def locHomTable(toplexes,graph,ascdict={},neighborhood = 1,outfile = None):
# Computes the local homology for all faces in the ASC generated by the toplexes
# and returns a table of the dimensions of H1, H2, and H3
# Takes a neighborhood size 0,1,2, and an output file name
# if nodes are named, this can go in ascdict={nodeNumber:"name"} for the table
# otherwise names will be given by the concatenation of the index numbers
k = 1
ASC = closure(toplexes)
sh.printAS(toplexes,"Flag complex from SH")
sh.printAS(ASC,"ASC")
ofile = open(outfile, 'w')
ofile.write("Local Homology (neighborhood=%d) of flag complex generated by %s\n" % (neighborhood, graph))
if outfile == None:
print " ", "\t\t", "H1" , "\t" , "H2", "\t", "H3", "\t\t", "FACE"
print "-"*50
else:
ofile.write(" \t\t" + "H1" + "\t" + "H2" + "\t" + "H3" + "\t\t" + "name" + "\n")
for splx in ASC:
if neighborhood == 0:
complx = [splx]
elif neighborhood == 1:
complx = closure([splx])
else:
complx = closure(sstar(toplexes, closure([splx])))
A = sstar(toplexes, complx)
H1=sh.localHomology(toplexes,1,A).shape[1]
H2=sh.localHomology(toplexes,2,A).shape[1]
H3=sh.localHomology(toplexes,3,A).shape[1]
name = ""
if ascdict != {}:
for idx in range(len(A[0])):
name += ascdict[A[0][idx]]
if name == "":
name = ','.join(map(str,splx))
if outfile == None:
print k, "\t\t", H1 , "\t" , H2, "\t", H3, "\t\t", name
k += 1
else:
ofile.write(str(k) + "\t\t" + str(H1) + "\t" + str(H2) + "\t" + str(H3) + "\t\t" + str(name) + "\n")
k += 1
ofile.close()
def locHomTable(toplexes, ascdict={}, neighborhood = 1, ofile = None):
# Computes the local homology for all faces in the ASC generated by the toplexes
# and returns a table of the dimensions of H1, H2, and H3
# Takes a neighborhood size 0,1,2, and an output file name
# if nodes are named, this can go in ascdict={nodeNumber:"name"} for the table
# otherwise names will be given by the concatenation of the index numbers
k = 1
ASC = closure(toplexes)
if ofile == None:
print " ", "\t\t", "H1" , "\t" , "H2", "\t", "H3", "\t\t", "FACE"
print "-"*50
else:
ofile.write(" \t\t" + "H1" + "\t" + "H2" + "\t" + "H3" + "\t\t" + "name" + "\n")
for cnt,splx in enumerate(ASC):
# print cnt+1, len(ASC), splx
if neighborhood == 0:
complx = [splx]
elif neighborhood == 1:
complx = closure([splx])
else:
complx = closure(sstar(toplexes, closure([splx])))
A = sstar(toplexes, complx)
H1=sh.localHomology(1,toplexes,A,True)
H2=sh.localHomology(2,toplexes,A,True)
H3=sh.localHomology(3,toplexes,A,True)
name = ""
if ascdict != {}:
for idx in range(len(A[0])):
name += ascdict[A[0][idx]]
if name == "":
name = ','.join(map(str,splx))
if ofile == None:
print k, "\t\t", H1 , "\t" , H2, "\t", H3, "\t\t", name
k += 1
else:
ofile.write(str(k) + "\t\t" + str(H1) + "\t" + str(H2) + "\t" + str(H3) + "\t\t" + str(name) + "\n")
k += 1
def locHomTable(toplexes, ascdict={}):
ASC = closure(toplexes)
print "FACE" , "\t\t\t" , "H0" , "\t" , "H1" , "\t" , "H2"
print "-"*50
for splx in ASC:
complx = [splx]
A = sstar(toplexes,closure(complx))
H0=sh.localHomology(0,toplexes,A,True)
H1=sh.localHomology(1,toplexes,A,True)
H2=sh.localHomology(2,toplexes,A,True)
name = ""
if ascdict != {}:
for idx in range(len(complx[0])):
name += ascdict[complx[0][idx]]
if name == "":
name = ','.join(map(str,splx))
print name, "\t\t\t" , H0 , "\t" , H1 , "\t" , H2
graph_file = "usa.txt" # ALL OF THESE ARE FOR N0 NEIGHBORHOODS g = nx.read_edgelist(graph_file, nodetype=int) gflag = None gedgelist = map(list,g.edges(data=False)) startTime = tm.time() print "finding flag complex" cplx = sh.flag(gedgelist,3) print "getting simplices" cplx_grph=sh.ksimplices(cplx,0)+sh.ksimplices(cplx,1)+sh.ksimplices(cplx,2)+sh.ksimplices(cplx,3) print "creating colors1" colors_grph_1=[sh.localHomology(1,cplx,[spx],True) for spx in cplx_grph] print "creating colors2" colors_grph_2=[sh.localHomology(2,cplx,[spx],True) for spx in cplx_grph] print "creating colors3" colors_grph_3=[sh.localHomology(3,cplx,[spx],True) for spx in cplx_grph] endTime = tm.time() print "\n**** Total time = %f s ****\n" % (endTime-startTime) print "creating locations array" locations = [[coords[states[i]][0], -coords[states[i]][1]] for i in range(1,50)] locations = [[0,0]] + locations plt.figure(figsize=(24,16), tight_layout=True) #plt.figure() plt.hold(True)
i * len(angles)]]
else:
cplx += [[
i * len(angles) + j, i * len(angles) + j + 1,
(i - 1) * len(angles) + j
],
[(i - 1) * len(angles) + j + 1,
(i - 1) * len(angles) + j, i * len(angles) + j + 1]]
startTime = tm.time()
cplx_annulus = cplx + sh.ksimplices(cplx, 1) + sh.ksimplices(cplx, 0)
print 'colors_annulus_1'
colors_annulus_1 = [
sh.localHomology(1, cplx, [spx], True) for spx in cplx_annulus
]
print 'colors_annulus_2'
colors_annulus_2 = [
sh.localHomology(2, cplx, [spx], True) for spx in cplx_annulus
]
endTime = tm.time()
print "\n**** Total time = %f s ****\n" % (endTime - startTime)
plt.figure()
plt.hold(True)
plt.subplot(121)
pc.plot_complex(locations_annulus, cplx_annulus, colors_annulus_1)
plt.subplot(122)
pc.plot_complex(locations_annulus, cplx_annulus, colors_annulus_2)
cplx += [
[i * len(angles) + j, i * len(angles), (i - 1) * len(angles) + j],
[(i - 1) * len(angles), (i - 1) * len(angles) + j, i * len(angles)],
]
else:
cplx += [
[i * len(angles) + j, i * len(angles) + j + 1, (i - 1) * len(angles) + j],
[(i - 1) * len(angles) + j + 1, (i - 1) * len(angles) + j, i * len(angles) + j + 1],
]
startTime = tm.time()
cplx_annulus = cplx + sh.ksimplices(cplx, 1) + sh.ksimplices(cplx, 0)
print "colors_annulus_1"
colors_annulus_1 = [sh.localHomology(1, cplx, [spx], True) for spx in cplx_annulus]
print "colors_annulus_2"
colors_annulus_2 = [sh.localHomology(2, cplx, [spx], True) for spx in cplx_annulus]
endTime = tm.time()
print "\n**** Total time = %f s ****\n" % (endTime - startTime)
plt.figure()
plt.hold(True)
plt.subplot(121)
pc.plot_complex(locations_annulus, cplx_annulus, colors_annulus_1)
plt.subplot(122)
pc.plot_complex(locations_annulus, cplx_annulus, colors_annulus_2)
plt.savefig("annulus.png")
import numpy.random as random
import matplotlib.pyplot as plt
import simplicialHomology as sh
import plotComplex as pc
# Example: A "thick" graph
startTime = tm.time()
random.seed(100)
locations = []
while len(locations) < 100:
loc = random.rand(2)
if np.sqrt((loc[0] - 0.5)**2 + (loc[1] - 0.5)**2) < 0.5:
locations.append(loc)
cplx = sh.vietorisRips(locations, 0.1, maxdim=2)
cplx_grph = sh.ksimplices(cplx, 0) + sh.ksimplices(cplx, 1) + sh.ksimplices(
cplx, 2)
colors_grph_1 = [sh.localHomology(1, cplx, [spx], True) for spx in cplx_grph]
colors_grph_2 = [sh.localHomology(2, cplx, [spx], True) for spx in cplx_grph]
endTime = tm.time()
print "\n**** Total time = %f s ****\n" % (endTime - startTime)
plt.figure()
plt.hold(True)
plt.subplot(121)
pc.plot_complex(locations, cplx_grph, colors_grph_1)
plt.subplot(122)
pc.plot_complex(locations, cplx_grph, colors_grph_2)
plt.savefig('thick_graph.png')
# Unit tests for local homology computations
#
# Copyright (c) 2015-2017, Michael Robinson, Chris Capraro
# Distribution of unaltered copies permitted for noncommercial use only
# All other uses require express permission of the author
# This software comes with no warrantees express or implied
import simplicialHomology as sh
# Test 1: line segment localized to the edge
toplexes = [[1, 2]]
H0 = sh.localHomology(0, toplexes, [[1, 2]], True)
H1 = sh.localHomology(1, toplexes, [[1, 2]], True)
H2 = sh.localHomology(2, toplexes, [[1, 2]], True)
if H0 != 0 or H1 != 1 or H2 != 0:
print "Test 1a failed"
print "H0=" + str(H0)
print "H1=" + str(H1)
print "H2=" + str(H2)
else:
print "Test 1a passed"
H0 = sh.localHomology(0, toplexes, [[1, 2]])
H1 = sh.localHomology(1, toplexes, [[1, 2]])
H2 = sh.localHomology(2, toplexes, [[1, 2]])
if H0.shape[1] != 0 or H1.shape[1] != 1 or H2.shape[1] != 0:
print "Test 1b failed"
print "H0=" + H0.__repr__()
# Unit tests for local homology computations
#
# Copyright (c) 2015, Michael Robinson
# Distribution of unaltered copies permitted for noncommercial use only
# All other uses require express permission of the author
# This software comes with no warrantees express or implied
import simplicialHomology as sh
# Test 1: line segment localized to the edge
toplexes=[[1,2]]
H0=sh.localHomology(0,toplexes,[[1,2]],True)
H1=sh.localHomology(1,toplexes,[[1,2]],True)
H2=sh.localHomology(2,toplexes,[[1,2]],True)
if H0 != 0 or H1 != 1 or H2 != 0:
print "Test 1a failed"
print "H0="+ str(H0)
print "H1="+ str(H1)
print "H2="+ str(H2)
else:
print "Test 1a passed"
H0=sh.localHomology(0,toplexes,[[1,2]])
H1=sh.localHomology(1,toplexes,[[1,2]])
H2=sh.localHomology(2,toplexes,[[1,2]])
if H0.shape[1] != 0 or H1.shape[1] != 1 or H2.shape[1] != 0:
print "Test 1b failed"
print "H0="+ H0.__repr__()
# Unit tests for local homology computations
#
# Copyright (c) 2015, Michael Robinson
# Distribution of unaltered copies permitted for noncommercial use only
# All other uses require express permission of the author
# This software comes with no warrantees express or implied
import numpy as np
import simplicialHomology as sh
# Test 1: line segment localized to the edge
toplexes=[[1,2]]
H0=sh.localHomology(toplexes,0,[[1,2]])
H1=sh.localHomology(toplexes,1,[[1,2]])
H2=sh.localHomology(toplexes,2,[[1,2]])
if H0.shape[1] != 0 or H1.shape[1] != 1 or H2.shape[1] != 0:
print "Test 1 failed"
print "H0="+ H0.__repr__()
print "H1="+ H1.__repr__()
print "H2="+ H2.__repr__()
else:
print "Test 1 passed"
# Test 2: line segment localized to the star over one vertex
# (using localHomology())
toplexes=[[1,2]]
H0=sh.localHomology(toplexes,0,[[1]])
H1=sh.localHomology(toplexes,1,[[1]])