# Topcat Python Interface

``````

In [1]:

from topcat import *
from scipy.spatial.distance import pdist, squareform
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
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(list(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(list(map(lambda x: r*x/np.linalg.norm(x), points)))

def square(r, n_points):
return list(map(lambda x: 2*r*np.asarray([random.random()-0.5, random.random()-0.5]), [i for i in range(n_points)]))

``````
``````

In [7]:

#Data set
points = noisy_circle(1, 20, 0)
#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 [14]:

#Compute the persistence modules
persistencemodules = persistenceModules(points, distances, np.asarray(filtrationValues), 2)
for p in persistencemodules:
print(p)

``````
``````

13:36:00.369 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Starting to compute simplicial complex...
13:36:00.375 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Finished computing simplicial complex. (Computed 12332 number of simplices.)
13:36:00.375 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Starting to compute filtrationValues for each simplex...
13:36:00.384 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Finished computing filtrationValues.
13:36:00.384 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting to compute homology functors...
13:36:00.384 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting to compute basis change in each position...
13:36:00.385 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 0 ]
13:36:00.385 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 1 ]
13:36:00.386 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 2 ]
13:36:00.386 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 0 ]
13:36:00.386 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 1 ]
13:36:00.386 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 3 ]
13:36:00.387 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 2 ]
13:36:00.387 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 4 ]
13:36:00.387 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 3 ]
13:36:00.387 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 5 ]
13:36:00.388 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 6 ]
13:36:00.388 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 4 ]
13:36:00.388 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 5 ]
13:36:00.389 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 7 ]
13:36:00.389 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 6 ]
13:36:00.389 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 8 ]
13:36:00.390 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 7 ]
13:36:00.390 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 0 ]
13:36:00.391 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 8 ]
13:36:00.391 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 1 ]
13:36:00.392 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 0 ]
13:36:00.392 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 2 ]
13:36:00.394 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 1 ]
13:36:00.394 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 3 ]
13:36:00.394 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 2 ]
13:36:00.394 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 4 ]
13:36:00.395 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 5 ]
13:36:00.397 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 3 ]
13:36:00.397 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 6 ]
13:36:00.398 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 4 ]
13:36:00.398 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 7 ]
13:36:00.399 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 5 ]
13:36:00.399 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 8 ]
13:36:00.399 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 0 ]
13:36:00.400 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 0 ]
13:36:00.400 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 1 ]
13:36:00.401 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 6 ]
13:36:00.401 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 2 ]
13:36:00.402 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 8 ]
13:36:00.403 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 3 ]
13:36:00.403 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 1 ]
13:36:00.403 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 4 ]
13:36:00.403 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 5 ]
13:36:00.410 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 2 ]
13:36:00.411 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 7 ]
13:36:00.411 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 6 ]
13:36:00.413 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 7 ]
13:36:00.413 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 4 ]
13:36:00.419 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 8 ]
13:36:00.422 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 5 ]
13:36:00.422 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 0 ]
13:36:00.423 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 6 ]
13:36:00.423 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 1 ]
13:36:00.423 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 2 ]
13:36:00.423 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 3 ]
13:36:00.425 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 3 ]
13:36:00.427 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 7 ]
13:36:00.427 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 4 ]
13:36:00.427 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 5 ]
13:36:00.429 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 6 ]
13:36:00.429 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 8 ]
13:36:00.429 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 0 ]
13:36:00.433 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 1 ]
13:36:00.433 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 7 ]
13:36:00.436 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 2 ]
13:36:00.437 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 8 ]
13:36:00.444 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 0 ]
13:36:00.444 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 1 ]
13:36:00.445 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 2 ]
13:36:00.445 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 4 ]
13:36:00.445 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 3 ]
13:36:00.448 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 0 ]
13:36:00.455 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 1 ]
13:36:00.455 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 4 ]
13:36:00.455 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 5 ]
13:36:00.456 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 6 ]
13:36:00.459 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 2 ]
13:36:00.462 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 7 ]
13:36:00.465 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 4 ]
13:36:00.465 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 8 ]
13:36:00.472 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 7 ]
13:36:00.472 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 0 ]
13:36:00.472 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 3 ]
13:36:00.472 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 1 ]
13:36:00.476 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 1 ]
13:36:00.476 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 2 ]
13:36:00.479 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 8 ]
13:36:00.479 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 3 ]
13:36:00.485 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 6 ]
13:36:00.486 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 5 ]
13:36:00.486 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 4 ]
13:36:00.486 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 5 ]
13:36:00.487 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 3 ]
13:36:00.488 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 6 ]
13:36:00.488 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 7 ]
13:36:00.489 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 0 ]
13:36:00.490 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 5 ]
13:36:00.490 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 2 ]
13:36:00.490 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 6 ]
13:36:00.492 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 8 ]
13:36:00.492 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 7 ]
13:36:00.493 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 3 ]
13:36:00.493 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 8 ]
13:36:00.494 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 0 ]
13:36:00.495 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 1 ]
13:36:00.495 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 2 ]
13:36:00.496 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 3 ]
13:36:00.497 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 4 ]
13:36:00.502 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 0 ]
13:36:00.512 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 1 ]
13:36:00.514 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 5 ]
13:36:00.515 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 2 ]
13:36:00.515 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 6 ]
13:36:00.516 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 7 ]
13:36:00.516 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 7 ]
13:36:00.518 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 8 ]
13:36:00.528 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 5 ]
13:36:00.529 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 0 ]
13:36:00.531 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 0 ]
13:36:00.531 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 1 ]
13:36:00.534 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 4 ]
13:36:00.535 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 2 ]
13:36:00.537 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 1 ]
13:36:00.537 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 3 ]
13:36:00.539 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 6 ]
13:36:00.539 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 4 ]
13:36:00.544 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 3 ]
13:36:00.545 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 5 ]
13:36:00.547 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 8 ]
13:36:00.547 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 6 ]
13:36:00.553 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 4 ]
13:36:00.553 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 7 ]
13:36:00.565 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 2 ]
13:36:00.566 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 8 ]
13:36:00.583 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 5 ]
13:36:00.583 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 0 ]
13:36:00.584 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 6 ]
13:36:00.584 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 1 ]
13:36:00.584 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 0 ]
13:36:00.584 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 2 ]
13:36:00.591 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 1 ]
13:36:00.591 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 3 ]
13:36:00.604 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 3 ]
13:36:00.604 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 4 ]
13:36:00.604 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 7 ]
13:36:00.604 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 5 ]
13:36:00.614 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 8 ]
13:36:00.614 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 6 ]
13:36:00.638 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 2 ]
13:36:00.638 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 7 ]
13:36:00.670 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 5 ]
13:36:00.670 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 8 ]
13:36:00.675 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 4 ]
13:36:00.694 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 6 ]
13:36:00.699 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 7 ]
13:36:00.703 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 8 ]
13:36:00.735 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 3 ]
13:36:00.786 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 5 ]
13:36:00.792 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 4 ]
13:36:00.799 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 6 ]
13:36:00.816 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 7 ]
13:36:00.818 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 8 ]
13:36:00.819 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished computing basis change.
13:36:00.819 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting to apply basis change...
13:36:00.925 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished applying basis change.
13:36:00.926 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting verification...
13:36:00.933 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Basis change map dimension 0 OK.
13:36:00.937 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Homology functor dimension 0 OK.
13:36:00.973 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Basis change map dimension 1 OK.
13:36:00.974 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Homology functor dimension 1 OK.
13:36:00.974 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished verification.
13:36:00.974 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished computing homology functors.
[ 0, 0 ]:
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0:1:[ 4, 8 ]:
0:1:[ 5, 0 ]:
0:1:[ 5, 1 ]:
0:1:[ ]
[ ]
[ ]
[ 5, 2 ]:
0:[ 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 ]
[ 5, 3 ]:
0:[ 0 0 ]
[ 0 0 ]
[ 0 0 ]
[ 0 0 ]
[ 0 0 ]
[ 1 0 ]
[ 0 0 ]
[ 0 0 ]
[ 0 0 ]
1:[ 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 1 0 0 0 ]
[ 0 0 0 0 0 ]
[ 0 0 1 0 0 ]
[ 0 0 0 1 0 ]
[ 5, 5 ]:
0:[ 0 0 0 0 ]
1:[ 1 0 0 0 ]
[ 0 0 0 1 ]
[ 5, 6 ]:
0:[ 0 0 ]
1:[][ 5, 7 ]:
0:[ ]
1:[ 5, 8 ]:
0:[ ]
1:[ 6, 0 ]:
0:1:[ 6, 1 ]:
0:1:[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ 6, 2 ]:
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 1 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 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 0 0 0 ]
[ 0 0 0 0 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, 3 ]:
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 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 0 0 0 0 0 0 0 0 ]
[ 0 0 0 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:[ 1 0 0 0 0 ]
[ 0 0 0 0 0 ]
[ 0 0 0 0 0 ]
[ 0 0 1 0 0 ]
[ 0 0 0 0 0 ]
1:[ 0 0 0 0 0 ]
[ 6, 5 ]:
0:[ 0 ]
[ 0 ]
[ 0 ]
1:[ 1 ]
[ 6, 6 ]:
0:[ 0 ]
1:[ 1 ]
[ 6, 7 ]:
0:[ 0 ]
1:[ 1 ]
[ 6, 8 ]:
0:[ 0 ]
1:[ 1 ]
[ 7, 0 ]:
0:1:[ 7, 1 ]:
0:1:[ ]
[ ]
[ ]
[ ]
[ ]
[ 7, 2 ]:
0:[ 0 0 0 0 0 ]
[ 0 0 0 0 0 ]
[ 0 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 ]
[ 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 ]
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 ]
[ 7, 4 ]:
0:[ 0 0 0 0 0 ]
1:[ 0 0 0 0 0 ]
[ 0 0 0 0 0 ]
[ 0 0 0 0 0 ]
[ 7, 5 ]:
0:[ 0 0 0 ]
1:[ 0 0 0 ]
[ 7, 6 ]:
0:[ 0 ]
1:[ 1 ]
[ 7, 7 ]:
0:[ 0 ]
1:[ 1 ]
[ 7, 8 ]:
0:[ 0 ]
1:[ 1 ]
[ 8, 0 ]:
0:1:[ 8, 1 ]:
0:1:[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ 8, 2 ]:
0:[ 1 0 0 0 0 0 0 ]
[ 0 1 0 0 0 0 0 ]
[ 0 0 1 0 0 0 0 ]
[ 0 0 0 1 0 0 0 ]
[ 0 0 0 0 1 0 0 ]
[ 0 0 0 0 0 1 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 ]
[ 8, 3 ]:
0:[ 1 0 0 0 0 0 0 0 0 0 ]
[ 0 1 0 0 0 0 0 0 0 0 ]
[ 0 0 1 0 0 0 0 0 0 0 ]
[ 0 0 0 1 0 0 0 0 0 0 ]
[ 0 0 0 0 1 0 0 0 0 0 ]
[ 0 0 0 0 0 1 0 0 0 0 ]
[ 0 0 0 0 0 0 1 0 0 0 ]
[ 0 0 0 0 0 0 0 1 0 0 ]
[ 0 0 0 0 0 0 0 0 1 0 ]
[ 0 0 0 0 0 0 0 0 0 1 ]
1:[ 0 0 0 0 0 0 0 0 0 0 ]
[ 8, 4 ]:
0:[ 1 ]
1:[ 1 ]
[ 8, 5 ]:
0:[ 1 ]
1:[ 1 ]
[ 8, 6 ]:
0:[ 1 ]
1:[ 1 ]
[ 8, 7 ]:
0:[ 1 ]
1:[ 1 ]
[ 8, 8 ]:
0:[ 1 ]
1:[ 1 ]

``````
``````

In [15]:

len(persistencemodules)

``````
``````

Out[15]:

2

``````
``````

In [16]:

#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.  4.  7.  0.  0.  0.  0.  0.  0.  0.]
[ 0.  0.  0.  2.  0.  0.  0.  0.  0.  0.  0.]
[ 0.  1.  1.  4.  1.  0.  0.  0.  0.  0.  0.]
[ 0.  4.  3.  6.  3.  1.  0.  0.  0.  0.  0.]
[ 0.  1.  1.  5.  5.  2.  2.  0.  0.  0.  0.]
[ 0.  1.  4.  7.  6.  2.  3.  2.  0.  0.  0.]
[ 0. 10.  7.  4.  3.  1.  1.  0.  0.  0.  0.]
[17. 17.  9.  3.  9.  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.  7. 10.  1.  0.  0.  0.  0.  0.  0.]
[ 0.  0.  2.  4.  3.  3.  1.  0.  0.  0.  0.]
[ 0.  0.  5.  8.  5.  1.  0.  0.  0.  0.  0.]
[ 0.  0.  3.  1.  5.  1.  0.  0.  0.  0.  0.]
[ 0.  0.  0.  2.  1.  1.  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.]]
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.  5. 14. 15.  3.  1.  0.  0.  0.  0.]
[ 0.  0.  4.  8.  7.  4.  3.  0.  0.  0.  0.]
[ 0.  0.  1.  6. 13.  6.  0.  0.  0.  0.  0.]
[ 0.  0.  0.  4.  2.  3.  2.  2.  0.  0.  0.]
[ 0.  0.  0.  1.  2.  1.  1.  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.]]

``````
``````

In [18]:

#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.  1.  0.  0.  0.  0.  0.]
[ 0.  0.  0.  0.  1.  0.  0.  0.  0.  0.  0.]
[ 0.  0.  0.  2.  0.  0.  0.  0.  0.  0.  0.]
[ 0.  0. 22.  0.  0.  0.  0.  0.  0.  0.  0.]
[ 0. 38.  0.  0.  0.  0.  0.  0.  0.  0.  0.]
[56.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]]

``````
``````

In [19]:

#Persistence landscapes
landscapes = list(persistencemodules[1].module.persistenceLandscape(2).vectorize())

for i in range(3):
fig = plt.figure()

# Make data
X = np.arange(0, len(filtrationValues[0]), 1)
Y = np.arange(0, len(filtrationValues[1]), 1)
x, y = np.meshgrid(X, Y)
z = np.asarray(list(landscapes[i])).reshape((len(filtrationValues[0]), len(filtrationValues[1])))

# Plot the surface
ax.plot_surface(x, y, z, color='b')

``````
``````

``````
``````

In [8]:

#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])

``````
``````

13:45:41.550 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Starting to compute simplicial complex...
13:45:41.551 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Finished computing simplicial complex. (Computed 119 number of simplices.)
13:45:41.552 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Starting to compute filtrationValues for each simplex...
13:45:41.553 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Finished computing filtrationValues.
13:45:41.553 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting to compute homology functors...
13:45:41.553 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting to compute basis change in each position...
13:45:41.555 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 0 ]
13:45:41.555 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 0 ]
13:45:41.556 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 1 ]
13:45:41.556 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 1 ]
13:45:41.558 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 2 ]
13:45:41.559 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 2 ]
13:45:41.564 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 3 ]
13:45:41.565 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 3 ]
13:45:41.566 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 4 ]
13:45:41.567 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 4 ]
13:45:41.567 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 5 ]
13:45:41.568 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 6 ]
13:45:41.568 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 5 ]
13:45:41.568 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 7 ]
13:45:41.569 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 7 ]
13:45:41.569 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 6 ]
13:45:41.570 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 8 ]
13:45:41.571 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 8 ]
13:45:41.571 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 0 ]
13:45:41.571 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 0 ]
13:45:41.572 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 1 ]
13:45:41.572 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 1 ]
13:45:41.572 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 2 ]
13:45:41.572 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 2 ]
13:45:41.572 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 3 ]
13:45:41.572 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 3 ]
13:45:41.572 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 4 ]
13:45:41.573 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 4 ]
13:45:41.573 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 5 ]
13:45:41.573 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 5 ]
13:45:41.573 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 6 ]
13:45:41.574 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 6 ]
13:45:41.574 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 7 ]
13:45:41.574 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 7 ]
13:45:41.574 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 8 ]
13:45:41.574 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 8 ]
13:45:41.574 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 0 ]
13:45:41.574 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 0 ]
13:45:41.575 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 1 ]
13:45:41.575 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 1 ]
13:45:41.575 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 2 ]
13:45:41.575 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 2 ]
13:45:41.575 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 3 ]
13:45:41.575 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 3 ]
13:45:41.575 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 4 ]
13:45:41.575 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 4 ]
13:45:41.575 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 5 ]
13:45:41.576 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 5 ]
13:45:41.576 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 6 ]
13:45:41.577 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 6 ]
13:45:41.578 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 7 ]
13:45:41.578 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 8 ]
13:45:41.578 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 7 ]
13:45:41.578 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 0 ]
13:45:41.579 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 8 ]
13:45:41.579 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 1 ]
13:45:41.579 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 2 ]
13:45:41.579 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 4 ]
13:45:41.579 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 3 ]
13:45:41.579 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 0 ]
13:45:41.579 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 5 ]
13:45:41.579 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 6 ]
13:45:41.579 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 7 ]
13:45:41.579 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 1 ]
13:45:41.579 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 8 ]
13:45:41.579 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 2 ]
13:45:41.580 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 0 ]
13:45:41.580 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 1 ]
13:45:41.580 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 3 ]
13:45:41.580 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 4 ]
13:45:41.580 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 5 ]
13:45:41.580 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 6 ]
13:45:41.580 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 2 ]
13:45:41.581 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 7 ]
13:45:41.581 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 8 ]
13:45:41.584 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 3 ]
13:45:41.584 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 0 ]
13:45:41.585 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 1 ]
13:45:41.585 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 4 ]
13:45:41.585 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 5 ]
13:45:41.586 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 6 ]
13:45:41.586 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 7 ]
13:45:41.586 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 2 ]
13:45:41.586 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 8 ]
13:45:41.586 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 0 ]
13:45:41.587 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 3 ]
13:45:41.587 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 1 ]
13:45:41.587 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 2 ]
13:45:41.588 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 4 ]
13:45:41.589 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 5 ]
13:45:41.590 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 6 ]
13:45:41.590 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 7 ]
13:45:41.590 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 3 ]
13:45:41.591 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 8 ]
13:45:41.591 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 0 ]
13:45:41.591 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 4 ]
13:45:41.591 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 1 ]
13:45:41.591 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 2 ]
13:45:41.592 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 5 ]
13:45:41.593 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 6 ]
13:45:41.593 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 7 ]
13:45:41.593 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 8 ]
13:45:41.593 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 3 ]
13:45:41.593 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 0 ]
13:45:41.593 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 1 ]
13:45:41.594 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 4 ]
13:45:41.594 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 2 ]
13:45:41.594 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 3 ]
13:45:41.594 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 5 ]
13:45:41.595 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 6 ]
13:45:41.596 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 7 ]
13:45:41.596 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 4 ]
13:45:41.596 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 8 ]
13:45:41.596 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 0 ]
13:45:41.597 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 1 ]
13:45:41.597 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 5 ]
13:45:41.597 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 2 ]
13:45:41.598 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 3 ]
13:45:41.598 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 6 ]
13:45:41.598 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 7 ]
13:45:41.598 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 8 ]
13:45:41.599 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 0 ]
13:45:41.599 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 4 ]
13:45:41.599 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 1 ]
13:45:41.600 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 2 ]
13:45:41.601 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 5 ]
13:45:41.601 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 3 ]
13:45:41.602 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 4 ]
13:45:41.602 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 6 ]
13:45:41.603 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 7 ]
13:45:41.603 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 0 ]
13:45:41.603 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 5 ]
13:45:41.603 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 8 ]
13:45:41.603 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 1 ]
13:45:41.604 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 2 ]
13:45:41.604 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 6 ]
13:45:41.605 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 3 ]
13:45:41.605 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 7 ]
13:45:41.605 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 4 ]
13:45:41.605 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 8 ]
13:45:41.605 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 0 ]
13:45:41.606 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 5 ]
13:45:41.606 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 1 ]
13:45:41.606 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 2 ]
13:45:41.606 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 3 ]
13:45:41.606 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 6 ]
13:45:41.607 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 4 ]
13:45:41.609 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 7 ]
13:45:41.609 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 5 ]
13:45:41.610 [pool-4-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 8 ]
13:45:41.610 [pool-4-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 0 ]
13:45:41.611 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 6 ]
13:45:41.612 [pool-4-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 1 ]
13:45:41.612 [pool-4-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 2 ]
13:45:41.612 [pool-4-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 3 ]
13:45:41.613 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 7 ]
13:45:41.614 [pool-4-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 4 ]
13:45:41.614 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 8 ]
13:45:41.614 [pool-4-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 5 ]
13:45:41.616 [pool-4-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 6 ]
13:45:41.620 [pool-4-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 8 ]
13:45:41.621 [pool-4-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 7 ]
13:45:41.623 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished computing basis change.
13:45:41.623 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting to apply basis change...
13:45:41.639 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished applying basis change.
13:45:41.640 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting verification...
13:45:41.647 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Basis change map dimension 0 OK.
13:45:41.655 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Homology functor dimension 0 OK.
13:45:41.658 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Basis change map dimension 1 OK.
13:45:41.660 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Homology functor dimension 1 OK.
13:45:41.660 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished verification.
13:45:41.660 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished computing homology functors.
13:45:41.670 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.05
13:45:41.683 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.683 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:45:41.683 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:45:41.683 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.1
13:45:41.699 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.700 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:45:41.700 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:45:41.700 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.15
13:45:41.730 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.731 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:45:41.731 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:45:41.731 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.2
13:45:41.755 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.755 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:45:41.755 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:45:41.755 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.3
13:45:41.789 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.789 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:45:41.789 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:45:41.789 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.4
13:45:41.838 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.838 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:45:41.839 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:45:41.839 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.5
13:45:41.881 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.881 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:45:41.881 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:45:41.881 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.9
13:45:41.919 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.920 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:45:41.920 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:45:41.920 [Thread-1] DEBUG topcat.persistence.PersistenceModule - [[ 0.0, 20 ], [ 0.05, 20 ], [ 0.1, 20 ], [ 0.15, 20 ], [ 0.2, 20 ], [ 0.3, 20 ], [ 0.4, 20 ], [ 0.5, 20 ], [ 0.9, 20 ]]
0: [[ 0.0, 20 ], [ 0.05, 20 ], [ 0.1, 20 ], [ 0.15, 20 ], [ 0.2, 20 ], [ 0.3, 20 ], [ 0.4, 20 ], [ 0.5, 20 ], [ 0.9, 20 ]]
13:45:41.921 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.05
13:45:41.922 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.922 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:45:41.922 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:45:41.922 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.1
13:45:41.922 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.922 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:45:41.922 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:45:41.922 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.15
13:45:41.922 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.922 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:45:41.922 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:45:41.922 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.2
13:45:41.922 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.922 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:45:41.922 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:45:41.922 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.3
13:45:41.922 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.922 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:45:41.922 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:45:41.923 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.4
13:45:41.923 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.923 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:45:41.923 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:45:41.923 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.5
13:45:41.923 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.923 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:45:41.923 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:45:41.923 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.9
13:45:41.923 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:45:41.923 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:45:41.923 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:45:41.923 [Thread-1] DEBUG topcat.persistence.PersistenceModule - [[ 0.0, 1 ], [ 0.05, 1 ], [ 0.1, 1 ], [ 0.15, 1 ], [ 0.2, 1 ], [ 0.3, 1 ], [ 0.4, 1 ], [ 0.5, 1 ], [ 0.9, 1 ]]
1: [[ 0.0, 1 ], [ 0.05, 1 ], [ 0.1, 1 ], [ 0.15, 1 ], [ 0.2, 1 ], [ 0.3, 1 ], [ 0.4, 1 ], [ 0.5, 1 ], [ 0.9, 1 ]]

``````
``````

In [9]:

#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 [10]:

#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])

``````
``````

13:46:03.552 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Starting to compute simplicial complex...
13:46:03.554 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Finished computing simplicial complex. (Computed 119 number of simplices.)
13:46:03.555 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Starting to compute filtrationValues for each simplex...
13:46:03.557 [Thread-1] DEBUG t.p.simplex.SimplicialComplex - Finished computing filtrationValues.
13:46:03.557 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting to compute homology functors...
13:46:03.557 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting to compute basis change in each position...
13:46:03.558 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 0 ]
13:46:03.558 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 1 ]
13:46:03.558 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 0 ]
13:46:03.559 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 2 ]
13:46:03.559 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 1 ]
13:46:03.559 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 3 ]
13:46:03.560 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 2 ]
13:46:03.561 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 4 ]
13:46:03.561 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 5 ]
13:46:03.561 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 3 ]
13:46:03.562 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 6 ]
13:46:03.563 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 4 ]
13:46:03.563 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 7 ]
13:46:03.564 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 5 ]
13:46:03.565 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 6 ]
13:46:03.565 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 0, 8 ]
13:46:03.566 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 7 ]
13:46:03.567 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 1 ]
13:46:03.567 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 0 ]
13:46:03.567 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 2 ]
13:46:03.567 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 4 ]
13:46:03.567 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 3 ]
13:46:03.568 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 0, 8 ]
13:46:03.568 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 5 ]
13:46:03.568 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 6 ]
13:46:03.569 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 7 ]
13:46:03.569 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 1 ]
13:46:03.569 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 1, 8 ]
13:46:03.569 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 0 ]
13:46:03.569 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 2 ]
13:46:03.570 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 4 ]
13:46:03.570 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 3 ]
13:46:03.570 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 0 ]
13:46:03.570 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 5 ]
13:46:03.570 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 6 ]
13:46:03.571 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 1 ]
13:46:03.571 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 7 ]
13:46:03.571 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 1, 8 ]
13:46:03.571 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 2 ]
13:46:03.571 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 3 ]
13:46:03.571 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 5 ]
13:46:03.571 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 4 ]
13:46:03.572 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 0 ]
13:46:03.572 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 6 ]
13:46:03.572 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 7 ]
13:46:03.572 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 1 ]
13:46:03.572 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 2, 8 ]
13:46:03.572 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 0 ]
13:46:03.572 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 2 ]
13:46:03.572 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 3 ]
13:46:03.572 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 5 ]
13:46:03.573 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 4 ]
13:46:03.573 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 1 ]
13:46:03.574 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 6 ]
13:46:03.574 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 7 ]
13:46:03.574 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 2 ]
13:46:03.575 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 2, 8 ]
13:46:03.576 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 0 ]
13:46:03.576 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 3 ]
13:46:03.576 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 4 ]
13:46:03.576 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 5 ]
13:46:03.577 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 6 ]
13:46:03.578 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 1 ]
13:46:03.578 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 7 ]
13:46:03.579 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 3, 8 ]
13:46:03.579 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 2 ]
13:46:03.579 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 0 ]
13:46:03.580 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 1 ]
13:46:03.580 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 3 ]
13:46:03.580 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 4 ]
13:46:03.581 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 5 ]
13:46:03.582 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 6 ]
13:46:03.582 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 2 ]
13:46:03.583 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 8 ]
13:46:03.583 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 3, 7 ]
13:46:03.583 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 3 ]
13:46:03.583 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 0 ]
13:46:03.584 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 1 ]
13:46:03.584 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 4 ]
13:46:03.584 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 5 ]
13:46:03.584 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 6 ]
13:46:03.584 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 7 ]
13:46:03.584 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 2 ]
13:46:03.584 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 4, 8 ]
13:46:03.585 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 0 ]
13:46:03.585 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 3 ]
13:46:03.585 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 1 ]
13:46:03.585 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 2 ]
13:46:03.585 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 4 ]
13:46:03.586 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 6 ]
13:46:03.586 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 5 ]
13:46:03.587 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 3 ]
13:46:03.587 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 7 ]
13:46:03.587 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 4, 8 ]
13:46:03.587 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 0 ]
13:46:03.588 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 1 ]
13:46:03.588 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 4 ]
13:46:03.588 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 2 ]
13:46:03.588 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 5 ]
13:46:03.588 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 6 ]
13:46:03.588 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 7 ]
13:46:03.588 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 3 ]
13:46:03.588 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 5, 8 ]
13:46:03.588 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 0 ]
13:46:03.589 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 1 ]
13:46:03.589 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 2 ]
13:46:03.589 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 4 ]
13:46:03.589 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 3 ]
13:46:03.589 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 5 ]
13:46:03.589 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 6 ]
13:46:03.590 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 7 ]
13:46:03.590 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 4 ]
13:46:03.590 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 5, 8 ]
13:46:03.590 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 0 ]
13:46:03.590 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 1 ]
13:46:03.590 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 2 ]
13:46:03.590 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 5 ]
13:46:03.590 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 3 ]
13:46:03.591 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 6 ]
13:46:03.591 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 7 ]
13:46:03.591 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 6, 8 ]
13:46:03.591 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 0 ]
13:46:03.591 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 4 ]
13:46:03.591 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 1 ]
13:46:03.591 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 2 ]
13:46:03.591 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 3 ]
13:46:03.591 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 4 ]
13:46:03.591 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 5 ]
13:46:03.591 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 6 ]
13:46:03.592 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 7 ]
13:46:03.592 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 6, 8 ]
13:46:03.593 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 0 ]
13:46:03.593 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 5 ]
13:46:03.593 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 1 ]
13:46:03.593 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 2 ]
13:46:03.593 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 3 ]
13:46:03.593 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 4 ]
13:46:03.593 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 6 ]
13:46:03.593 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 7 ]
13:46:03.593 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 7, 8 ]
13:46:03.594 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 0 ]
13:46:03.594 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 1 ]
13:46:03.594 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 5 ]
13:46:03.594 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 2 ]
13:46:03.594 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 4 ]
13:46:03.594 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 3 ]
13:46:03.594 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 5 ]
13:46:03.594 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 6 ]
13:46:03.595 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 7 ]
13:46:03.596 [pool-5-thread-2] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 7, 8 ]
13:46:03.596 [pool-5-thread-10] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 0 ]
13:46:03.596 [pool-5-thread-7] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 1 ]
13:46:03.596 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 6 ]
13:46:03.596 [pool-5-thread-8] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 2 ]
13:46:03.596 [pool-5-thread-4] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 4 ]
13:46:03.596 [pool-5-thread-3] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 3 ]
13:46:03.597 [pool-5-thread-5] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 5 ]
13:46:03.597 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 7 ]
13:46:03.597 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Starting basis change computation of position: [ 8, 8 ]
13:46:03.599 [pool-5-thread-9] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 6 ]
13:46:03.601 [pool-5-thread-6] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 7 ]
13:46:03.601 [pool-5-thread-1] DEBUG t.p.homology.HomologyWorker - Finished basis change computation of position: [ 8, 8 ]
13:46:03.601 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished computing basis change.
13:46:03.601 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting to apply basis change...
13:46:03.606 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished applying basis change.
13:46:03.606 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Starting verification...
13:46:03.608 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Basis change map dimension 0 OK.
13:46:03.609 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Homology functor dimension 0 OK.
13:46:03.610 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Basis change map dimension 1 OK.
13:46:03.611 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Homology functor dimension 1 OK.
13:46:03.612 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished verification.
13:46:03.612 [Thread-1] DEBUG t.persistence.homology.HomologyUtil - Finished computing homology functors.
13:46:03.615 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.05
13:46:03.618 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.618 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:46:03.618 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:46:03.618 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.1
13:46:03.623 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.623 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:46:03.624 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:46:03.624 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.15
13:46:03.633 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.633 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:46:03.634 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:46:03.634 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.2
13:46:03.640 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.640 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:46:03.640 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:46:03.640 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.3
13:46:03.648 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.649 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:46:03.649 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:46:03.649 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.4
13:46:03.658 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.659 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:46:03.659 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:46:03.659 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.5
13:46:03.669 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.669 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:46:03.669 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:46:03.669 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.9
13:46:03.684 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.684 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
13:46:03.684 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 20
13:46:03.684 [Thread-1] DEBUG topcat.persistence.PersistenceModule - [[ 0.0, 20 ], [ 0.05, 20 ], [ 0.1, 20 ], [ 0.15, 20 ], [ 0.2, 20 ], [ 0.3, 20 ], [ 0.4, 20 ], [ 0.5, 20 ], [ 0.9, 20 ]]
0: [[ 0.0, 20 ], [ 0.05, 20 ], [ 0.1, 20 ], [ 0.15, 20 ], [ 0.2, 20 ], [ 0.3, 20 ], [ 0.4, 20 ], [ 0.5, 20 ], [ 0.9, 20 ]]
13:46:03.684 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.05
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.1
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.15
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.2
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.3
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.4
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.5
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Shift value: 0.9
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Seach space contains 1 number of elements.
13:46:03.685 [Thread-1] INFO  t.m.rankminimization.RankTreeSearch - Dimensions: 0,
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - Bar: 1
13:46:03.685 [Thread-1] DEBUG topcat.persistence.PersistenceModule - [[ 0.0, 1 ], [ 0.05, 1 ], [ 0.1, 1 ], [ 0.15, 1 ], [ 0.2, 1 ], [ 0.3, 1 ], [ 0.4, 1 ], [ 0.5, 1 ], [ 0.9, 1 ]]
1: [[ 0.0, 1 ], [ 0.05, 1 ], [ 0.1, 1 ], [ 0.15, 1 ], [ 0.2, 1 ], [ 0.3, 1 ], [ 0.4, 1 ], [ 0.5, 1 ], [ 0.9, 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

``````
``````

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