Topcat Python Interface

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


    

    




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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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[ 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 ]
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[ 0 0 0 0 0 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 ]
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[ 0 0 0 0 0 0 0 0 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 ]
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[ 0 0 0 0 0 0 0 0 0 0 0 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 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 ]
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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 1 0 0 0 0 0 0 0 0 0 0 ]
[ 0 0 0 1 0 0 0 0 0 0 0 0 0 ]
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1:[ 0 0 0 0 0 0 0 0 0 0 0 0 1 ]
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0:[ 1 ]
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0:1:[ 0, 1 ]:
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0:1:[ 2, 4 ]:
0:1:[ 2, 5 ]:
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0:1:[ 3, 0 ]:
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0:[ ]
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0:[ ]
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0:[ ]
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0:[ ]
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0:[ ]
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0:[ ]
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0:1:[ 5, 2 ]:
0:1:[ ]
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0:[ 1 ]
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1:[ 1 ]

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 [ ]: