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
|
""" This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
Author(s): Vincent Rouvreau
Copyright (C) 2016 Inria
Modification(s):
- YYYY/MM Author: Description of the modification
"""
from gudhi import AlphaComplex, SimplexTree
import math
import numpy as np
import pytest
try:
# python3
from itertools import zip_longest
except ImportError:
# python2
from itertools import izip_longest as zip_longest
__author__ = "Vincent Rouvreau"
__copyright__ = "Copyright (C) 2016 Inria"
__license__ = "MIT"
def test_empty_alpha():
alpha_complex = AlphaComplex(points=[[0, 0]])
assert alpha_complex.__is_defined() == True
def test_infinite_alpha():
point_list = [[0, 0], [1, 0], [0, 1], [1, 1]]
alpha_complex = AlphaComplex(points=point_list)
assert alpha_complex.__is_defined() == True
simplex_tree = alpha_complex.create_simplex_tree()
assert simplex_tree.__is_persistence_defined() == False
assert simplex_tree.num_simplices() == 11
assert simplex_tree.num_vertices() == 4
assert simplex_tree.get_filtration() == [
([0], 0.0),
([1], 0.0),
([2], 0.0),
([3], 0.0),
([0, 1], 0.25),
([0, 2], 0.25),
([1, 3], 0.25),
([2, 3], 0.25),
([1, 2], 0.5),
([0, 1, 2], 0.5),
([1, 2, 3], 0.5),
]
assert simplex_tree.get_star([0]) == [
([0], 0.0),
([0, 1], 0.25),
([0, 1, 2], 0.5),
([0, 2], 0.25),
]
assert simplex_tree.get_cofaces([0], 1) == [([0, 1], 0.25), ([0, 2], 0.25)]
assert point_list[0] == alpha_complex.get_point(0)
assert point_list[1] == alpha_complex.get_point(1)
assert point_list[2] == alpha_complex.get_point(2)
assert point_list[3] == alpha_complex.get_point(3)
try:
alpha_complex.get_point(4) == []
except IndexError:
pass
else:
assert False
try:
alpha_complex.get_point(125) == []
except IndexError:
pass
else:
assert False
def test_filtered_alpha():
point_list = [[0, 0], [1, 0], [0, 1], [1, 1]]
filtered_alpha = AlphaComplex(points=point_list)
simplex_tree = filtered_alpha.create_simplex_tree(max_alpha_square=0.25)
assert simplex_tree.num_simplices() == 8
assert simplex_tree.num_vertices() == 4
assert point_list[0] == filtered_alpha.get_point(0)
assert point_list[1] == filtered_alpha.get_point(1)
assert point_list[2] == filtered_alpha.get_point(2)
assert point_list[3] == filtered_alpha.get_point(3)
try:
filtered_alpha.get_point(4) == []
except IndexError:
pass
else:
assert False
try:
filtered_alpha.get_point(125) == []
except IndexError:
pass
else:
assert False
assert simplex_tree.get_filtration() == [
([0], 0.0),
([1], 0.0),
([2], 0.0),
([3], 0.0),
([0, 1], 0.25),
([0, 2], 0.25),
([1, 3], 0.25),
([2, 3], 0.25),
]
assert simplex_tree.get_star([0]) == [([0], 0.0), ([0, 1], 0.25), ([0, 2], 0.25)]
assert simplex_tree.get_cofaces([0], 1) == [([0, 1], 0.25), ([0, 2], 0.25)]
def test_safe_alpha_persistence_comparison():
#generate periodic signal
time = np.arange(0, 10, 1)
signal = [math.sin(x) for x in time]
delta = math.pi
delayed = [math.sin(x + delta) for x in time]
#construct embedding
embedding1 = [[signal[i], -signal[i]] for i in range(len(time))]
embedding2 = [[signal[i], delayed[i]] for i in range(len(time))]
#build alpha complex and simplex tree
alpha_complex1 = AlphaComplex(points=embedding1)
simplex_tree1 = alpha_complex1.create_simplex_tree()
alpha_complex2 = AlphaComplex(points=embedding2)
simplex_tree2 = alpha_complex2.create_simplex_tree()
diag1 = simplex_tree1.persistence()
diag2 = simplex_tree2.persistence()
for (first_p, second_p) in zip_longest(diag1, diag2):
assert first_p[0] == pytest.approx(second_p[0])
assert first_p[1] == pytest.approx(second_p[1])
|