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cwcomplex.py
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cwcomplex.py
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#cwcomplex
import networkx as nx
import numpy as np
import linalg
class TwoComplex(nx.Graph):
def __init__(self,vertices,edges,faces,systolelength):
super(TwoComplex, self).__init__()
self.add_nodes_from(vertices)
self.add_edges_from(edges)
self.fac = faces
self.systole = systolelength
def vertices(self):
return self.nodes()
def faces(self):
return self.fac
def nVertices(self):
return len(self.nodes())
def nEdges(self):
return len(self.edges())
def nFaces(self):
return len(self.fac)
def dist(self,x,y):
return nx.shortest_path_length(self,x,y)
def shortestPath(self,x,y):
return nx.shortest_path(self,x,y)
def bound1(self):
return nx.incidence_matrix(self).astype(int)
def bound2(self):
mat = np.zeros((self.nEdges(), self.nFaces()),dtype = np.int)
edgelist = [set(e) for e in self.edges()]
for i in range(len(self.fac)):
for j in range(len(self.fac[i])):
mat[edgelist.index(set(self.fac[i][j]))][i] = 1
return mat
def bettiNumber(self):
d_k = self.bound1()
d_kplus1 = self.bound2()
A, B = np.copy(d_k), np.copy(d_kplus1)
linalg.simultaneousReduce(A, B)
linalg.finishRowReducing(B)
dimKChains = A.shape[1]
#here is a bug: need rank of A and B in F2
kernelDim = dimKChains - linalg.numPivotCols(A)
imageDim = linalg.numPivotRows(B)
return kernelDim - imageDim
class pointCluster(object):
def __init__(self,complex):
self.defects = []
self.compl = complex
def diam(self): #this is very, very, very inefficient!
nodes = self.defects
len = []
while nodes:
v = nodes.pop()
for u in nodes:
len.append(nx.all_pairs_dijkstra_path_length(self.compl,v,u))
return max(len)