def test_from_convex_hull(self):
# simple 2d
points = [
np.array([0.,0.]),
np.array([1.,0.]),
np.array([0.,1.])
]
p = Polyhedron.from_convex_hull(points)
A = np.array([
[-1., 0.],
[0., -1.],
[1., 1.],
])
b = np.array([0.,0.,1.])
self.assertTrue(same_rows(
np.column_stack((A, b)),
np.column_stack((p.A, p.b))
))
# simple 3d
points = [
np.array([0.,0.,0.]),
np.array([1.,0.,0.]),
np.array([0.,1.,0.]),
np.array([0.,0.,1.])
]
p = Polyhedron.from_convex_hull(points)
A = np.array([
[-1., 0., 0.],
[0., -1., 0.],
[0., 0., -1.],
[1., 1., 1.],
])
b = np.array([0.,0.,0.,1.])
self.assertTrue(same_rows(
np.column_stack((A, b)),
np.column_stack((p.A, p.b))
))
# another 2d with internal point
points = [
np.array([0.,0.]),
np.array([1.,0.]),
np.array([0.,1.]),
np.array([1.,1.]),
np.array([.5,.5]),
]
p = Polyhedron.from_convex_hull(points)
A = np.array([
[-1., 0.],
[0., -1.],
[1., 0.],
[0., 1.],
])
b = np.array([0.,0.,1.,1.])
self.assertTrue(same_rows(
np.column_stack((A, b)),
np.column_stack((p.A, p.b))
))
def test_convex_hull_method(self):
np.random.seed(3)
# cube from n-dimensions to n-1-dimensions
for n in range(2, 6):
x_min = - np.ones(n)
x_max = - x_min
p = Polyhedron.from_bounds(x_min, x_max)
E = np.vstack((
np.eye(n-1),
- np.eye(n-1)
))
f = np.ones(2*(n-1))
vertices = [np.array(v) for v in product([1., -1.], repeat=n-1)]
E_chm, f_chm, vertices_chm = convex_hull_method(p.A, p.b, range(n-1))
p_chm = Polyhedron(E_chm, f_chm)
p_chm.remove_redundant_inequalities()
self.assertTrue(same_rows(
np.column_stack((E, f)),
np.column_stack((p_chm.A, p_chm.b))
))
self.assertTrue(same_vectors(vertices, vertices_chm))
# test with random polytopes wiith m facets
m = 10
# dimension of the higher dimensional polytope
for n in range(3, 6):
# dimension of the lower dimensional polytope
for n_proj in range(2, n):
# higher dimensional polytope
A = np.random.randn(m, n)
b = np.random.rand(m)
p = Polyhedron(A, b)
# if not empty or unbounded
if p.vertices is not None:
points = [v[:n_proj] for v in p.vertices]
p = Polyhedron.from_convex_hull(points)
# check half spaces
p.remove_redundant_inequalities()
E_chm, f_chm, vertices_chm = convex_hull_method(A, b, range(n_proj))
p_chm = Polyhedron(E_chm, f_chm)
p_chm.remove_redundant_inequalities()
self.assertTrue(same_rows(
np.column_stack((p.A, p.b)),
np.column_stack((p_chm.A, p_chm.b))
))
# check vertices
self.assertTrue(same_vectors(p.vertices, vertices_chm))
