def test_unused_variable(self):
m = pyo.ConcreteModel()
m.x = pyo.Var(initialize=1.0)
m.y = pyo.Var(initialize=1.0)
m.z = pyo.Var(initialize=1.0)
m.eqn = pyo.Constraint(expr=m.x**2 + m.y**2 == 1.0)
variables = [m.x, m.y, m.z]
expected_hess = np.array([[2, 0, 0], [0, 2, 0], [0, 0, 0]])
hess = get_hessian_of_constraint(m.eqn, variables).toarray()
np.testing.assert_allclose(hess, expected_hess, rtol=1e-8)
def test_simple_model_1(self):
model = SimpleModel1()
m = model.make_model()
m.x.set_value(2.0)
m.y.set_value(2.0)
con = m.residual_eqn
expected_hess = np.array([[2.0, 0.0], [0.0, 2.0]])
hess = get_hessian_of_constraint(con)
self.assertTrue(np.all(expected_hess == hess.toarray()))
expected_hess = np.array([[2.0]])
hess = get_hessian_of_constraint(con, [m.x])
self.assertTrue(np.all(expected_hess == hess.toarray()))
con = m.external_eqn
expected_hess = np.array([[0.0, 1.0], [1.0, 0.0]])
hess = get_hessian_of_constraint(con)
self.assertTrue(np.all(expected_hess == hess.toarray()))
def test_explicit_zeros(self):
m = pyo.ConcreteModel()
m.x = pyo.Var(initialize=1.0)
m.y = pyo.Var(initialize=0.0)
m.eqn = pyo.Constraint(expr=m.x**2 + m.y**3 == 1.0)
variables = [m.x, m.y]
row = np.array([0, 1])
col = np.array([0, 1])
data = np.array([2.0, 0.0])
expected_hess = sps.coo_matrix((data, (row, col)), shape=(2, 2))
hess = get_hessian_of_constraint(m.eqn, variables)
np.testing.assert_allclose(hess.row, row, atol=0)
np.testing.assert_allclose(hess.col, col, atol=0)
np.testing.assert_allclose(hess.data, data, rtol=1e-8)
def test_polynomial(self):
m = pyo.ConcreteModel()
n_x = 3
x1 = 1.1
x2 = 1.2
x3 = 1.3
m.x = pyo.Var(range(1, n_x + 1), initialize={1: x1, 2: x2, 3: x3})
m.eqn = pyo.Constraint(expr=5 * (m.x[1]**5) + # T1
5 * (m.x[1]**4) * (m.x[2]) + # T2
5 * (m.x[1]**3) * (m.x[2]) * (m.x[3]) + # T3
5 * (m.x[1]) * (m.x[2]**2) * (m.x[3]**2) + # T4
4 * (m.x[1]**2) * (m.x[2]) * (m.x[3]) + # T5
4 * (m.x[2]**2) * (m.x[3]**2) + # T6
4 * (m.x[3]**4) + # T7
3 * (m.x[1]) * (m.x[2]) * (m.x[3]) + # T8
3 * (m.x[2]**3) + # T9
3 * (m.x[2]**2) * (m.x[3]) + # T10
2 * (m.x[1]) * (m.x[2]) + # T11
2 * (m.x[2]) * (m.x[3]) # T12
== 0)
rcd = []
rcd.append((
0,
0,
(
# wrt x1, x1
5 * 5 * 4 * x1**3 + # T1
5 * 4 * 3 * x1**2 * x2 + # T2
5 * 3 * 2 * x1 * x2 * x3 + # T3
4 * 2 * 1 * x2 * x3 # T5
)))
rcd.append((
1,
1,
(
# wrt x2, x2
5 * x1 * 2 * x3**2 + # T4
4 * 2 * x3**2 + # T6
3 * 3 * 2 * x2 + # T9
3 * 2 * x3 # T10
)))
rcd.append((
2,
2,
(
# wrt x3, x3
5 * x1 * x2**2 * 2 + # T4
4 * x2**2 * 2 + # T6
4 * 4 * 3 * x3**2 # T7
)))
rcd.append((
1,
0,
(
# wrt x2, x1
5 * 4 * x1**3 + # T2
5 * 3 * x1**2 * x3 + # T3
5 * 2 * x2 * x3**2 + # T4
4 * 2 * x1 * x3 + # T5
3 * x3 + # T8
2 # T11
)))
rcd.append((
2,
0,
(
# wrt x3, x1
5 * 3 * x1**2 * x2 + # T3
5 * x2**2 * 2 * x3 + # T4
4 * 2 * x1 * x2 + # T5
3 * x2 # T8
)))
rcd.append((
2,
1,
(
# wrt x3, x2
5 * x1**3 + # T3
5 * x1 * 2 * x2 * 2 * x3 + # T4
4 * x1**2 + # T5
4 * 2 * x2 * 2 * x3 + # T6
3 * x1 + # T8
3 * 2 * x2 + # T10
2 # T12
)))
row = [r for r, _, _ in rcd]
col = [c for _, c, _ in rcd]
data = [d for _, _, d in rcd]
expected_hess = sps.coo_matrix((data, (row, col)), shape=(n_x, n_x))
expected_hess_array = expected_hess.toarray()
expected_hess_array = (expected_hess_array +
np.transpose(expected_hess_array) -
np.diag(np.diagonal(expected_hess_array)))
hess = get_hessian_of_constraint(m.eqn, list(m.x.values()))
hess_array = hess.toarray()
np.testing.assert_allclose(expected_hess_array, hess_array, rtol=1e-8)
