def setUp(self):
self.sc1 = SimplicialComplex(simplices=[(1, 2), (2, 3), (1, 2, 3)])
self.sc2 = AlphaComplex(ring, 0.05)
self.ring1d = SimplicialComplex(simplices=ring1d_sc)
self.cylinder = SimplicialComplex(simplices=cylinder_sc)
self.torus = SimplicialComplex(simplices=torus_sc)
self.twosphere = SimplicialComplex(simplices=twosphere_c)
def betti(complex):
betti = []
# find max dimension
sim_com = SimplicialComplex(simplices=complex)
for i in range(3):
betti.append(sim_com.betti_number(i))
return (betti)
def _parse_result(graph, data_array=[]):
if len(data_array) > 0:
col_names = data_array.columns
data_array = np.array(data_array)
data = {"nodes": [], "links": [], "betti": []}
# nodes
node_keys = graph['nodes'].keys()
name2id = {}
i = 1
nodes_detail = {}
for key in node_keys:
name2id[key] = i
cluster = graph['nodes'][key]
nodes_detail[i] = cluster
if len(data_array) > 0:
cluster_data = data_array[cluster]
cluster_avg = np.mean(cluster_data, axis=0)
cluster_avg_dict = {}
for j in range(len(col_names)):
cluster_avg_dict[col_names[j]] = cluster_avg[j]
data['nodes'].append({
"id": str(i),
"size": len(graph['nodes'][key]),
"avgs": cluster_avg_dict,
"vertices": cluster
})
else:
data['nodes'].append({
"id": str(i),
"size": len(graph['nodes'][key]),
"vertices": cluster
})
i += 1
with open(APP_STATIC + "/uploads/nodes_detail.json", "w") as f:
json.dump(nodes_detail, f)
# links
links = set()
for link_from in graph['links'].keys():
for link_to in graph['links'][link_from]:
from_id = name2id[link_from]
to_id = name2id[link_to]
left_id = min(from_id, to_id)
right_id = max(from_id, to_id)
links.add((left_id, right_id))
for link in links:
data['links'].append({"source": link[0], "target": link[1]})
betti0 = int(
SimplicialComplex(simplices=graph['simplices']).betti_number(0))
betti1 = int(
SimplicialComplex(simplices=graph['simplices']).betti_number(1))
betti2 = int(
SimplicialComplex(simplices=graph['simplices']).betti_number(2))
data['betti'].append(betti0)
data['betti'].append(betti1)
data['betti'].append(betti2)
return data
class test_simcomplex(unittest.TestCase):
def setUp(self):
self.sc1 = SimplicialComplex(simplices=[(1, 2), (2, 3), (1, 2, 3)])
self.sc2 = AlphaComplex(ring, 0.05)
self.ring1d = SimplicialComplex(simplices=ring1d_sc)
self.cylinder = SimplicialComplex(simplices=cylinder_sc)
self.torus = SimplicialComplex(simplices=torus_sc)
self.twosphere = SimplicialComplex(simplices=twosphere_c)
def tearDown(self):
pass
def test_ring1d(self):
self.assertEqual(self.ring1d.betti_number(0), 1)
self.assertEqual(self.ring1d.betti_number(1), 1)
self.assertEqual(self.ring1d.betti_number(2), 0)
def test_cylinder(self):
self.assertEqual(self.cylinder.betti_number(0), 1)
self.assertEqual(self.cylinder.betti_number(1), 0)
self.assertEqual(self.cylinder.betti_number(2), 1)
def test_torus(self):
self.assertEqual(self.torus.betti_number(0), 1)
self.assertEqual(self.torus.betti_number(1), 2)
self.assertEqual(self.torus.betti_number(2), 1)
def test_twosphere(self):
self.assertEqual(self.twosphere.betti_number(0), 1)
self.assertEqual(self.twosphere.betti_number(1), 0)
self.assertEqual(self.twosphere.betti_number(2), 1)
def test_sc1(self):
self.assertEqual(self.sc1.betti_number(0), 1)
self.assertEqual(self.sc1.betti_number(1), 0)
def test_sc2(self):
self.assertEqual(self.sc2.betti_number(0), 1)
self.assertEqual(self.sc2.betti_number(1), 1)
self.assertEqual(self.sc2.betti_number(2), 0)
def test_betti():
C = [(1, 2, 3), (3, 4), (4, 2)]
torus_sc = [(1, 2, 4), (4, 2, 5), (2, 3, 5), (3, 5, 6), (5, 6, 1),
(1, 6, 2), (6, 7, 2), (7, 3, 2), (1, 3, 4), (3, 4, 6),
(4, 6, 7), (4, 5, 7), (5, 7, 1), (7, 3, 1)]
torus_c = SimplicialComplex(simplices=torus_sc)
t1 = timeit.default_timer()
print(betti_numbers('complexes/1.0/circle.txt', 0))
t2 = timeit.default_timer()
print('cas circle:', t2 - t1)
print(betti_numbers('complexes/1.0/line.txt', 0))
t3 = timeit.default_timer()
print('cas line', t3 - t2)
print(betti_numbers('complexes/1.0/sphere.txt', 0))
t4 = timeit.default_timer()
print('cas sphere', t4 - t3)
print(betti_numbers('complexes/1.0/torus.txt', 0))
t5 = timeit.default_timer()
print('cas torus:', t5 - t4)
print(betti_numbers('complexes/1.0/plane.txt', 0))
t6 = timeit.default_timer()
print('cas plane:', t6 - t5)
# connect neurons ##############################################################
nest.CopyModel("static_synapse", "inhibitory", {"weight": (-1) * g})
nest.CopyModel("static_synapse", "excitatory", {"weight": g})
num_synapse = 0
for i in range(N):
for j in range(N):
if (M[i][j] == "1"):
# nest.Connect(neurons[i],neurons[j], syn_spec="inhibitory")
nest.Connect(neurons[i], neurons[j], syn_spec="excitatory")
num_synapse += 1
# print("connecting neuron " + str(i) + " to " + str(j))
# measure original homology of network #########################################
simps = mogulist_from_simplist(matrix_name)
SC = SimplicialComplex(simplices=simps)
bettis = [
SC.betti_number(0),
SC.betti_number(1),
SC.betti_number(2),
SC.betti_number(3),
SC.betti_number(4),
SC.betti_number(5),
SC.betti_number(6)
]
print(bettis)
proceed = raw_input("proceed? ")
if (proceed != "y"):
print(asdasd)
# -*- coding: utf-8 -*-
# -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.#
#* File Name : topological_data_analysis.py
#
#* Purpose :
#
#* Creation Date : 28-12-2019
#
#* Last Modified : Saturday 28 December 2019 01:00:22 PM IST
#
#* Created By :
#_._._._._._._._._._._._._._._._._._._._._.#
import numpy as np
from mogutda import SimplicialComplex
torus_sc = [(1,2,4), (4,2,5), (2,3,5), (3,5,6), (5,6,1), (1,6,2), (6,7,2), (7,3,2),
(1,3,4), (3,4,6), (4,6,7), (4,5,7), (5,7,1), (7,3,1)]
torus_c = SimplicialComplex(simplices=torus_sc)
print(torus_c.betti_number(0)) # print 1
print(torus_c.betti_number(1)) # print 2
print(torus_c.betti_number(2)) # print 1
import numpy as np from mogutda import SimplicialComplex e1 = [[255, 255], [255, 0]] sc1 = SimplicialComplex(e1) print(sc1.betti_number(0))