def test_creation_of_particular_halfspaces(self):
"""Test that can create a given halfspace array representation"""
A = np.array([[3, 3], [2, 5], [0, 6]])
expected_halfspace = np.array(
[
[3.0, 3.0, -1.0],
[2.0, 5.0, -1.0],
[0.0, 6.0, -1.0],
[-1.0, -0.0, 0.0],
[-0.0, -1.0, 0.0],
]
)
halfspace = build_halfspaces(A)
self.assertTrue(np.array_equal(halfspace, expected_halfspace))
B = np.array([[3, 2], [2, 6], [3, 1]])
expected_halfspace = np.array(
[
[3.0, 2.0, 3.0, -1.0],
[2.0, 6.0, 1.0, -1.0],
[-1.0, -0.0, -0.0, 0.0],
[-0.0, -1.0, -0.0, 0.0],
[-0.0, -0.0, -1.0, 0.0],
]
)
halfspace = build_halfspaces(B.transpose())
self.assertTrue(np.array_equal(halfspace, expected_halfspace))
def test_labelling_of_particular_vertices(self):
A = np.array([[3, 3], [2, 5], [0, 6]])
halfspaces = build_halfspaces(A)
vertices = non_trivial_vertices(halfspaces)
expected_labels = sorted(
[set([0, 1]), set([0, 4]), set([1, 2]), set([2, 3])], key=list
)
labels_ = sorted((labels(v, halfspaces) for v, l in vertices), key=list)
for label, expected_label in zip(labels_, expected_labels):
self.assertTrue(
np.array_equal(label, expected_label),
msg="{} != {}".format(label, expected_label),
)
B = np.array([[3, 2], [2, 6], [3, 1]])
halfspaces = build_halfspaces(B.transpose())
vertices = non_trivial_vertices(halfspaces)
expected_labels = sorted(
[
set([0, 2, 3]),
set([0, 3, 4]),
set([0, 1, 2]),
set([1, 2, 4]),
set([0, 1, 4]),
],
key=list,
)
labels_ = sorted((labels(v, halfspaces) for v, l in vertices), key=list)
for label, expected_label in zip(labels_, expected_labels):
self.assertTrue(
np.array_equal(label, expected_label),
msg="{} != {}".format(label, expected_label),
)
def test_creation_of_particular_non_trivial_vertices(self):
"""Test that vertices are obtained"""
A = np.array([[3, 3], [2, 5], [0, 6]])
halfspaces = build_halfspaces(A)
vertices_generator = non_trivial_vertices(halfspaces)
self.assertIsInstance(vertices_generator, GeneratorType)
expected_vertices = sorted(
[
np.array([1 / 3, 0]),
np.array([0, 1 / 6]),
np.array([2 / 9, 1 / 9]),
np.array([1 / 12, 1 / 6]),
],
key=lambda a: list(np.round(a, 5)),
)
vertices = sorted(
(v for v, l in vertices_generator),
key=lambda a: list(np.round(a, 5)),
)
for vertex, expected_vertex in zip(vertices, expected_vertices):
self.assertTrue(all(np.isclose(vertex, expected_vertex)))
B = np.array([[3, 2], [2, 6], [3, 1]])
halfspaces = build_halfspaces(B.transpose())
vertices_generator = non_trivial_vertices(halfspaces)
self.assertIsInstance(vertices_generator, GeneratorType)
expected_vertices = sorted(
[
np.array([0, 0, 1 / 3]),
np.array([0, 1 / 8, 1 / 4]),
np.array([0, 1 / 6, 0]),
np.array([2 / 7, 1 / 14, 0]),
np.array([1 / 3, 0, 0]),
],
key=lambda a: list(np.round(a, 5)),
)
vertices = sorted(
(v for v, l in vertices_generator),
key=lambda a: list(np.round(a, 5)),
)
for vertex, expected_vertex in zip(vertices, expected_vertices):
self.assertTrue(
all(np.isclose(vertex, expected_vertex)),
msg="{} != {}".format(vertex, expected_vertex),
)
def test_creation_of_particular_feasible_point(self):
A = np.array([[3, 3], [2, 5], [0, 6]])
halfspaces = build_halfspaces(A)
feasible_point = find_feasible_point(halfspaces)
self.assertTrue(
all(np.isclose(feasible_point, np.array([0.08074176,
0.08074176]))))
B = np.array([[3, 2], [2, 6], [3, 1]])
halfspaces = build_halfspaces(B.transpose())
feasible_point = find_feasible_point(halfspaces)
self.assertTrue(
all(
np.isclose(feasible_point,
np.array([0.06492189, 0.06492189, 0.06492189]))))
def test_creation_of_halfspaces(self, A):
"""Test that can create a bi matrix game"""
halfspace = build_halfspaces(A)
number_of_strategies, dimension = A.shape
self.assertEqual(halfspace.shape,
(number_of_strategies + dimension, dimension + 1))
self.assertTrue(
np.array_equal(halfspace[number_of_strategies:, :-1],
-np.eye(dimension)))
def test_creation_of_non_trivial_vertices(self, A):
"""Test that can create a bi matrix game"""
halfspaces = build_halfspaces(A)
vertices_generator = non_trivial_vertices(halfspaces)
number_of_strategies, dimension = A.shape
self.assertIsInstance(vertices_generator, GeneratorType)
for vertex, labels_set in vertices_generator:
self.assertEqual(len(vertex), dimension)
for label in labels_set:
self.assertGreaterEqual(label, 0)
self.assertLessEqual(label, number_of_strategies + dimension)
def test_creation_of_feasible_point(self, A):
halfspaces = build_halfspaces(A)
feasible_point = find_feasible_point(halfspaces)
M, b = halfspaces[:, :-1], halfspaces[:, -1]
self.assertTrue(all(np.dot(M, feasible_point) <= -b))