In [1]:
from topcat import *
from scipy.spatial.distance import pdist, squareform
import numpy as np
import matplotlib.pyplot as plt
import random
import math
%matplotlib inline
In [2]:
def circlepoint(r):
alpha = 2 * math.pi * random.random()
return [r * math.cos(alpha), r * math.sin(alpha)]
def circle(r, n_points):
return np.asarray([circlepoint(r) for _ in range(n_points)])
def noisy_circle(r, n_points, noise_level):
circle_points = circle(r, n_points)
return np.asarray(map(lambda x : x+noise_level*(np.random.random(x.shape)-0.5), circle_points))
def sphere(r, n_points):
points = map(lambda x: np.asarray([random.random()-0.5, random.random()-0.5, random.random()-0.5]), [i for i in range(n_points)])
return np.asarray(map(lambda x: r*x/np.linalg.norm(x), points))
def square(r, n_points):
return map(lambda x: 2*r*np.asarray([random.random()-0.5, random.random()-0.5]), [i for i in range(n_points)])
In [9]:
#Data set
points = noisy_circle(1, 100, 1)
#points = sphere(1, 500)
distances = ["euclidean_codensity"] #yields a bifiltration with euclidean distance and codensity
#Filtration values
filtrationValues = [[0.0, 0.05, 0.1, 0.15, 0.2, 0.3,0.4, 0.5, 0.9], [-100.0, -50.0, -40.0, -30.0, -20.0, -15.0, -10.0, -1.0, 0.0]]
In [13]:
#Compute the persistence modules
persistencemodules = persistenceModules(points, distances, np.asarray(filtrationValues), 2)
for p in persistencemodules:
print p
[ 0, 0 ]:
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0:1:[ 4, 2 ]:
0:1:[ ]
[ 4, 3 ]:
0:[ 0 ]
[ 1 ]
[ 0 ]
1:[][ 4, 4 ]:
0:[ ]
[ ]
[ ]
[ ]
1:[ 4, 5 ]:
0:[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
1:[ 4, 6 ]:
0:[ ]
[ ]
[ ]
[ ]
1:[ 4, 7 ]:
0:[ ]
[ ]
[ ]
[ ]
1:[ 4, 8 ]:
0:[ ]
[ ]
[ ]
[ ]
1:[ 5, 0 ]:
0:1:[ 5, 1 ]:
0:1:[ 5, 2 ]:
0:1:[ ]
[ ]
[ ]
[ 5, 3 ]:
0:[ 0 0 0 ]
[ 0 1 0 ]
[ 0 0 0 ]
[ 0 0 1 ]
1:[ 0 0 0 ]
[ 0 0 0 ]
[ 0 0 0 ]
[ 0 0 0 ]
[ 5, 4 ]:
0:[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 1 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
1:[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 5, 5 ]:
0:[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 1 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 1 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 1 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
1:[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 1 ]
[ 5, 6 ]:
0:[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
1:[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 1 ]
[ 0 0 0 0 ]
[ 5, 7 ]:
0:[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
1:[ 1 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 1 ]
[ 5, 8 ]:
0:[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
1:[ 1 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 1 ]
[ 6, 0 ]:
0:1:[ 6, 1 ]:
0:1:[ 6, 2 ]:
0:1:[ ]
[ ]
[ ]
[ ]
[ 6, 3 ]:
0:[ 0 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 1 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
1:[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 6, 4 ]:
0:[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 1 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 1 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 1 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
1:[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 1 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 1 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 6, 5 ]:
0:[ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
1:[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ]
[ 6, 6 ]:
0:[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
1:[ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 6, 7 ]:
0:[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
1:[ 1 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 1 ]
[ 6, 8 ]:
0:[ 0 0 0 0 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
1:[ 1 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 1 ]
[ 7, 0 ]:
0:1:[ 7, 1 ]:
0:1:[ 7, 2 ]:
0:[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
1:[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ 7, 3 ]:
0:[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 1 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
1:[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 ]
[ 7, 4 ]:
0:[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
1:[ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 7, 5 ]:
0:[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
1:[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 7, 6 ]:
0:[ 0 0 0 0 0 0 0 0 0 0 0 0 ]
1:[ 0 1 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 1 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 7, 7 ]:
0:[ 0 0 0 ]
1:[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 1 ]
[ 7, 8 ]:
0:[ 0 0 0 ]
1:[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 1 ]
[ 8, 0 ]:
0:1:[ 8, 1 ]:
0:1:[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
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[ 8, 4 ]:
0:[ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ]
1:[ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ]
[ 8, 5 ]:
0:[ 1 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 1 ]
1:[ 0 0 0 1 ]
[ 8, 6 ]:
0:[ 1 ]
1:[ 1 ]
[ 8, 7 ]:
0:[ 1 ]
1:[ 1 ]
[ 8, 8 ]:
0:[ 1 ]
1:[ 1 ]
In [15]:
#Compute the betti-0 table (dimension table) of the 0th and 1st persistence modules
def bettiTable(P, n):
resolution = P.module.getFunctor().projectiveResolution()
gens = resolution[n].betti0()
D = np.zeros((11, 11))
for g in gens:
D[10-g.get(0), g.get(1)] += 1
return D
print("The generators of the 0th persistence module")
print bettiTable(persistencemodules[0], 0)
print("The first syzygy module of the 0th persistence module")
print bettiTable(persistencemodules[0], 1)
print("The generators of the 1st persistence module")
print bettiTable(persistencemodules[1], 0)
print("The first syzygy module of the 1st persistence module")
print bettiTable(persistencemodules[1], 1)
The generators of the 0th persistence module
[[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[100. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]
The first syzygy module of the 0th persistence module
[[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 41. 32. 5. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 13. 12. 1. 1. 0. 0. 0. 0.]
[ 0. 0. 0. 11. 28. 8. 5. 1. 0. 0. 0.]
[ 0. 0. 0. 5. 16. 11. 16. 9. 0. 0. 0.]
[ 0. 0. 0. 2. 7. 7. 15. 12. 0. 0. 0.]
[ 0. 0. 0. 3. 3. 4. 4. 13. 0. 0. 0.]
[ 0. 0. 0. 0. 3. 3. 9. 0. 0. 0. 0.]
[ 0. 0. 0. 3. 2. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]
The generators of the 1st persistence module
[[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 15. 94. 28. 1. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 8. 24. 15. 8. 1. 0. 0. 0.]
[ 0. 0. 0. 2. 11. 18. 13. 1. 0. 0. 0.]
[ 0. 0. 0. 2. 4. 7. 3. 3. 0. 0. 0.]
[ 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]
The first syzygy module of the 1st persistence module
[[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 23. 121. 46. 12. 1. 0. 0. 0.]
[ 0. 0. 0. 2. 18. 36. 29. 10. 0. 0. 0.]
[ 0. 0. 0. 1. 4. 14. 19. 17. 0. 0. 0.]
[ 0. 0. 0. 0. 2. 3. 7. 3. 0. 0. 0.]
[ 0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]
In [14]:
#Computes a slice of the rank invariant
def rankInv(P, direction):
D = np.zeros((11, 11))
for i, j in zip(range(11), range(11)):
D[10-i, j] = P.rank([i, j], [i+direction[0], j+direction[1]])
print D
rankInv(persistencemodules[0], [2, 1])
[[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 4. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 20. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 62. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 92. 0. 0. 0. 0. 0. 0. 0. 0.]
[ 0. 100. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[100. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]
In [10]:
#Stable rank example with standard contour
stablerank = stableRank(points, distances, np.asarray(filtrationValues), 2)
for sr in stablerank:
plt.figure()
plt.plot(sr[0], sr[1])
In [11]:
#Define a custom step contour
persistenceContour = [[[1.0, 2.0, 0.3, 4.0, 5.0], [0.1, 0.2, 0.3, 0.4, 0.5]], [[4.0, 3.0, 1.0, 0.5, 2.0], [-1.0, -0.6, -0.4, -0.3, -0.1]]]
for contour in persistenceContour:
plt.figure()
plt.step(contour[1], contour[0])
In [12]:
#Stable rank example with custom step contour
stablerank = stableRank(points, distances, np.asarray(filtrationValues), 2, persistenceContour)
for sr in stablerank:
plt.figure()
plt.plot(sr[0], sr[1])
In [16]:
#You can also define your own distances and pass the distance matrices to Topcat. But transferring
#the data from python to java might take time.
points = circle(1, 100)
#Distance matrices
distanceMatrix1 = squareform(pdist(points, 'euclidean'))
distanceMatrix2 = squareform(pdist(points, 'cosine'))
filtrationValues = [[0.0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3,0.4, 0.5], [0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.1, 0.15]]
In [17]:
persistencemodules = persistenceModules_dist(np.asarray([distanceMatrix1, distanceMatrix2]), np.asarray(filtrationValues), 2)
for p in persistencemodules:
print p
[ 0, 0 ]:
0:[ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
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In [18]:
stablerank = stableRank_dist(np.asarray([distanceMatrix1, distanceMatrix2]), np.asarray(filtrationValues), 2)
for sr in stablerank:
plt.figure()
plt.plot(sr[0], sr[1])
In [ ]:
Content source: olivergafvert/topcat
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