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
|
import matplotlib.pyplot as plt
import numpy as np
"""This file is part of the Gudhi Library. The Gudhi library
(Geometric Understanding in Higher Dimensions) is a generic C++
library for computational topology.
Author(s): Vincent Rouvreau
Copyright (C) 2016 INRIA
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
"""
__author__ = "Vincent Rouvreau"
__copyright__ = "Copyright (C) 2016 INRIA"
__license__ = "GPL v3"
def __min_birth_max_death(persistence):
"""This function returns (min_birth, max_death) from the persistence.
:param persistence: The persistence to plot.
:type persistence: list of tuples(dimension, tuple(birth, death)).
:returns: (float, float) -- (min_birth, max_death).
"""
# Look for minimum birth date and maximum death date for plot optimisation
max_death = 0
min_birth = persistence[0][1][0]
for interval in reversed(persistence):
if float(interval[1][1]) != float('inf'):
if float(interval[1][1]) > max_death:
max_death = float(interval[1][1])
if float(interval[1][0]) > max_death:
max_death = float(interval[1][0])
if float(interval[1][0]) < min_birth:
min_birth = float(interval[1][0])
return (min_birth, max_death)
"""
Only 13 colors for the palette
"""
palette = ['#ff0000', '#00ff00', '#0000ff', '#00ffff', '#ff00ff', '#ffff00',
'#000000', '#880000', '#008800', '#000088', '#888800', '#880088',
'#008888']
def show_palette_values(alpha=0.6):
"""This function shows palette color values in function of the dimension.
:param alpha: alpha value in [0.0, 1.0] for horizontal bars (default is 0.6).
:type alpha: float.
:returns: plot -- An horizontal bar plot of dimensions color.
"""
colors = []
for color in palette:
colors.append(color)
y_pos = np.arange(len(palette))
plt.barh(y_pos, y_pos + 1, align='center', alpha=alpha, color=colors)
plt.ylabel('Dimension')
plt.title('Dimension palette values')
plt.show()
def plot_persistence_barcode(persistence, alpha=0.6):
"""This function plots the persistence bar code.
:param persistence: The persistence to plot.
:type persistence: list of tuples(dimension, tuple(birth, death)).
:param alpha: alpha value in [0.0, 1.0] for horizontal bars (default is 0.6).
:type alpha: float.
:returns: plot -- An horizontal bar plot of persistence.
"""
(min_birth, max_death) = __min_birth_max_death(persistence)
ind = 0
delta = ((max_death - min_birth) / 10.0)
# Replace infinity values with max_death + delta for bar code to be more
# readable
infinity = max_death + delta
axis_start = min_birth - delta
# Draw horizontal bars in loop
for interval in reversed(persistence):
if float(interval[1][1]) != float('inf'):
# Finite death case
plt.barh(ind, (interval[1][1] - interval[1][0]), height=0.8,
left = interval[1][0], alpha=alpha,
color = palette[interval[0]])
else:
# Infinite death case for diagram to be nicer
plt.barh(ind, (infinity - interval[1][0]), height=0.8,
left = interval[1][0], alpha=alpha,
color = palette[interval[0]])
ind = ind + 1
plt.title('Persistence barcode')
# Ends plot on infinity value and starts a little bit before min_birth
plt.axis([axis_start, infinity, 0, ind])
plt.show()
def plot_persistence_diagram(persistence, alpha=0.6):
"""This function plots the persistence diagram.
:param persistence: The persistence to plot.
:type persistence: list of tuples(dimension, tuple(birth, death)).
:param alpha: alpha value in [0.0, 1.0] for points and horizontal infinity line (default is 0.6).
:type alpha: float.
:returns: plot -- An diagram plot of persistence.
"""
(min_birth, max_death) = __min_birth_max_death(persistence)
ind = 0
delta = ((max_death - min_birth) / 10.0)
# Replace infinity values with max_death + delta for diagram to be more
# readable
infinity = max_death + delta
axis_start = min_birth - delta
# line display of equation : birth = death
x = np.linspace(axis_start, infinity, 1000)
# infinity line and text
plt.plot(x, x, color='k', linewidth=1.0)
plt.plot(x, [infinity] * len(x), linewidth=1.0, color='k', alpha=alpha)
plt.text(axis_start, infinity, r'$\infty$', color='k', alpha=alpha)
# Draw points in loop
for interval in reversed(persistence):
if float(interval[1][1]) != float('inf'):
# Finite death case
plt.scatter(interval[1][0], interval[1][1], alpha=alpha,
color = palette[interval[0]])
else:
# Infinite death case for diagram to be nicer
plt.scatter(interval[1][0], infinity, alpha=alpha,
color = palette[interval[0]])
ind = ind + 1
plt.title('Persistence diagram')
plt.xlabel('Birth')
plt.ylabel('Death')
# Ends plot on infinity value and starts a little bit before min_birth
plt.axis([axis_start, infinity, axis_start, infinity + delta])
plt.show()
|
