 = v1 * int((random()-0.5)*100) + offset
v4 = v1 * int((random()-0.5)*100) + offset
v1 += offset
self.assertRaises(DihedralGeometryError,dihedral,v1,v2,v3,v4)
def test_dihedral_identical(self):
"""The dihedral function should fail if two vectors are the same."""
# except for the first and last (the vectors form a triangle),
# in which case the dihedral angle should be 0.0
for i in range(100):
v1 = self.get_random_array()
v2 = self.get_random_array()
v3 = self.get_random_array()
self.assertRaises(DihedralGeometryError,dihedral,v1,v1,v2,v3)
self.assertRaises(DihedralGeometryError,dihedral,v1,v2,v1,v3)
self.assertRaises(DihedralGeometryError,dihedral,v1,v2,v2,v3)
self.assertRaises(DihedralGeometryError,dihedral,v1,v2,v3,v3)
self.assertRaises(DihedralGeometryError,dihedral,v1,v3,v2,v3)
# now the triangular case
# make sure that 359.999998 is equal to 0.0
torsion = dihedral(v1,v2,v3,v1) + 0.000001
if torsion > 360.0: torsion -= 360.0
self.assertAlmostEqualAngle(torsion,0.0,5)
SCIPY_ANGLES = [
[(-4.4891521637990852, -1.2310927013330153, -0.96969777583098771),
(4.2147455310344171, -3.5069051036633514, 2.2430685816310305),
2.2088870817461759] ,
[(0.13959847081794097, 1.7204537912940399, -1.9303780516641089),
(0.35412687539602361, -2.9493521724340743, -4.865941405480644),
1.2704043143950585] ,
[(2.3192363837822327, -3.6376441859213848, -2.2337816400479813),
(-1.0271253661119029, -2.5736009846920425, -4.1470855710278975),
0.83609068310373857] ,
[(-0.38347986357358477, -4.1453876196041719, -2.1354583394773785),
(0.27416747968044608, -2.5747732838982551, -0.68554680652905264),
0.28348352552436806] ,
[(-2.4928231204363449, 1.9263125976608209, -0.34275964486924715),
(0.6721152528064811, 1.5270465172130598, -3.5720133753579564),
1.3701121510959966] ,
[(-1.50101403139692, 2.3218275982958292, 1.044582416480222),
(-3.044743729573085, 2.0655933798619532, 2.9037849925327897),
0.46218988498537578] ,
[(4.9648826388927603, -1.7439743270051977, 1.0432135258334796),
(-3.3694557299188608, 3.7697639370274052, 2.6962018714965055),
2.3004031013653625] ,
[(-3.3337033325729051, -0.79660906888508021, -3.4875326261817454),
(1.4735023133671066, -0.066399047153666846, 0.94171530437632489),
2.8293957790283595] ,
[(-2.1249404252000517, 2.7456001658201568, 1.6891202129451799),
(-0.66412553435299504, 3.371012200444512, -1.1548086037901306),
0.89846374464990042] ,
[(3.3993205618602018, 1.2047703532166887, -1.5839949555795063),
(-4.6759756026580863, -2.8551222890449646, 4.888270217692785),
2.7825564894291754] ,
[(-3.966467296275785, 0.75617096138383189, -3.1711352932360248),
(2.1054362220912326, 4.2867761689586601, -0.65739369331424213),
1.6933117193742961] ,
[(0.44413554305522851, 4.6000690382282361, -3.8338383756621819),
(-2.4947413565865029, 1.8136080147734013, -4.0295344084655405),
0.73110709489481174] ,
[(-1.0971777991639065, -3.3166205797568815, 2.7098739534055563),
(2.1536566381847289, 4.7817155120086055, -0.068554664323454695),
2.4878958372925202] ,
[(2.2696914760438136, 4.8841630875833673, 4.9524177412608861),
(1.2249510822623111, 0.73008672334971658, 1.131607772478449),
0.45741431674591532] ,
[(-2.4456899797216938, 4.7894200033986447, -2.839449354837468),
(0.95035116225980154, 4.2179212878828238, -1.801158217734109),
0.63144509227951684] ,
[(-4.6954041297179474, -2.8326266911591391, -1.1804869511610427),
(3.2585456362256924, -2.2325171051479265, -2.0527260317826901),
1.8363466110668369] ,
[(2.1416146613604283, 3.8577375591718677, 3.1463493245087939),
(-0.32185887240442468, 2.2163051363839505, 2.4704882512058224),
0.52534998201320993] ,
[(-2.8493351354335941, -3.8203784990110954, 2.4657357720402273),
(-2.7799043389229383, 4.358406526726669, -2.8319872383058744),
2.0906833125217235] ,
[(2.274223250163784, -3.6086250253596406, 1.7143006579401876),
(3.2763334328544347, -0.89908959703552171, -4.4068824993431557),
1.4477009361020545] ,
[(0.66737672421842809, -3.4628508908383848, 3.9044108358095366),
(-1.9078974719893915, -0.53231141116878433, 1.3323584972786728),
1.0932781951137689] ,
]
if __name__== '__main__':
main()
|
