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_full_space_lagrangian_hessians(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)
# Note that these multiplier calculations are dependent on x,
# so if we switch their order, we will get "wrong" answers.
# (This is wrong in the sense that the residual and external
# multipliers won't necessarily correspond).
external_model.set_external_constraint_multipliers(lam)
hlxx, hlxy, hlyy = \
external_model.get_full_space_lagrangian_hessians()
pred_hlxx, pred_hlxy, pred_hlyy = \
model.calculate_full_space_lagrangian_hessians(lam, x)
# TODO: Is comparing the array representation sufficient here?
# Should I make sure I get the sparse representation I expect?
np.testing.assert_allclose(hlxx.toarray(), pred_hlxx, rtol=1e-8)
np.testing.assert_allclose(hlxy.toarray(), pred_hlxy, rtol=1e-8)
np.testing.assert_allclose(hlyy.toarray(), pred_hlyy, rtol=1e-8)
