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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)
ret = parent.children.setdefault(last, node)
if ret == node:
self.__count += 1
self.__top_dim = max(self.__top_dim, p)
return ret
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.children)
# 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:
if not graph.mask[simplex[0], simplex[1]]:
cplx.add(simplex, graph[simplex[0], simplex[1]])
else:
for simplex in to_add:
codim1faces = itertools.combinations(simplex, p)
weight = 0.0
all_faces_in = True
for face in codim1faces:
if face in cplx:
weight = max(cplx.find(face).w, weight)
else:
all_faces_in = False
break
if all_faces_in:
cplx.add(simplex, weight)
return cplx
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