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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