def test_from_functions(self):
# row vector input
x = np.ones((1, 5))
self.assertRaises(ValueError, Polyhedron.from_lower_bound, x)
# from lower bound
x = np.ones((2, 1))
p = Polyhedron.from_lower_bound(x)
A_lb = np.array([[-1., 0.], [0., -1.]])
b_lb = np.array([[-1.], [-1.]])
self.assertTrue(
same_rows(np.hstack((A_lb, b_lb)), np.hstack((p.A, p.b))))
# from upper bound
p = Polyhedron.from_upper_bound(x)
A_ub = np.array([[1., 0.], [0., 1.]])
b_ub = np.array([[1.], [1.]])
self.assertTrue(
same_rows(np.hstack((A_ub, b_ub)), np.hstack((p.A, p.b))))
# from upper and lower bounds
p = Polyhedron.from_bounds(x, x)
A = np.vstack((A_lb, A_ub))
b = np.vstack((b_lb, b_ub))
self.assertTrue(same_rows(np.hstack((A, b)), np.hstack((p.A, p.b))))
# different size lower and upper bound
y = np.ones((3, 1))
self.assertRaises(ValueError, Polyhedron.from_bounds, x, y)
# from lower bound of not all the variables
indices = [1, 2]
n = 3
p = Polyhedron.from_lower_bound(x, indices, n)
A_lb = np.array([[0., -1., 0.], [0., 0., -1.]])
b_lb = np.array([[-1.], [-1.]])
self.assertTrue(
same_rows(np.hstack((A_lb, b_lb)), np.hstack((p.A, p.b))))
# from lower bound of not all the variables
indices = [0, 2]
n = 3
p = Polyhedron.from_upper_bound(x, indices, n)
A_ub = np.array([[1., 0., 0.], [0., 0., 1.]])
b_ub = np.array([[1.], [1.]])
self.assertTrue(
same_rows(np.hstack((A_ub, b_ub)), np.hstack((p.A, p.b))))
# from upper and lower bounds of not all the variables
indices = [0, 1]
n = 3
p = Polyhedron.from_bounds(x, x, indices, n)
A = np.array([[-1., 0., 0.], [0., -1., 0.], [1., 0., 0.], [0., 1.,
0.]])
b = np.array([[-1.], [-1.], [1.], [1.]])
self.assertTrue(same_rows(np.hstack((A, b)), np.hstack((p.A, p.b))))
# too many indices
indices = [1, 2, 3]
n = 5
self.assertRaises(ValueError, Polyhedron.from_lower_bound, x, indices,
n)
self.assertRaises(ValueError, Polyhedron.from_upper_bound, x, indices,
n)
self.assertRaises(ValueError, Polyhedron.from_bounds, x, x, indices, n)
def test_from_functions(self):
# row vector input
x = np.ones((1,5))
self.assertRaises(ValueError, Polyhedron.from_lower_bound, x)
# from lower bound
x = np.ones(2)
p = Polyhedron.from_lower_bound(x)
A_lb = np.array([[-1., 0.], [0., -1.]])
b_lb = np.array([-1.,-1.])
self.assertTrue(same_rows(
np.column_stack((A_lb, b_lb)),
np.column_stack((p.A, p.b))
))
# from upper bound
p = Polyhedron.from_upper_bound(x)
A_ub = np.array([[1., 0.], [0., 1.]])
b_ub = np.array([1.,1.])
self.assertTrue(same_rows(
np.column_stack((A_ub, b_ub)),
np.column_stack((p.A, p.b))
))
# from upper and lower bounds
p = Polyhedron.from_bounds(x, x)
A = np.vstack((A_lb, A_ub))
b = np.concatenate((b_lb, b_ub))
self.assertTrue(same_rows(
np.column_stack((A, b)),
np.column_stack((p.A, p.b))
))
# different size lower and upper bound
y = np.ones((3,1))
self.assertRaises(ValueError, Polyhedron.from_bounds, x, y)
# from lower bound of not all the variables
indices = [1, 2]
n = 3
p = Polyhedron.from_lower_bound(x, indices, n)
A_lb = np.array([[0., -1., 0.], [0., 0., -1.]])
b_lb = np.array([-1.,-1.])
self.assertTrue(same_rows(
np.column_stack((A_lb, b_lb)),
np.column_stack((p.A, p.b))
))
# from lower bound of not all the variables
indices = [0, 2]
n = 3
p = Polyhedron.from_upper_bound(x, indices, n)
A_ub = np.array([[1., 0., 0.], [0., 0., 1.]])
b_ub = np.array([1.,1.])
self.assertTrue(same_rows(
np.column_stack((A_ub, b_ub)),
np.column_stack((p.A, p.b))
))
# from upper and lower bounds of not all the variables
indices = [0, 1]
n = 3
p = Polyhedron.from_bounds(x, x, indices, n)
A = np.array([[-1., 0., 0.], [0., -1., 0.], [1., 0., 0.], [0., 1., 0.]])
b = np.array([-1.,-1.,1.,1.])
self.assertTrue(same_rows(
np.column_stack((A, b)),
np.column_stack((p.A, p.b))
))
# too many indices
indices = [1, 2, 3]
n = 5
self.assertRaises(ValueError, Polyhedron.from_lower_bound, x, indices, n)
self.assertRaises(ValueError, Polyhedron.from_upper_bound, x, indices, n)
self.assertRaises(ValueError, Polyhedron.from_bounds, x, x, indices, n)
# from symbolic
n = 5
m = 3
x = sp.Matrix([sp.Symbol('x'+str(i), real=True) for i in range(n)])
A = np.random.rand(m, n)
b = np.random.rand(m)
ineq = sp.Matrix(A)*x - sp.Matrix(b)
P = Polyhedron.from_symbolic(x, ineq)
np.testing.assert_array_almost_equal(P.A, A)
np.testing.assert_array_almost_equal(P.b, b)
C = np.random.rand(m, n)
d = np.random.rand(m)
eq = sp.Matrix(C)*x - sp.Matrix(d)
P = Polyhedron.from_symbolic(x, ineq, eq)
np.testing.assert_array_almost_equal(P.A, A)
np.testing.assert_array_almost_equal(P.b, b)
np.testing.assert_array_almost_equal(P.C, C)
np.testing.assert_array_almost_equal(P.d, d)
