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
|
import numpy as np
import itertools
class Node:
def __init__(self, x, i, w, parent):
self.x = x
self.i = i
self.w = w
self.parent = parent
self.children = dict()
def is_root(self):
return self.parent is None
def simplex(self):
s = []
node = self
if node.is_root():
return None
while True:
s.append(node.x)
node = node.parent
if node.is_root():
break
s.reverse()
return s
def boundary_nodes(self):
if self.is_root():
return None
if self.parent.is_root():
return []
ret = []
up = []
skip = self
while not skip.is_root():
down = list(up)
node = skip.parent
while len(down) != 0:
node = node.children[down.pop()]
ret.append(node)
up.append(skip.x)
skip = skip.parent
assert(len(ret) == self.dimension() + 1)
return ret
def boundary_simplices(self):
ret = []
for node in self.boundary_nodes():
ret.append(node.simplex())
return ret
def dimension(self):
ret = 0
if self.is_root():
return None
node = self
while not node.parent.is_root():
ret += 1
node = node.parent
return ret
class ComplexIterator:
def __init__(self, start):
self.__to_go = start.children.values()
def next(self):
if len(self.__to_go) == 0:
raise StopIteration
else:
ret = self.__to_go.pop(0)
self.__to_go.extend(ret.children.values())
return ret
class Complex:
def __init__(self):
self.__root = Node(None, None, None, None)
self.__count = 0
self.__top_dim = -1
self.__ordered = False
def size(self):
return self.__count
def top_dim(self):
return self.__top_dim
def is_ordered(self):
return self.__ordered
def order(self):
i = 0
for node in self:
node.i = i
i += 1
self.__ordered = True
def find(self, simplex): # The simplex must be sorted!
p = len(simplex) - 1
if p < -1:
return None
node = self.__root
for v in simplex:
if v in node.children:
node = node.children[v]
else:
return None
return node
def add(self, simplex, weight):
self.__ordered = False
simplex = sorted(simplex)
p = len(simplex) - 1
if p < 0:
return None
last = simplex[-1]
pre = simplex[0:p]
parent = self.find(pre)
node = Node(last, None, weight, parent)
self.__count += 1
self.__top_dim = max(self.__top_dim, p)
return parent.children.setdefault(last, node)
def __contains__(self, simplex):
return self.find(simplex) is not None
def __iter__(self):
return ComplexIterator(self.__root)
def __len__(self):
return self.__count
def num_vertices(self):
return len(self.__root.keys())
# Very naive temporary VR implementations.
def naive_vr_tmp(graph, top_dim):
assert(graph.shape[0] == graph.shape[1])
vertex_set = np.arange(0, graph.shape[0])
cplx = Complex()
for p in range(0, top_dim):
to_add = itertools.combinations(vertex_set, p+1)
if p == 0:
for v in vertex_set:
cplx.add([v], 0.0)
elif p == 1:
for simplex in to_add:
cplx.add(simplex, graph[simplex[0], simplex[1]])
else:
for simplex in to_add:
codim1faces = itertools.combinations(simplex, p)
weight = 0.0
for face in codim1faces:
weight = max(cplx.find(face).w, weight)
cplx.add(simplex, weight)
return cplx
|