def closure(complx):
n = max([len(lst) for lst in complx])
k = n-1
A1 = [] # A1 will contain the closure of A0
while k >= 0:
A1 += sh.ksimplices(complx,k)
k += -1
return A1
def closure(complx):
## returns the closure of the given complex - adds all of the sublists
n = max([len(lst) for lst in complx])
k = n-1
A1 = []
while k >= 0:
A1 += sh.ksimplices(complx,k)
k += -1
return A1
"ND" : [935,225] } 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)
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)
if i > 0:
if j == len(angles) - 1:
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)
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')
