3.1. Computing Wasserstein and Bottleneck Distances

from ripser import ripser
from teaspoon.MakeData.PointCloud import Torus, Annulus
import numpy as np
from teaspoon.TDA.Distance import wassersteinDist, bottleneckDist
numPts = 500
seed = 0

# Generate Torus
t = Torus(N=numPts,seed = seed)

# Generate Annulus
a = Annulus(N=numPts,seed = seed)

# Compute persistence diagrams
PD1 = ripser(t,2)['dgms'][1]
PD2 = ripser(a,1)['dgms'][1]

wassersteinDist(PD1,PD2,p=2,q=2)

1.8922819954736267

bottleneckDist(PD1, PD2, matching = True, plot = True)

(0.6366934925317764,
 array([[ 0.00000000e+00, -1.00000000e+00,  4.00471091e-02],
        [ 1.00000000e+00, -1.00000000e+00,  2.71813273e-02],
        [ 2.00000000e+00, -1.00000000e+00,  1.37364864e-02],
        [ 3.00000000e+00,  1.00000000e+00,  6.25133872e-01],
        [ 4.00000000e+00,  4.00000000e+00,  6.24991775e-01],
        [ 5.00000000e+00,  1.20000000e+01,  6.10377252e-01],
        [ 6.00000000e+00,  2.40000000e+01,  6.14972815e-01],
        [ 7.00000000e+00,  6.00000000e+00,  5.94342589e-01],
        [ 8.00000000e+00,  2.30000000e+01,  5.70441499e-01],
        [ 9.00000000e+00,  6.40000000e+01,  6.22471675e-01],
        [ 1.00000000e+01,  3.70000000e+01,  5.74341476e-01],
        [ 1.10000000e+01,  2.10000000e+01,  5.94332188e-01],
        [ 1.20000000e+01,  7.90000000e+01,  6.01736724e-01],
        [ 1.30000000e+01,  4.70000000e+01,  5.61174288e-01],
        [ 1.40000000e+01,  6.80000000e+01,  6.19526848e-01],
        [ 1.50000000e+01,  5.90000000e+01,  5.93475059e-01],
        [ 1.60000000e+01,  1.40000000e+01,  6.12821907e-01],
        [ 1.70000000e+01,  3.60000000e+01,  6.04333013e-01],
        [ 1.80000000e+01,  5.80000000e+01,  5.69075733e-01],
        [ 1.90000000e+01,  5.00000000e+00,  6.35556936e-01],
        [ 2.00000000e+01,  2.80000000e+01,  5.91972291e-01],
        [ 2.10000000e+01,  5.00000000e+01,  5.05411237e-01],
        [ 2.20000000e+01,  5.20000000e+01,  4.91183102e-01],
        [ 2.30000000e+01, -1.00000000e+00,  1.53810859e-01],
        [ 2.40000000e+01,  8.60000000e+01,  5.02688169e-01],
        [ 2.50000000e+01,  8.80000000e+01,  5.37646309e-01],
        [ 2.60000000e+01,  4.10000000e+01,  4.85158443e-01],
        [ 2.70000000e+01,  1.02000000e+02,  5.62547147e-01],
        [ 2.80000000e+01,  7.40000000e+01,  4.81191859e-01],
        [ 2.90000000e+01,  4.40000000e+01,  5.49388498e-01],
        [ 3.00000000e+01,  1.70000000e+01,  4.69869703e-01],
        [ 3.10000000e+01,  8.50000000e+01,  5.79165190e-01],
        [ 3.20000000e+01,  0.00000000e+00,  3.45806956e-01],
        [ 3.30000000e+01,  8.30000000e+01,  4.90191489e-01],
        [ 3.40000000e+01,  7.00000000e+00,  5.50218254e-01],
        [ 3.50000000e+01,  4.90000000e+01,  5.08215398e-01],
        [ 3.60000000e+01,  4.00000000e+01,  4.91077721e-01],
        [ 3.70000000e+01,  9.40000000e+01,  6.36319071e-01],
        [ 3.80000000e+01,  8.40000000e+01,  4.37877417e-01],
        [ 3.90000000e+01,  1.11000000e+02,  5.28377473e-01],
        [ 4.00000000e+01,  2.00000000e+00,  4.88982797e-01],
        [ 4.10000000e+01,  2.20000000e+01,  4.26122889e-01],
        [ 4.20000000e+01, -1.00000000e+00,  2.01255441e-01],
        [ 4.30000000e+01,  1.08000000e+02,  4.98728067e-01],
        [ 4.40000000e+01,  2.60000000e+01,  6.21646851e-01],
        [ 4.50000000e+01, -1.00000000e+00,  2.30730712e-01],
        [ 4.60000000e+01,  8.00000000e+01,  5.58013529e-01],
        [ 4.70000000e+01,  7.50000000e+01,  4.05672327e-01],
        [ 4.80000000e+01,  1.00000000e+02,  5.63187107e-01],
        [ 4.90000000e+01, -1.00000000e+00,  1.55224830e-01],
        [ 5.00000000e+01,  4.50000000e+01,  6.23585433e-01],
        [ 5.10000000e+01,  9.00000000e+00,  6.30193621e-01],
        [ 5.20000000e+01,  5.40000000e+01,  3.58591825e-01],
        [ 5.30000000e+01,  1.30000000e+01,  5.82507074e-01],
        [ 5.40000000e+01,  1.50000000e+01,  2.93366134e-01],
        [ 5.50000000e+01, -1.00000000e+00,  1.84884369e-02],
        [ 5.60000000e+01, -1.00000000e+00,  8.92637074e-02],
        [ 5.70000000e+01,  1.00000000e+01,  5.54640710e-01],
        [ 5.80000000e+01,  4.20000000e+01,  3.44508752e-01],
        [ 5.90000000e+01, -1.00000000e+00,  1.84549183e-01],
        [ 6.00000000e+01,  6.20000000e+01,  6.24789238e-01],
        [ 6.10000000e+01, -1.00000000e+00,  1.89112216e-01],
        [ 6.20000000e+01, -1.00000000e+00,  9.76866484e-03],
        [ 6.30000000e+01, -1.00000000e+00,  3.27083468e-03],
        [ 6.40000000e+01, -1.00000000e+00,  3.15819949e-01],
        [ 6.50000000e+01,  8.90000000e+01,  4.51657131e-01],
        [ 6.60000000e+01, -1.00000000e+00,  2.99509466e-02],
        [ 6.70000000e+01,  1.60000000e+01,  3.92686695e-01],
        [ 6.80000000e+01, -1.00000000e+00,  5.61060607e-02],
        [ 6.90000000e+01,  3.50000000e+01,  5.68416148e-01],
        [ 7.00000000e+01,  1.10000000e+01,  3.08061302e-01],
        [ 7.10000000e+01,  2.70000000e+01,  3.48432913e-01],
        [ 7.20000000e+01, -1.00000000e+00,  2.18237072e-01],
        [ 7.30000000e+01, -1.00000000e+00,  2.49618351e-01],
        [ 7.40000000e+01,  1.07000000e+02,  4.26221788e-01],
        [ 7.50000000e+01,  1.04000000e+02,  5.78848407e-01],
        [ 7.60000000e+01, -1.00000000e+00,  1.54110909e-01],
        [ 7.70000000e+01,  2.90000000e+01,  2.80739784e-01],
        [ 7.80000000e+01, -1.00000000e+00,  2.31105447e-01],
        [ 7.90000000e+01,  1.80000000e+01,  2.53880560e-01],
        [ 8.00000000e+01, -1.00000000e+00,  1.22905701e-01],
        [ 8.10000000e+01, -1.00000000e+00,  2.65246928e-02],
        [ 8.20000000e+01, -1.00000000e+00,  1.52449235e-01],
        [ 8.30000000e+01,  1.06000000e+02,  3.73621762e-01],
        [ 8.40000000e+01,  3.00000000e+00,  5.06627142e-01],
        [ 8.50000000e+01,  4.60000000e+01,  4.36542779e-01],
        [ 8.60000000e+01, -1.00000000e+00,  2.92968094e-01],
        [ 8.70000000e+01,  9.30000000e+01,  3.54303300e-01],
        [ 8.80000000e+01,  8.00000000e+00,  5.84330589e-01],
        [ 8.90000000e+01, -1.00000000e+00,  2.52512455e-01],
        [ 9.00000000e+01, -1.00000000e+00,  2.74253979e-01],
        [ 9.10000000e+01, -1.00000000e+00,  6.36693493e-01],
        [ 9.20000000e+01, -1.00000000e+00,  7.14935958e-02],
        [ 9.30000000e+01, -1.00000000e+00,  1.20996982e-02],
        [ 9.40000000e+01, -1.00000000e+00,  2.99180150e-02],
        [ 9.50000000e+01, -1.00000000e+00,  3.11482698e-02],
        [ 9.60000000e+01,  6.50000000e+01,  2.65198678e-01],
        [ 9.70000000e+01,  1.16000000e+02,  3.37533318e-01],
        [ 9.80000000e+01,  1.12000000e+02,  3.94425884e-01],
        [ 9.90000000e+01,  5.70000000e+01,  4.30781990e-01],
        [ 1.00000000e+02, -1.00000000e+00,  1.36743784e-02],
        [ 1.01000000e+02,  3.00000000e+01,  3.20468366e-01],
        [ 1.02000000e+02,  1.01000000e+02,  4.99496475e-01],
        [ 1.03000000e+02, -1.00000000e+00,  1.21596754e-02],
        [ 1.04000000e+02, -1.00000000e+00,  1.41060799e-02],
        [ 1.05000000e+02,  2.50000000e+01,  1.75237477e-01],
        [ 1.06000000e+02, -1.00000000e+00,  6.92397356e-02],
        [ 1.07000000e+02,  8.20000000e+01,  5.11952758e-01],
        [ 1.08000000e+02,  5.60000000e+01,  2.13363960e-01],
        [ 1.09000000e+02, -1.00000000e+00,  6.39622211e-02],
        [ 1.10000000e+02, -1.00000000e+00,  3.37317288e-02],
        [ 1.11000000e+02,  1.17000000e+02,  4.30798046e-01],
        [ 1.12000000e+02, -1.00000000e+00,  7.26116598e-02],
        [ 1.13000000e+02,  7.70000000e+01,  2.68923864e-01],
        [ 1.14000000e+02,  2.00000000e+01,  1.49338126e-01],
        [ 1.15000000e+02, -1.00000000e+00,  1.34231299e-02],
        [ 1.16000000e+02,  1.13000000e+02,  2.79534213e-01],
        [ 1.17000000e+02,  5.50000000e+01,  2.12662250e-01],
        [ 1.18000000e+02,  3.30000000e+01,  1.71612278e-01],
        [ 1.19000000e+02,  4.30000000e+01,  2.26397738e-01],
        [ 1.20000000e+02,  6.70000000e+01,  2.63867706e-01],
        [ 1.21000000e+02,  1.90000000e+01,  1.80421382e-01],
        [ 1.22000000e+02, -1.00000000e+00,  2.56633759e-02],
        [ 1.23000000e+02, -1.00000000e+00,  3.68491560e-02],
        [ 1.24000000e+02, -1.00000000e+00,  2.47931331e-02],
        [ 1.25000000e+02, -1.00000000e+00,  1.76113844e-03],
        [ 1.26000000e+02, -1.00000000e+00,  6.34832680e-03],
        [ 1.27000000e+02,  6.10000000e+01,  1.50503203e-01],
        [ 1.28000000e+02, -1.00000000e+00,  2.19387710e-02],
        [ 1.29000000e+02,  5.30000000e+01,  1.59247160e-01],
        [ 1.30000000e+02, -1.00000000e+00,  1.22604668e-02],
        [ 1.31000000e+02,  4.80000000e+01,  1.00676760e-01],
        [ 1.32000000e+02,  3.40000000e+01,  5.09298742e-02],
        [ 1.33000000e+02,  3.80000000e+01,  6.54186010e-02],
        [ 1.34000000e+02,  6.90000000e+01,  7.37212300e-02],
        [ 1.35000000e+02,  3.10000000e+01,  4.78426814e-02],
        [-1.00000000e+00,  3.20000000e+01,  8.66083801e-03],
        [-1.00000000e+00,  3.90000000e+01,  3.12919617e-02],
        [-1.00000000e+00,  5.10000000e+01,  4.13046703e-02],
        [-1.00000000e+00,  6.00000000e+01,  3.59383970e-02],
        [-1.00000000e+00,  6.30000000e+01,  6.48078173e-02],
        [-1.00000000e+00,  6.60000000e+01,  4.32454273e-02],
        [-1.00000000e+00,  7.00000000e+01,  4.45385501e-02],
        [-1.00000000e+00,  7.10000000e+01,  2.49823928e-03],
        [-1.00000000e+00,  7.20000000e+01,  7.58492127e-02],
        [-1.00000000e+00,  7.30000000e+01,  5.37747145e-03],
        [-1.00000000e+00,  7.60000000e+01,  4.18755412e-03],
        [-1.00000000e+00,  7.80000000e+01,  2.83078104e-03],
        [-1.00000000e+00,  8.10000000e+01,  5.16147166e-03],
        [-1.00000000e+00,  8.70000000e+01,  6.52091205e-03],
        [-1.00000000e+00,  9.00000000e+01,  1.11295059e-02],
        [-1.00000000e+00,  9.10000000e+01,  1.12642422e-02],
        [-1.00000000e+00,  9.20000000e+01,  2.80567855e-02],
        [-1.00000000e+00,  9.50000000e+01,  1.24959499e-02],
        [-1.00000000e+00,  9.60000000e+01,  2.50186846e-02],
        [-1.00000000e+00,  9.70000000e+01,  4.74356934e-02],
        [-1.00000000e+00,  9.80000000e+01,  8.76357406e-03],
        [-1.00000000e+00,  9.90000000e+01,  9.97943431e-03],
        [-1.00000000e+00,  1.03000000e+02,  3.08658928e-03],
        [-1.00000000e+00,  1.05000000e+02,  8.10882449e-03],
        [-1.00000000e+00,  1.09000000e+02,  9.55005363e-03],
        [-1.00000000e+00,  1.10000000e+02,  8.60956684e-03],
        [-1.00000000e+00,  1.14000000e+02,  1.03326328e-02],
        [-1.00000000e+00,  1.15000000e+02,  1.48827359e-02]]))