def test_dmdc_for_highdim_system(data_drss):
Y, U, A, B, C = data_drss
DMDc = regression.DMDc(svd_rank=7, svd_output_rank=5)
model = Koopman(regressor=DMDc)
model.fit(Y, U)
# Check spectrum
Aest = model.state_transition_matrix
W, V = np.linalg.eig(A)
West, Vest = np.linalg.eig(Aest)
idxTrue = np.argsort(W)
idxEst = np.argsort(West)
assert_allclose(W[idxTrue], West[idxEst], 1e-07, 1e-12)
# Check eigenvector reconstruction
r = 5
Uc, sc, Vch = np.linalg.svd(C, full_matrices=False)
Sc = np.diag(sc[:r])
Cinv = np.dot(Vch[:, :r].T, np.dot(np.linalg.inv(Sc), Uc[:, :r].T))
P = model.projection_matrix_output
Atilde = np.dot(Cinv, np.dot(np.dot(P, np.dot(Aest, P.T)), C))
Wtilde, Vtilde = np.linalg.eig(Atilde)
idxTilde = np.argsort(Wtilde)
assert_allclose(W[idxTrue], Wtilde[idxTilde], 1e-07, 1e-12)
# Evecs may be accurate up to a sign; ensured by seeding random generator
# when producing the data set
assert_allclose(V[:, idxTrue], Vtilde[:, idxTilde], 1e-07, 1e-12)
def test_simulate_accuracy_dmdc(data_2D_linear_control_system):
X, C, _, _ = data_2D_linear_control_system
DMDc = regression.DMDc(svd_rank=3)
model = Koopman(regressor=DMDc).fit(X, C)
n_steps = len(C)
x_pred = model.simulate(X[0, :], C, n_steps=n_steps - 1)
assert_allclose(X[1:n_steps, :], x_pred, 1e-07, 1e-12)
def test_if_dmdc_model_is_accurate_with_known_controlmatrix(
data_2D_linear_control_system, ):
X, C, A, B = data_2D_linear_control_system
model = Koopman()
DMDc = regression.DMDc(svd_rank=3, control_matrix=B)
model = Koopman(regressor=DMDc).fit(X, C)
Aest = model.state_transition_matrix
assert_allclose(Aest, A, 1e-07, 1e-12)