def test_sigma_max(self) -> None:
"""Test sigma_max.
"""
expr = cp.sigma_max(self.A)
self.A.value = [[1, 0], [0, 2]]
self.assertItemsAlmostEqual(expr.grad[self.A].toarray(), [0, 0, 0, 1])
self.A.value = [[1, 0], [0, 1]]
self.assertItemsAlmostEqual(expr.grad[self.A].toarray(), [1, 0, 0, 0])
def test_largest_singvalue(self) -> None:
np.random.seed(3)
rows, cols = 3, 4
A = np.random.randn(rows, cols)
A_sv = np.linalg.svd(A, compute_uv=False)
X = cp.Variable(shape=(rows, cols))
sigma = cp.suppfunc(X, [cp.sigma_max(X) <= 1])
Y = cp.Variable(shape=(rows, cols))
cons = [Y == A]
prob = cp.Problem(cp.Minimize(sigma(Y)), cons)
prob.solve(solver='SCS', eps=1e-8)
actual = prob.value
expect = np.sum(A_sv)
self.assertLessEqual(abs(actual - expect), 1e-6)
def addObjectiveValue(self, sls, objective_value):
C1 = sls._system_model._C1
D12 = sls._system_model._D12
Phi_x = sls._Phi_x
Phi_u = sls._Phi_u
horizon = len(Phi_x)
M = cp.hstack(
[C1 @ Phi_x[k] + D12 @ Phi_u[k] for k in range(1, horizon)])
self._objective_expression = cp.sigma_max(M)
return objective_value + self._objective_expression
