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""" This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
Author(s): Theo Lacombe
Copyright (C) 2019 Inria
Modification(s):
- YYYY/MM Author: Description of the modification
"""
from gudhi.wasserstein import wasserstein_distance as pot
from gudhi.hera import wasserstein_distance as hera
import numpy as np
__author__ = "Theo Lacombe"
__copyright__ = "Copyright (C) 2019 Inria"
__license__ = "MIT"
def _basic_wasserstein(wasserstein_distance, delta, test_infinity=True):
diag1 = np.array([[2.7, 3.7], [9.6, 14.0], [34.2, 34.974]])
diag2 = np.array([[2.8, 4.45], [9.5, 14.1]])
diag3 = np.array([[0, 2], [4, 6]])
diag4 = np.array([[0, 3], [4, 8]])
emptydiag = np.array([])
# We just need to handle positive numbers here
def approx(a, b):
f = 1 + delta
return a <= b*f and b <= a*f
assert wasserstein_distance(emptydiag, emptydiag, internal_p=2., order=1.) == 0.
assert wasserstein_distance(emptydiag, emptydiag, internal_p=np.inf, order=1.) == 0.
assert wasserstein_distance(emptydiag, emptydiag, internal_p=np.inf, order=2.) == 0.
assert wasserstein_distance(emptydiag, emptydiag, internal_p=2., order=2.) == 0.
assert approx(wasserstein_distance(diag3, emptydiag, internal_p=np.inf, order=1.), 2.)
assert approx(wasserstein_distance(diag3, emptydiag, internal_p=1., order=1.), 4.)
assert approx(wasserstein_distance(diag4, emptydiag, internal_p=1., order=2.), 5.) # thank you Pythagorician triplets
assert approx(wasserstein_distance(diag4, emptydiag, internal_p=np.inf, order=2.), 2.5)
assert approx(wasserstein_distance(diag4, emptydiag, internal_p=2., order=2.), 3.5355339059327378)
assert approx(wasserstein_distance(diag1, diag2, internal_p=2., order=1.) , 1.4453593023967701)
assert approx(wasserstein_distance(diag1, diag2, internal_p=2.35, order=1.74), 0.9772734057168739)
assert approx(wasserstein_distance(diag1, emptydiag, internal_p=2.35, order=1.7863), 3.141592214572228)
assert approx(wasserstein_distance(diag3, diag4, internal_p=1., order=1.), 3.)
assert approx(wasserstein_distance(diag3, diag4, internal_p=np.inf, order=1.), 3.) # no diag matching here
assert approx(wasserstein_distance(diag3, diag4, internal_p=np.inf, order=2.), np.sqrt(5))
assert approx(wasserstein_distance(diag3, diag4, internal_p=1., order=2.), np.sqrt(5))
assert approx(wasserstein_distance(diag3, diag4, internal_p=4.5, order=2.), np.sqrt(5))
if(not test_infinity):
return
diag5 = np.array([[0, 3], [4, np.inf]])
diag6 = np.array([[7, 8], [4, 6], [3, np.inf]])
assert wasserstein_distance(diag4, diag5) == np.inf
assert approx(wasserstein_distance(diag5, diag6, order=1, internal_p=np.inf), 4.)
def hera_wrap(delta):
def fun(*kargs,**kwargs):
return hera(*kargs,**kwargs,delta=delta)
return fun
def test_wasserstein_distance_pot():
_basic_wasserstein(pot, 1e-15, False)
def test_wasserstein_distance_hera():
_basic_wasserstein(hera_wrap(1e-12), 1e-12)
_basic_wasserstein(hera_wrap(.1), .1)
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