def test_vertices(self):
# basic eample
A = np.array([[-1, 0.],[0., -1.],[2., 1.],[-0.5, 1.]])
b = np.array([0.,0.,4.,2.])
p = Polyhedron(A,b)
u_list = [
np.array([0.,0.]),
np.array([2.,0.]),
np.array([0.,2.]),
np.array([.8,2.4])
]
self.assertTrue(same_vectors(p.vertices, u_list))
# 1d example
A = np.array([[-1],[1.]])
b = np.array([1.,1.])
p = Polyhedron(A,b)
u_list = [
np.array([-1.]),
np.array([1.])
]
self.assertTrue(same_vectors(p.vertices, u_list))
# unbounded
x_min = np.zeros(2)
p = Polyhedron.from_lower_bound(x_min)
self.assertTrue(p.vertices is None)
# lower dimensional (because of the inequalities)
x_max = np.array([1.,0.])
p.add_upper_bound(x_max)
self.assertTrue(p.vertices is None)
# empty
x_max = - np.ones(2)
p.add_upper_bound(x_max)
self.assertTrue(p.vertices is None)
# 3d case
x_min = - np.ones(3)
x_max = - x_min
p = Polyhedron.from_bounds(x_min, x_max)
u_list = [np.array(v) for v in product([1., -1.], repeat=3)]
self.assertTrue(same_vectors(p.vertices, u_list))
# 3d case with equalities
x_min = np.array([-1.,-2.])
x_max = - x_min
p = Polyhedron.from_bounds(x_min, x_max, [0,1], 3)
C = np.array([[1., 0., -1.]])
d = np.zeros(1)
p.add_equality(C, d)
u_list = [
np.array([1.,2.,1.]),
np.array([-1.,2.,-1.]),
np.array([1.,-2.,1.]),
np.array([-1.,-2.,-1.])
]
self.assertTrue(same_vectors(p.vertices, u_list))
def test_add_functions(self):
# add inequalities
A = np.eye(2)
b = np.ones(2)
p = Polyhedron(A, b)
A = np.ones((1, 2))
b = np.ones(1)
p.add_inequality(A, b)
A = np.ones((1, 1))
b = 3. * np.ones(1)
p.add_inequality(A, b, [1])
A = np.array([[1., 0.], [0., 1.], [1., 1.], [0., 1.]])
b = np.array([1., 1., 1., 3.])
self.assertTrue(
same_rows(np.column_stack((A, b)), np.column_stack((p.A, p.b))))
c = np.ones(2)
self.assertRaises(ValueError, p.add_inequality, A, c)
# add equalities
A = np.eye(2)
b = np.ones(2)
p.add_equality(A, b)
A = 3. * np.ones((1, 1))
b = np.ones(1)
p.add_equality(A, b, [0])
A = np.array([[1., 0.], [0., 1.], [3., 0.]])
b = np.array([[1.], [1.], [1.]])
self.assertTrue(
same_rows(np.column_stack((A, b)), np.column_stack((p.C, p.d))))
b = np.ones(2)
self.assertRaises(ValueError, p.add_equality, A, b)
# add lower bounds
A = np.zeros((0, 2))
b = np.zeros(0)
p = Polyhedron(A, b)
p.add_lower_bound(-np.ones(2))
p.add_upper_bound(2 * np.ones(2))
p.add_bounds(-3 * np.ones(2), 3 * np.ones(2))
p.add_lower_bound(-4 * np.ones(1), [0])
p.add_upper_bound(5 * np.ones(1), [0])
p.add_bounds(-6 * np.ones(1), 6 * np.ones(1), [1])
A = np.array([[-1., 0.], [0., -1.], [1., 0.], [0., 1.], [-1., 0.],
[0., -1.], [1., 0.], [0., 1.], [-1., 0.], [1., 0.],
[0., -1.], [0., 1.]])
b = np.array([1., 1., 2., 2., 3., 3., 3., 3., 4., 5., 6., 6.])
self.assertTrue(
same_rows(np.column_stack((A, b)), np.column_stack((p.A, p.b))))
# wrong size bounds
A = np.eye(3)
b = np.ones(3)
p = Polyhedron(A, b)
x = np.zeros(1)
indices = [0, 1]
self.assertRaises(ValueError, p.add_lower_bound, x, indices)
self.assertRaises(ValueError, p.add_upper_bound, x, indices)
self.assertRaises(ValueError, p.add_bounds, x, x, indices)
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)
def test_add_functions(self):
# add inequalities
A = np.eye(2)
b = np.ones(2)
p = Polyhedron(A, b)
A = np.ones((1, 2))
b = np.ones(1)
p.add_inequality(A, b)
A = np.ones((1, 1))
b = 3.*np.ones(1)
p.add_inequality(A, b, [1])
A = np.array([[1., 0.], [0., 1.], [1., 1.], [0., 1.]])
b = np.array([1.,1.,1.,3.])
self.assertTrue(same_rows(
np.column_stack((A, b)),
np.column_stack((p.A, p.b))
))
c = np.ones(2)
self.assertRaises(ValueError, p.add_inequality, A, c)
# add equalities
A = np.eye(2)
b = np.ones(2)
p.add_equality(A, b)
A = 3.*np.ones((1, 1))
b = np.ones(1)
p.add_equality(A, b, [0])
A = np.array([[1., 0.], [0., 1.], [3., 0.]])
b = np.array([[1.], [1.], [1.]])
self.assertTrue(same_rows(
np.column_stack((A, b)),
np.column_stack((p.C, p.d))
))
b = np.ones(2)
self.assertRaises(ValueError, p.add_equality, A, b)
# add lower bounds
A = np.zeros((0, 2))
b = np.zeros(0)
p = Polyhedron(A, b)
p.add_lower_bound(-np.ones(2))
p.add_upper_bound(2*np.ones(2))
p.add_bounds(-3*np.ones(2), 3*np.ones(2))
p.add_lower_bound(-4*np.ones(1), [0])
p.add_upper_bound(5*np.ones(1), [0])
p.add_bounds(-6*np.ones(1), 6*np.ones(1), [1])
A =np.array([[-1., 0.], [0., -1.], [1., 0.], [0., 1.], [-1., 0.], [0., -1.], [1., 0.], [0., 1.], [-1., 0.], [1., 0.], [0., -1.], [0., 1.] ])
b = np.array([1.,1.,2.,2.,3.,3.,3.,3.,4.,5.,6.,6.])
self.assertTrue(same_rows(
np.column_stack((A, b)),
np.column_stack((p.A, p.b))
))
# wrong size bounds
A = np.eye(3)
b = np.ones(3)
p = Polyhedron(A, b)
x = np.zeros(1)
indices = [0, 1]
self.assertRaises(ValueError, p.add_lower_bound, x, indices)
self.assertRaises(ValueError, p.add_upper_bound, x, indices)
self.assertRaises(ValueError, p.add_bounds, x, x, indices)
# add symbolic
n = 5
m = 3
A = np.random.rand(m, n)
b = np.random.rand(m)
C = np.random.rand(m, n)
d = np.random.rand(m)
P = Polyhedron(A, b)
x = sp.Matrix([sp.Symbol('x'+str(i), real=True) for i in range(n)])
ineq = sp.Matrix(A)*x - sp.Matrix(b)
P.add_symbolic_inequality(x, ineq)
np.testing.assert_array_almost_equal(P.A, np.vstack((A, A)))
np.testing.assert_array_almost_equal(P.b, np.concatenate((b, b)))
eq = sp.Matrix(C)*x - sp.Matrix(d)
P.add_symbolic_equality(x, eq)
np.testing.assert_array_almost_equal(P.C, C)
np.testing.assert_array_almost_equal(P.d, d)
# throw some errors here
P = Polyhedron(A, b)
x = sp.Matrix([sp.Symbol('x'+str(i), real=True) for i in range(n+1)])
A1 = np.random.rand(m, n+1)
ineq = sp.Matrix(A1)*x - sp.Matrix(b)
self.assertRaises(ValueError, P.add_symbolic_inequality, x, ineq)
P = Polyhedron(A, b, C, d)
C1 = np.random.rand(m, n+1)
eq = sp.Matrix(C1)*x - sp.Matrix(b)
self.assertRaises(ValueError, P.add_symbolic_equality, x, eq)