def test_hessian_SimpleModel2(self):
model = SimpleModel2()
m = model.make_model()
x_init_list = [
[-5.0], [-4.0], [-3.0], [-1.5], [0.5], [1.0], [2.0], [3.5]
]
external_model = ExternalPyomoModel(
[m.x], [m.y], [m.residual_eqn], [m.external_eqn],
)
for x in x_init_list:
external_model.set_input_values(x)
hess = external_model.evaluate_hessians_of_residuals()
self.assertAlmostEqual(
hess[0][0, 0],
model.evaluate_hessian(x[0]),
delta=1e-7,
)
def test_evaluate_hessian_equality_constraints_order(self):
model = Model2by2()
m = model.make_model()
m.x[0].set_value(1.0)
m.x[1].set_value(2.0)
m.y[0].set_value(3.0)
m.y[1].set_value(4.0)
x0_init_list = [-5.0, -3.0, 0.5, 1.0, 2.5]
x1_init_list = [0.5, 1.0, 1.5, 2.5, 4.1]
lam_init_list = [-2.5, -0.5, 0.0, 1.0, 2.0]
init_list = list(
itertools.product(x0_init_list, x1_init_list, lam_init_list))
external_model = ExternalPyomoModel(
list(m.x.values()),
list(m.y.values()),
list(m.residual_eqn.values()),
list(m.external_eqn.values()),
)
for x0, x1, lam in init_list:
x = [x0, x1]
lam = [lam]
external_model.set_equality_constraint_multipliers(lam)
external_model.set_input_values(x)
# Using evaluate_hessian_equality_constraints, which calculates
# external multiplier values, we can calculate the correct Hessian
# regardless of the order in which primal and dual variables are
# set.
hess = external_model.evaluate_hessian_equality_constraints()
pred_hess = model.calculate_reduced_lagrangian_hessian(lam, x)
# This test asserts that we are doing the block reduction properly.
np.testing.assert_allclose(hess.toarray(),
np.tril(pred_hess),
rtol=1e-8)
from_individual = external_model.evaluate_hessians_of_residuals()
hl_from_individual = sum(l * h
for l, h in zip(lam, from_individual))
# This test asserts that the block reduction is correct.
np.testing.assert_allclose(hess.toarray(),
np.tril(hl_from_individual),
rtol=1e-8)
def test_reduced_hessian_lagrangian(self):
model = Model2by2()
m = model.make_model()
m.x[0].set_value(1.0)
m.x[1].set_value(2.0)
m.y[0].set_value(3.0)
m.y[1].set_value(4.0)
x0_init_list = [-5.0, -3.0, 0.5, 1.0, 2.5]
x1_init_list = [0.5, 1.0, 1.5, 2.5, 4.1]
lam_init_list = [-2.5, -0.5, 0.0, 1.0, 2.0]
init_list = list(
itertools.product(x0_init_list, x1_init_list, lam_init_list))
external_model = ExternalPyomoModel(
list(m.x.values()),
list(m.y.values()),
list(m.residual_eqn.values()),
list(m.external_eqn.values()),
)
for x0, x1, lam in init_list:
x = [x0, x1]
lam = [lam]
external_model.set_input_values(x)
# Same comment as previous test regarding calculation order
external_model.set_external_constraint_multipliers(lam)
hlxx, hlxy, hlyy = \
external_model.get_full_space_lagrangian_hessians()
hess = external_model.calculate_reduced_hessian_lagrangian(
hlxx, hlxy, hlyy)
pred_hess = model.calculate_reduced_lagrangian_hessian(lam, x)
# This test asserts that we are doing the block reduction properly.
np.testing.assert_allclose(np.array(hess), pred_hess, rtol=1e-8)
from_individual = external_model.evaluate_hessians_of_residuals()
hl_from_individual = sum(l * h
for l, h in zip(lam, from_individual))
# This test asserts that the block reduction is correct.
np.testing.assert_allclose(np.array(hess),
hl_from_individual,
rtol=1e-8)
def test_hessian_SimpleModel2x2_1(self):
model = SimpleModel2by2_1()
m = model.make_model()
m.x[0].set_value(1.0)
m.x[1].set_value(2.0)
m.y[0].set_value(3.0)
m.y[1].set_value(4.0)
x0_init_list = [-5.0, -3.0, 0.5, 1.0, 2.5]
x1_init_list = [-4.5, -2.3, 0.0, 1.0, 4.1]
x_init_list = list(itertools.product(x0_init_list, x1_init_list))
external_model = ExternalPyomoModel(
list(m.x.values()),
list(m.y.values()),
list(m.residual_eqn.values()),
list(m.external_eqn.values()),
)
for x in x_init_list:
external_model.set_input_values(x)
hess = external_model.evaluate_hessians_of_residuals()
expected_hess = model.evaluate_hessian(x)
np.testing.assert_allclose(hess, expected_hess, rtol=1e-8)
