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import os
import sys
import matplotlib.pyplot as plt
import numpy as np
import pytest
import random
from sklearn.cluster import KMeans
# Vectorization
from gudhi.representations import (Landscape, Silhouette, BettiCurve, ComplexPolynomial,\
TopologicalVector, PersistenceImage, Entropy)
# Preprocessing
from gudhi.representations import (BirthPersistenceTransform, Clamping, DiagramScaler, Padding, ProminentPoints, \
DiagramSelector)
# Kernel
from gudhi.representations import (PersistenceWeightedGaussianKernel, \
PersistenceScaleSpaceKernel, SlicedWassersteinDistance,\
SlicedWassersteinKernel, PersistenceFisherKernel, WassersteinDistance)
def test_representations_examples():
# Disable graphics for testing purposes
plt.show = lambda: None
here = os.path.dirname(os.path.realpath(__file__))
sys.path.append(here + "/../example")
import diagram_vectorizations_distances_kernels
return None
from gudhi.representations.vector_methods import Atol
from gudhi.representations.metrics import *
from gudhi.representations.kernel_methods import *
def _n_diags(n):
l = []
for _ in range(n):
a = np.random.rand(50, 2)
a[:, 1] += a[:, 0] # So that y >= x
l.append(a)
return l
def test_multiple():
l1 = _n_diags(9)
l2 = _n_diags(11)
l1b = l1.copy()
d1 = pairwise_persistence_diagram_distances(l1, e=0.00001, n_jobs=4)
d2 = BottleneckDistance(epsilon=0.00001).fit_transform(l1)
d3 = pairwise_persistence_diagram_distances(l1, l1b, e=0.00001, n_jobs=4)
assert d1 == pytest.approx(d2)
assert d3 == pytest.approx(d2, abs=1e-5) # Because of 0 entries (on the diagonal)
d1 = pairwise_persistence_diagram_distances(l1, l2, metric="wasserstein", order=2, internal_p=2)
d2 = WassersteinDistance(order=2, internal_p=2, n_jobs=4).fit(l2).transform(l1)
print(d1.shape, d2.shape)
assert d1 == pytest.approx(d2, rel=0.02)
# Test sorted values as points order can be inverted, and sorted test is not documentation-friendly
# Note the test below must be up to date with the Atol class documentation
def test_atol_doc():
a = np.array([[1, 2, 4], [1, 4, 0], [1, 0, 4]])
b = np.array([[4, 2, 0], [4, 4, 0], [4, 0, 2]])
c = np.array([[3, 2, -1], [1, 2, -1]])
atol_vectoriser = Atol(quantiser=KMeans(n_clusters=2, random_state=202006))
# Atol will do
# X = np.concatenate([a,b,c])
# kmeans = KMeans(n_clusters=2, random_state=202006).fit(X)
# kmeans.labels_ will be : array([1, 0, 1, 0, 0, 1, 0, 0])
first_cluster = np.asarray([a[0], a[2], b[2]])
second_cluster = np.asarray([a[1], b[0], b[2], c[0], c[1]])
# Check the center of the first_cluster and second_cluster are in Atol centers
centers = atol_vectoriser.fit(X=[a, b, c]).centers
np.isclose(centers, first_cluster.mean(axis=0)).all(1).any()
np.isclose(centers, second_cluster.mean(axis=0)).all(1).any()
vectorization = atol_vectoriser.transform(X=[a, b, c])
assert np.allclose(vectorization[0], atol_vectoriser(a))
assert np.allclose(vectorization[1], atol_vectoriser(b))
assert np.allclose(vectorization[2], atol_vectoriser(c))
def test_dummy_atol():
a = np.array([[1, 2, 4], [1, 4, 0], [1, 0, 4]])
b = np.array([[4, 2, 0], [4, 4, 0], [4, 0, 2]])
c = np.array([[3, 2, -1], [1, 2, -1]])
for weighting_method in ["cloud", "iidproba"]:
for contrast in ["gaussian", "laplacian", "indicator"]:
atol_vectoriser = Atol(
quantiser=KMeans(n_clusters=1, random_state=202006),
weighting_method=weighting_method,
contrast=contrast,
)
atol_vectoriser.fit([a, b, c])
atol_vectoriser(a)
atol_vectoriser.transform(X=[a, b, c])
from gudhi.representations.vector_methods import BettiCurve
def test_infinity():
a = np.array([[1.0, 8.0], [2.0, np.inf], [3.0, 4.0]])
c = BettiCurve(20, [0.0, 10.0])(a)
assert c[1] == 0
assert c[7] == 3
assert c[9] == 2
def test_preprocessing_empty_diagrams():
empty_diag = np.empty(shape = [0, 2])
assert not np.any(BirthPersistenceTransform()(empty_diag))
assert not np.any(Clamping().fit_transform(empty_diag))
assert not np.any(DiagramScaler()(empty_diag))
assert not np.any(Padding()(empty_diag))
assert not np.any(ProminentPoints()(empty_diag))
assert not np.any(DiagramSelector()(empty_diag))
def pow(n):
return lambda x: np.power(x[1]-x[0],n)
def test_vectorization_empty_diagrams():
empty_diag = np.empty(shape = [0, 2])
random_resolution = random.randint(50,100)*10 # between 500 and 1000
print("resolution = ", random_resolution)
lsc = Landscape(resolution=random_resolution)(empty_diag)
assert not np.any(lsc)
assert lsc.shape[0]%random_resolution == 0
slt = Silhouette(resolution=random_resolution, weight=pow(2))(empty_diag)
assert not np.any(slt)
assert slt.shape[0] == random_resolution
btc = BettiCurve(resolution=random_resolution)(empty_diag)
assert not np.any(btc)
assert btc.shape[0] == random_resolution
cpp = ComplexPolynomial(threshold=random_resolution, polynomial_type="T")(empty_diag)
assert not np.any(cpp)
assert cpp.shape[0] == random_resolution
tpv = TopologicalVector(threshold=random_resolution)(empty_diag)
assert tpv.shape[0] == random_resolution
assert not np.any(tpv)
prmg = PersistenceImage(resolution=[random_resolution,random_resolution])(empty_diag)
assert not np.any(prmg)
assert prmg.shape[0] == random_resolution * random_resolution
sce = Entropy(mode="scalar", resolution=random_resolution)(empty_diag)
assert not np.any(sce)
assert sce.shape[0] == 1
scv = Entropy(mode="vector", normalized=False, resolution=random_resolution)(empty_diag)
assert not np.any(scv)
assert scv.shape[0] == random_resolution
def test_entropy_miscalculation():
diag_ex = np.array([[0.0,1.0], [0.0,1.0], [0.0,2.0]])
def pe(pd):
l = pd[:,1] - pd[:,0]
l = l/sum(l)
return -np.dot(l, np.log(l))
sce = Entropy(mode="scalar")
assert [[pe(diag_ex)]] == sce.fit_transform([diag_ex])
sce = Entropy(mode="vector", resolution=4, normalized=False, keep_endpoints=True)
pef = [-1/4*np.log(1/4)-1/4*np.log(1/4)-1/2*np.log(1/2),
-1/4*np.log(1/4)-1/4*np.log(1/4)-1/2*np.log(1/2),
-1/2*np.log(1/2),
0.0]
assert all(([pef] == sce.fit_transform([diag_ex]))[0])
sce = Entropy(mode="vector", resolution=4, normalized=True)
pefN = (sce.fit_transform([diag_ex]))[0]
area = np.linalg.norm(pefN, ord=1)
assert area==pytest.approx(1)
def test_kernel_empty_diagrams():
empty_diag = np.empty(shape = [0, 2])
assert SlicedWassersteinDistance(num_directions=100)(empty_diag, empty_diag) == 0.
assert SlicedWassersteinKernel(num_directions=100, bandwidth=1.)(empty_diag, empty_diag) == 1.
assert WassersteinDistance(mode="hera", delta=0.0001)(empty_diag, empty_diag) == 0.
assert WassersteinDistance(mode="pot")(empty_diag, empty_diag) == 0.
assert BottleneckDistance(epsilon=.001)(empty_diag, empty_diag) == 0.
assert BottleneckDistance()(empty_diag, empty_diag) == 0.
# PersistenceWeightedGaussianKernel(bandwidth=1., kernel_approx=None, weight=arctan(1.,1.))(empty_diag, empty_diag)
# PersistenceWeightedGaussianKernel(kernel_approx=RBFSampler(gamma=1./2, n_components=100000).fit(np.ones([1,2])), weight=arctan(1.,1.))(empty_diag, empty_diag)
# PersistenceScaleSpaceKernel(bandwidth=1.)(empty_diag, empty_diag)
# PersistenceScaleSpaceKernel(kernel_approx=RBFSampler(gamma=1./2, n_components=100000).fit(np.ones([1,2])))(empty_diag, empty_diag)
# PersistenceFisherKernel(bandwidth_fisher=1., bandwidth=1.)(empty_diag, empty_diag)
# PersistenceFisherKernel(bandwidth_fisher=1., bandwidth=1., kernel_approx=RBFSampler(gamma=1./2, n_components=100000).fit(np.ones([1,2])))(empty_diag, empty_diag)
def test_silhouette_permutation_invariance():
dgm = _n_diags(1)[0]
dgm_permuted = dgm[np.random.permutation(dgm.shape[0]).astype(int)]
random_resolution = random.randint(50, 100) * 10
slt = Silhouette(resolution=random_resolution, weight=pow(2))
assert np.all(np.isclose(slt(dgm), slt(dgm_permuted)))
def test_silhouette_multiplication_invariance():
dgm = _n_diags(1)[0]
n_repetitions = np.random.randint(2, high=10)
dgm_augmented = np.repeat(dgm, repeats=n_repetitions, axis=0)
random_resolution = random.randint(50, 100) * 10
slt = Silhouette(resolution=random_resolution, weight=pow(2))
assert np.all(np.isclose(slt(dgm), slt(dgm_augmented)))
def test_silhouette_numeric():
dgm = np.array([[2., 3.], [5., 6.]])
slt = Silhouette(resolution=9, weight=pow(1), sample_range=[2., 6.])
#slt.fit([dgm])
# x_values = array([2., 2.5, 3., 3.5, 4., 4.5, 5., 5.5, 6.])
expected_silhouette = np.array([0., 0.5, 0., 0., 0., 0., 0., 0.5, 0.])/np.sqrt(2)
output_silhouette = slt(dgm)
assert np.all(np.isclose(output_silhouette, expected_silhouette))
def test_landscape_small_persistence_invariance():
dgm = np.array([[2., 6.], [2., 5.], [3., 7.]])
small_persistence_pts = np.random.rand(10, 2)
small_persistence_pts[:, 1] += small_persistence_pts[:, 0]
small_persistence_pts += np.min(dgm)
dgm_augmented = np.concatenate([dgm, small_persistence_pts], axis=0)
lds = Landscape(num_landscapes=2, resolution=5)
lds_dgm, lds_dgm_augmented = lds(dgm), lds(dgm_augmented)
assert np.all(np.isclose(lds_dgm, lds_dgm_augmented))
def test_landscape_numeric():
dgm = np.array([[2., 6.], [3., 5.]])
lds_ref = np.array([
0., 0.5, 1., 1.5, 2., 1.5, 1., 0.5, 0., # tent of [2, 6]
0., 0., 0., 0.5, 1., 0.5, 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0.,
])
lds_ref *= np.sqrt(2)
lds = Landscape(num_landscapes=4, resolution=9, sample_range=[2., 6.])
lds_dgm = lds(dgm)
assert np.all(np.isclose(lds_dgm, lds_ref))
def test_landscape_nan_range():
dgm = np.array([[2., 6.], [3., 5.]])
lds = Landscape(num_landscapes=2, resolution=9, sample_range=[np.nan, 6.])
lds_dgm = lds(dgm)
assert (lds.sample_range_fixed[0] == 2) & (lds.sample_range_fixed[1] == 6)
assert lds.new_resolution == 10
def test_endpoints():
diags = [ np.array([[2., 3.]]) ]
for vec in [ Landscape(), Silhouette(), BettiCurve(), Entropy(mode="vector") ]:
vec.fit(diags)
assert vec.grid_[0] > 2 and vec.grid_[-1] < 3
for vec in [ Landscape(keep_endpoints=True), Silhouette(keep_endpoints=True), BettiCurve(keep_endpoints=True), Entropy(mode="vector", keep_endpoints=True)]:
vec.fit(diags)
assert vec.grid_[0] == 2 and vec.grid_[-1] == 3
vec = BettiCurve(resolution=None)
vec.fit(diags)
assert np.equal(vec.grid_, [-np.inf, 2., 3.]).all()
def test_get_params():
for vec in [ Landscape(), Silhouette(), BettiCurve(), Entropy(mode="vector") ]:
vec.get_params()
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