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
|
# -*- coding: utf-8 -*-
import numpy as np
class Interval:
def __init__(self, birth, death = None):
if death is not None and death < birth:
raise ValueError("Death must be at least birth.")
self.birth = birth
self.death = death
def is_finite(self):
return self.death is not None
def __str__(self):
if self.is_finite():
return "(%s, %s)" %(str(self.birth), str(self.death))
else:
return "(%s, ∞)" %(str(self.birth))
def __repr__(self):
if self.is_finite():
return "Interval(%s, %s)" %(repr(self.birth), repr(self.death))
else:
return "Interval(%s)" %(repr(self.birth))
def size(self):
if self.is_finite():
return self.death - self.birth
else:
return float("inf")
def finitize(barcode, max_scale):
ret = []
for bar in barcode:
if bar.is_finite():
ret.append(bar)
else:
ret.append(Interval(bar.birth, max_scale))
return ret
def betti_curve(barcode, min_scale, max_scale):
xs = []
for interval in pd:
xs.append((interval.l, 1))
if interval.is_finite():
xs.append((interval.u, -1))
if not xs:
return np.zeros((2,1))
xs.sort()
scales = [min_scale]
bettis = [0]
for (t, delta) in xs:
if scales[-1] == t:
bettis[-1] += delta
else:
scales.append(t)
bettis.append(bettis[-1] + delta)
if scales[-1] < max_scale:
scales.append(max_scale)
bettis.append(bettis[-1])
return (np.array(scales), np.array(bettis, dtype=int))
|
