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))
def test_remove_redundant_inequalities(self):
# minimal facets only inequalities
A = np.array([[1., 1.], [-1., 1.], [0., -1.], [0., 1.], [0., 1.],
[2., 2.]])
b = np.array([[1.], [1.], [1.], [1.], [2.], [2.]])
p = Polyhedron(A, b)
mf = set(p.minimal_facets())
self.assertTrue(mf == set([1, 2, 0]) or mf == set([1, 2, 5]))
# add nasty redundant inequality
A = np.zeros((1, 2))
b = np.ones((1, 1))
p.add_inequality(A, b)
mf = set(p.minimal_facets())
self.assertTrue(mf == set([1, 2, 0]) or mf == set([1, 2, 5]))
# remove redundant facets
p.remove_redundant_inequalities()
A_min = np.array([[-1., 1.], [0., -1.], [1., 1.]])
b_min = np.array([[1.], [1.], [1.]])
self.assertTrue(
same_rows(np.hstack((A_min, b_min)), np.hstack((p.A, p.b))))
# both inequalities and equalities
x_min = -np.ones((2, 1))
x_max = -x_min
p = Polyhedron.from_bounds(x_min, x_max)
C = np.ones((1, 2))
d = np.ones((1, 1))
p.add_equality(C, d)
self.assertEqual([2, 3], sorted(p.minimal_facets()))
p.remove_redundant_inequalities()
A_min = np.array([[1., 0.], [0., 1.]])
b_min = np.array([[1.], [1.]])
self.assertTrue(
same_rows(np.hstack((A_min, b_min)), np.hstack((p.A, p.b))))
# add (redundant) inequality coincident with the equality
p.add_inequality(C, d)
p.remove_redundant_inequalities()
self.assertTrue(
same_rows(np.hstack((A_min, b_min)), np.hstack((p.A, p.b))))
# add (redundant) inequality
p.add_inequality(np.array([[-1., 1.]]), np.array([[1.1]]))
p.remove_redundant_inequalities()
self.assertTrue(
same_rows(np.hstack((A_min, b_min)), np.hstack((p.A, p.b))))
# add unfeasible equality (raises: 'empty polyhedron, cannot remove redundant inequalities.')
C = np.ones((1, 2))
d = -np.ones((1, 1))
p.add_equality(C, d)
self.assertRaises(ValueError, p.remove_redundant_inequalities)
# empty polyhderon (raises: 'empty polyhedron, cannot remove redundant inequalities.')
x_min = np.ones((2, 1))
x_max = np.zeros((2, 1))
p = Polyhedron.from_bounds(x_min, x_max)
self.assertRaises(ValueError, p.remove_redundant_inequalities)