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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): Vincent Rouvreau
Copyright (C) 2016 Inria
Modification(s):
- YYYY/MM Author: Description of the modification
"""
import gudhi as gd
import math
import numpy as np
import pytest
try:
# python3
from itertools import zip_longest
except ImportError:
# python2
from itertools import izip_longest as zip_longest
__author__ = "Vincent Rouvreau"
__copyright__ = "Copyright (C) 2016 Inria"
__license__ = "MIT"
def _empty_alpha(precision):
alpha_complex = gd.AlphaComplex(points=[[0, 0]], precision = precision)
assert alpha_complex.__is_defined() == True
def test_empty_alpha():
for precision in ['fast', 'safe', 'exact']:
_empty_alpha(precision)
def _infinite_alpha(precision):
point_list = [[0, 0], [1, 0], [0, 1], [1, 1]]
alpha_complex = gd.AlphaComplex(points=point_list, precision = precision)
assert alpha_complex.__is_defined() == True
simplex_tree = alpha_complex.create_simplex_tree()
assert simplex_tree.__is_persistence_defined() == False
assert simplex_tree.num_simplices() == 11
assert simplex_tree.num_vertices() == 4
assert list(simplex_tree.get_filtration()) == [
([0], 0.0),
([1], 0.0),
([2], 0.0),
([3], 0.0),
([0, 1], 0.25),
([0, 2], 0.25),
([1, 3], 0.25),
([2, 3], 0.25),
([1, 2], 0.5),
([0, 1, 2], 0.5),
([1, 2, 3], 0.5),
]
assert simplex_tree.get_star([0]) == [
([0], 0.0),
([0, 1], 0.25),
([0, 1, 2], 0.5),
([0, 2], 0.25),
]
assert simplex_tree.get_cofaces([0], 1) == [([0, 1], 0.25), ([0, 2], 0.25)]
assert point_list[0] == alpha_complex.get_point(0)
assert point_list[1] == alpha_complex.get_point(1)
assert point_list[2] == alpha_complex.get_point(2)
assert point_list[3] == alpha_complex.get_point(3)
try:
alpha_complex.get_point(4) == []
except IndexError:
pass
else:
assert False
try:
alpha_complex.get_point(125) == []
except IndexError:
pass
else:
assert False
def test_infinite_alpha():
for precision in ['fast', 'safe', 'exact']:
_infinite_alpha(precision)
def _filtered_alpha(precision):
point_list = [[0, 0], [1, 0], [0, 1], [1, 1]]
filtered_alpha = gd.AlphaComplex(points=point_list, precision = precision)
simplex_tree = filtered_alpha.create_simplex_tree(max_alpha_square=0.25)
assert simplex_tree.num_simplices() == 8
assert simplex_tree.num_vertices() == 4
assert point_list[0] == filtered_alpha.get_point(0)
assert point_list[1] == filtered_alpha.get_point(1)
assert point_list[2] == filtered_alpha.get_point(2)
assert point_list[3] == filtered_alpha.get_point(3)
try:
filtered_alpha.get_point(4) == []
except IndexError:
pass
else:
assert False
try:
filtered_alpha.get_point(125) == []
except IndexError:
pass
else:
assert False
assert list(simplex_tree.get_filtration()) == [
([0], 0.0),
([1], 0.0),
([2], 0.0),
([3], 0.0),
([0, 1], 0.25),
([0, 2], 0.25),
([1, 3], 0.25),
([2, 3], 0.25),
]
assert simplex_tree.get_star([0]) == [([0], 0.0), ([0, 1], 0.25), ([0, 2], 0.25)]
assert simplex_tree.get_cofaces([0], 1) == [([0, 1], 0.25), ([0, 2], 0.25)]
def test_filtered_alpha():
for precision in ['fast', 'safe', 'exact']:
_filtered_alpha(precision)
def _safe_alpha_persistence_comparison(precision):
#generate periodic signal
time = np.arange(0, 10, 1)
signal = [math.sin(x) for x in time]
delta = math.pi
delayed = [math.sin(x + delta) for x in time]
#construct embedding
embedding1 = [[signal[i], -signal[i]] for i in range(len(time))]
embedding2 = [[signal[i], delayed[i]] for i in range(len(time))]
#build alpha complex and simplex tree
alpha_complex1 = gd.AlphaComplex(points=embedding1, precision = precision)
simplex_tree1 = alpha_complex1.create_simplex_tree()
alpha_complex2 = gd.AlphaComplex(points=embedding2, precision = precision)
simplex_tree2 = alpha_complex2.create_simplex_tree()
diag1 = simplex_tree1.persistence()
diag2 = simplex_tree2.persistence()
for (first_p, second_p) in zip_longest(diag1, diag2):
assert first_p[0] == pytest.approx(second_p[0])
assert first_p[1] == pytest.approx(second_p[1])
def test_safe_alpha_persistence_comparison():
# Won't work for 'fast' version
_safe_alpha_persistence_comparison('safe')
_safe_alpha_persistence_comparison('exact')
def _delaunay_complex(precision):
point_list = [[0, 0], [1, 0], [0, 1], [1, 1]]
filtered_alpha = gd.AlphaComplex(points=point_list, precision = precision)
simplex_tree = filtered_alpha.create_simplex_tree(default_filtration_value = True)
assert simplex_tree.num_simplices() == 11
assert simplex_tree.num_vertices() == 4
assert point_list[0] == filtered_alpha.get_point(0)
assert point_list[1] == filtered_alpha.get_point(1)
assert point_list[2] == filtered_alpha.get_point(2)
assert point_list[3] == filtered_alpha.get_point(3)
try:
filtered_alpha.get_point(4) == []
except IndexError:
pass
else:
assert False
try:
filtered_alpha.get_point(125) == []
except IndexError:
pass
else:
assert False
for filtered_value in simplex_tree.get_filtration():
assert math.isnan(filtered_value[1])
for filtered_value in simplex_tree.get_star([0]):
assert math.isnan(filtered_value[1])
for filtered_value in simplex_tree.get_cofaces([0], 1):
assert math.isnan(filtered_value[1])
def test_delaunay_complex():
for precision in ['fast', 'safe', 'exact']:
_delaunay_complex(precision)
def _3d_points_on_a_plane(precision, default_filtration_value):
alpha = gd.AlphaComplex(off_file='alphacomplexdoc.off', precision = precision)
simplex_tree = alpha.create_simplex_tree(default_filtration_value = default_filtration_value)
assert simplex_tree.dimension() == 2
assert simplex_tree.num_vertices() == 7
assert simplex_tree.num_simplices() == 25
def test_3d_points_on_a_plane():
off_file = open("alphacomplexdoc.off", "w")
off_file.write("OFF \n" \
"7 0 0 \n" \
"1.0 1.0 0.0\n" \
"7.0 0.0 0.0\n" \
"4.0 6.0 0.0\n" \
"9.0 6.0 0.0\n" \
"0.0 14.0 0.0\n" \
"2.0 19.0 0.0\n" \
"9.0 17.0 0.0\n" )
off_file.close()
for default_filtration_value in [True, False]:
for precision in ['fast', 'safe', 'exact']:
_3d_points_on_a_plane(precision, default_filtration_value)
def _3d_tetrahedrons(precision):
points = 10*np.random.rand(10, 3)
alpha = gd.AlphaComplex(points=points, precision = precision)
st_alpha = alpha.create_simplex_tree(default_filtration_value = False)
# New AlphaComplex for get_point to work
delaunay = gd.AlphaComplex(points=points, precision = precision)
st_delaunay = delaunay.create_simplex_tree(default_filtration_value = True)
delaunay_tetra = []
for sk in st_delaunay.get_skeleton(4):
if len(sk[0]) == 4:
tetra = [delaunay.get_point(sk[0][0]),
delaunay.get_point(sk[0][1]),
delaunay.get_point(sk[0][2]),
delaunay.get_point(sk[0][3]) ]
delaunay_tetra.append(sorted(tetra, key=lambda tup: tup[0]))
alpha_tetra = []
for sk in st_alpha.get_skeleton(4):
if len(sk[0]) == 4:
tetra = [alpha.get_point(sk[0][0]),
alpha.get_point(sk[0][1]),
alpha.get_point(sk[0][2]),
alpha.get_point(sk[0][3]) ]
alpha_tetra.append(sorted(tetra, key=lambda tup: tup[0]))
# Check the tetrahedrons from one list are in the second one
assert len(alpha_tetra) == len(delaunay_tetra)
for tetra_from_del in delaunay_tetra:
assert tetra_from_del in alpha_tetra
def test_3d_tetrahedrons():
for precision in ['fast', 'safe', 'exact']:
_3d_tetrahedrons(precision)
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