def H(self):
k = self.neqs
Lk = tsa.elimination_matrix(k)
Kkk = tsa.commutation_matrix(k, k)
Ik = np.eye(k)
# B = chain_dot(Lk, np.eye(k**2) + commutation_matrix(k, k),
# np.kron(self.P, np.eye(k)), Lk.T)
# return np.dot(Lk.T, L.inv(B))
B = chain_dot(Lk, np.dot(np.kron(Ik, self.P), Kkk) + np.kron(self.P, Ik), Lk.T)
return np.dot(Lk.T, L.inv(B))
def H(self):
k = self.neqs
Lk = tsa.elimination_matrix(k)
Kkk = tsa.commutation_matrix(k, k)
Ik = np.eye(k)
# B = chain_dot(Lk, np.eye(k**2) + commutation_matrix(k, k),
# np.kron(self.P, np.eye(k)), Lk.T)
# return np.dot(Lk.T, L.inv(B))
B = chain_dot(Lk,
np.dot(np.kron(Ik, self.P), Kkk) + np.kron(self.P, Ik),
Lk.T)
return np.dot(Lk.T, L.inv(B))
def test_commutation_matrix():
m = np.random.randn(4, 3)
K = tools.commutation_matrix(4, 3)
assert(np.array_equal(vec(m.T), np.dot(K, vec(m))))
