def test_care_g(self):
A = array([[-2, -1], [-1, -1]])
Q = array([[0, 0], [0, 1]])
B = array([[1, 0], [0, 4]])
R = array([[2, 0], [0, 1]])
S = array([[0, 0], [0, 0]])
E = array([[2, 1], [1, 2]])
X, L, G = care(A, B, Q, R, S, E)
# print "The solution obtained is", X
assert_array_almost_equal(dot(A.T,dot(X,E)) + dot(E.T,dot(X,A)) - \
dot(dot(dot(E.T,dot(X,B))+S,inv(R) ) ,
dot(B.T,dot(X,E))+S.T ) + Q , \
zeros((2,2)))
assert_array_almost_equal(dot(inv(R), dot(B.T, dot(X, E)) + S.T), G)
A = array([[-2, -1], [-1, -1]])
Q = array([[0, 0], [0, 1]])
B = array([[1], [0]])
R = 1
S = array([[1], [0]])
E = array([[2, 1], [1, 2]])
X, L, G = care(A, B, Q, R, S, E)
# print "The solution obtained is", X
assert_array_almost_equal(dot(A.T,dot(X,E)) + dot(E.T,dot(X,A)) - \
dot( dot( dot(E.T,dot(X,B))+S,1/R ) , dot(B.T,dot(X,E))+S.T ) \
+ Q , zeros((2,2)))
assert_array_almost_equal(dot(1 / R, dot(B.T, dot(X, E)) + S.T), G)
def test_care_g2(self):
A = array([[-2, -1],[-1, -1]])
Q = array([[0, 0],[0, 1]])
B = array([[1],[0]])
R = 1
S = array([[1],[0]])
E = array([[2, 1],[1, 2]])
X,L,G = care(A,B,Q,R,S,E)
# print("The solution obtained is", X)
Gref = 1/R * (B.T @ X @ E + S.T)
assert_array_almost_equal(
A.T @ X @ E + E.T @ X @ A
- (E.T @ X @ B + S) @ Gref + Q ,
zeros((2,2)))
assert_array_almost_equal(Gref , G)
# Compare methods
if slycot_check():
X_scipy, L_scipy, G_scipy = care(
A, B, Q, R, S, E, method='scipy')
X_slycot, L_slycot, G_slycot = care(
A, B, Q, R, S, E, method='slycot')
assert_array_almost_equal(X_scipy, X_slycot)
assert_array_almost_equal(L_scipy, L_slycot)
assert_array_almost_equal(G_scipy, G_slycot)
def test_care_g(self):
A = array([[-2, -1], [-1, -1]])
Q = array([[0, 0], [0, 1]])
B = array([[1, 0], [0, 4]])
R = array([[2, 0], [0, 1]])
S = array([[0, 0], [0, 0]])
E = array([[2, 1], [1, 2]])
X, L, G = care(A, B, Q, R, S, E)
# print("The solution obtained is", X)
Gref = solve(R, B.T.dot(X).dot(E) + S.T)
assert_array_almost_equal(Gref, G)
assert_array_almost_equal(
A.T.dot(X).dot(E) + E.T.dot(X).dot(A) -
(E.T.dot(X).dot(B) + S).dot(Gref) + Q, zeros((2, 2)))
A = array([[-2, -1], [-1, -1]])
Q = array([[0, 0], [0, 1]])
B = array([[1], [0]])
R = 1
S = array([[1], [0]])
E = array([[2, 1], [1, 2]])
X, L, G = care(A, B, Q, R, S, E)
# print("The solution obtained is", X)
Gref = 1 / R * (B.T.dot(X).dot(E) + S.T)
assert_array_almost_equal(
A.T.dot(X).dot(E) + E.T.dot(X).dot(A) -
(E.T.dot(X).dot(B) + S).dot(Gref) + Q, zeros((2, 2)))
assert_array_almost_equal(Gref, G)
def test_care_g(self):
A = array([[-2, -1],[-1, -1]])
Q = array([[0, 0],[0, 1]])
B = array([[1, 0],[0, 4]])
R = array([[2, 0],[0, 1]])
S = array([[0, 0],[0, 0]])
E = array([[2, 1],[1, 2]])
X,L,G = care(A,B,Q,R,S,E)
# print "The solution obtained is", X
assert_array_almost_equal(dot(A.T,dot(X,E)) + dot(E.T,dot(X,A)) - \
dot(dot(dot(E.T,dot(X,B))+S,inv(R) ) ,
dot(B.T,dot(X,E))+S.T ) + Q , \
zeros((2,2)))
assert_array_almost_equal(dot( inv(R) , dot(B.T,dot(X,E)) + S.T) , G)
A = array([[-2, -1],[-1, -1]])
Q = array([[0, 0],[0, 1]])
B = array([[1],[0]])
R = 1
S = array([[1],[0]])
E = array([[2, 1],[1, 2]])
X,L,G = care(A,B,Q,R,S,E)
# print "The solution obtained is", X
assert_array_almost_equal(dot(A.T,dot(X,E)) + dot(E.T,dot(X,A)) - \
dot( dot( dot(E.T,dot(X,B))+S,1/R ) , dot(B.T,dot(X,E))+S.T ) \
+ Q , zeros((2,2)))
assert_array_almost_equal(dot( 1/R , dot(B.T,dot(X,E)) + S.T) , G)
def test_care_g(self):
A = matrix([[-2, -1],[-1, -1]])
Q = matrix([[0, 0],[0, 1]])
B = matrix([[1, 0],[0, 4]])
R = matrix([[2, 0],[0, 1]])
S = matrix([[0, 0],[0, 0]])
E = matrix([[2, 1],[1, 2]])
X,L,G = care(A,B,Q,R,S,E)
# print("The solution obtained is", X)
assert_array_almost_equal(
A.T * X * E + E.T * X * A -
(E.T * X * B + S) * solve(R, B.T * X * E + S.T) + Q, zeros((2,2)))
assert_array_almost_equal(solve(R, B.T * X * E + S.T), G)
A = matrix([[-2, -1],[-1, -1]])
Q = matrix([[0, 0],[0, 1]])
B = matrix([[1],[0]])
R = 1
S = matrix([[1],[0]])
E = matrix([[2, 1],[1, 2]])
X,L,G = care(A,B,Q,R,S,E)
# print("The solution obtained is", X)
assert_array_almost_equal(
A.T * X * E + E.T * X * A -
(E.T * X * B + S) / R * (B.T * X * E + S.T) + Q , zeros((2,2)))
assert_array_almost_equal(dot( 1/R , dot(B.T,dot(X,E)) + S.T) , G)
def test_care_g(self):
A = matrix([[-2, -1], [-1, -1]])
Q = matrix([[0, 0], [0, 1]])
B = matrix([[1, 0], [0, 4]])
R = matrix([[2, 0], [0, 1]])
S = matrix([[0, 0], [0, 0]])
E = matrix([[2, 1], [1, 2]])
X, L, G = care(A, B, Q, R, S, E)
# print("The solution obtained is", X)
assert_array_almost_equal(
A.T * X * E + E.T * X * A - (E.T * X * B + S) * inv(R) *
(B.T * X * E + S.T) + Q, zeros((2, 2)))
assert_array_almost_equal(inv(R) * (B.T * X * E + S.T), G)
A = matrix([[-2, -1], [-1, -1]])
Q = matrix([[0, 0], [0, 1]])
B = matrix([[1], [0]])
R = 1
S = matrix([[1], [0]])
E = matrix([[2, 1], [1, 2]])
X, L, G = care(A, B, Q, R, S, E)
# print("The solution obtained is", X)
assert_array_almost_equal(
A.T * X * E + E.T * X * A - (E.T * X * B + S) / R *
(B.T * X * E + S.T) + Q, zeros((2, 2)))
assert_array_almost_equal(dot(1 / R, dot(B.T, dot(X, E)) + S.T), G)
def test_care(self, matarrayin):
"""Test stabilizing and anti-stabilizing feedbacks, continuous"""
A = matarrayin(np.diag([1, -1]))
B = matarrayin(np.identity(2))
Q = matarrayin(np.identity(2))
R = matarrayin(np.identity(2))
S = matarrayin(np.zeros((2, 2)))
E = matarrayin(np.identity(2))
X, L, G = care(A, B, Q, R, S, E, stabilizing=True)
assert np.all(np.real(L) < 0)
X, L, G = care(A, B, Q, R, S, E, stabilizing=False)
assert np.all(np.real(L) > 0)
def test_care(self):
#unit test for stabilizing and anti-stabilizing feedbacks
#continuous-time
A = np.diag([1,-1])
B = np.identity(2)
Q = np.identity(2)
R = np.identity(2)
S = 0 * B
E = np.identity(2)
X, L , G = care(A, B, Q, R, S, E, stabilizing=True)
assert np.all(np.real(L) < 0)
X, L , G = care(A, B, Q, R, S, E, stabilizing=False)
assert np.all(np.real(L) > 0)
def test_care(self):
#unit test for stabilizing and anti-stabilizing feedbacks
#continuous-time
A = np.diag([1,-1])
B = np.identity(2)
Q = np.identity(2)
R = np.identity(2)
S = 0 * B
E = np.identity(2)
X, L , G = care(A, B, Q, R, S, E, stabilizing=True)
assert np.all(np.real(L) < 0)
X, L , G = care(A, B, Q, R, S, E, stabilizing=False)
assert np.all(np.real(L) > 0)
def test_care(self, matarrayin):
"""Test stabilizing and anti-stabilizing feedback, continuous"""
A = matarrayin(np.diag([1, -1]))
B = matarrayin(np.identity(2))
Q = matarrayin(np.identity(2))
R = matarrayin(np.identity(2))
S = matarrayin(np.zeros((2, 2)))
E = matarrayin(np.identity(2))
X, L, G = care(A, B, Q, R, S, E, stabilizing=True)
assert np.all(np.real(L) < 0)
if slycot_check():
X, L, G = care(A, B, Q, R, S, E, stabilizing=False)
assert np.all(np.real(L) > 0)
else:
with pytest.raises(ControlArgument, match="'scipy' not valid"):
X, L, G = care(A, B, Q, R, S, E, stabilizing=False)
def test_care(self):
A = array([[-2, -1], [-1, -1]])
Q = array([[0, 0], [0, 1]])
B = array([[1, 0], [0, 4]])
X, L, G = care(A, B, Q)
# print("The solution obtained is", X)
M = A.T.dot(X) + X.dot(A) - X.dot(B).dot(B.T).dot(X) + Q
assert_array_almost_equal(M, zeros((2, 2)))
assert_array_almost_equal(B.T.dot(X), G)
def test_care(self):
A = matrix([[-2, -1], [-1, -1]])
Q = matrix([[0, 0], [0, 1]])
B = matrix([[1, 0], [0, 4]])
X, L, G = care(A, B, Q)
# print("The solution obtained is", X)
assert_array_almost_equal(A.T * X + X * A - X * B * B.T * X + Q,
zeros((2, 2)))
assert_array_almost_equal(B.T * X, G)
def test_care(self):
A = array([[-2, -1], [-1, -1]])
Q = array([[0, 0], [0, 1]])
B = array([[1, 0], [0, 4]])
X, L, G = care(A, B, Q)
# print "The solution obtained is", X
assert_array_almost_equal(dot(A.T,X) + dot(X,A) - \
dot(X,dot(B,dot(B.T,X))) + Q , zeros((2,2)))
assert_array_almost_equal(dot(B.T, X), G)
def test_care(self):
A = array([[-2, -1],[-1, -1]])
Q = array([[0, 0],[0, 1]])
B = array([[1, 0],[0, 4]])
X, L, G = care(A, B, Q)
# print("The solution obtained is", X)
M = A.T @ X + X @ A - X @ B @ B.T @ X + Q
assert_array_almost_equal(M,
zeros((2,2)))
assert_array_almost_equal(B.T @ X, G)
# Compare methods
if slycot_check():
X_scipy, L_scipy, G_scipy = care(A, B, Q, method='scipy')
X_slycot, L_slycot, G_slycot = care(A, B, Q, method='slycot')
assert_array_almost_equal(X_scipy, X_slycot)
assert_array_almost_equal(np.sort(L_scipy), np.sort(L_slycot))
assert_array_almost_equal(G_scipy, G_slycot)
def test_care(self):
A = array([[-2, -1],[-1, -1]])
Q = array([[0, 0],[0, 1]])
B = array([[1, 0],[0, 4]])
X,L,G = care(A,B,Q)
# print "The solution obtained is", X
assert_array_almost_equal(dot(A.T,X) + dot(X,A) - \
dot(X,dot(B,dot(B.T,X))) + Q , zeros((2,2)))
assert_array_almost_equal(dot(B.T,X) , G)
def test_care(self):
A = matrix([[-2, -1],[-1, -1]])
Q = matrix([[0, 0],[0, 1]])
B = matrix([[1, 0],[0, 4]])
X,L,G = care(A,B,Q)
# print("The solution obtained is", X)
assert_array_almost_equal(A.T * X + X * A - X * B * B.T * X + Q,
zeros((2,2)))
assert_array_almost_equal(B.T * X, G)
def test_raise(self):
""" Test exception raise for invalid inputs """
# correct shapes and forms
A = array([[1, 0], [-1, -1]])
Q = array([[2, 1], [1, 2]])
C = array([[1, 0], [0, 1]])
E = array([[2, 1], [1, 2]])
# these fail
Afq = array([[1, 0, 0], [-1, -1, 0]])
Qfq = array([[2, 1, 0], [1, 2, 0]])
Qfs = array([[2, 1], [-1, 2]])
Cfd = array([[1, 0, 0], [0, 1, 0]])
Efq = array([[2, 1, 0], [1, 2, 0]])
for cdlyap in [lyap, dlyap]:
with pytest.raises(ControlDimension):
cdlyap(Afq, Q)
with pytest.raises(ControlDimension):
cdlyap(A, Qfq)
with pytest.raises(ControlArgument):
cdlyap(A, Qfs)
with pytest.raises(ControlDimension):
cdlyap(Afq, Q, C)
with pytest.raises(ControlDimension):
cdlyap(A, Qfq, C)
with pytest.raises(ControlDimension):
cdlyap(A, Q, Cfd)
with pytest.raises(ControlDimension):
cdlyap(A, Qfq, None, E)
with pytest.raises(ControlDimension):
cdlyap(A, Q, None, Efq)
with pytest.raises(ControlArgument):
cdlyap(A, Qfs, None, E)
with pytest.raises(ControlArgument):
cdlyap(A, Q, C, E)
B = array([[1, 0], [0, 1]])
Bf = array([[1, 0], [0, 1], [1, 1]])
R = Q
Rfs = Qfs
Rfq = Qfq
S = array([[0, 0], [0, 0]])
Sf = array([[0, 0, 0], [0, 0, 0]])
E = array([[2, 1], [1, 2]])
Ef = array([[2, 1], [1, 2], [1, 2]])
with pytest.raises(ControlDimension):
care(Afq, B, Q)
with pytest.raises(ControlDimension):
care(A, B, Qfq)
with pytest.raises(ControlDimension):
care(A, Bf, Q)
with pytest.raises(ControlDimension):
care(1, B, 1)
with pytest.raises(ControlArgument):
care(A, B, Qfs)
with pytest.raises(ControlArgument):
dare(A, B, Q, Rfs)
for cdare in [care, dare]:
with pytest.raises(ControlDimension):
cdare(Afq, B, Q, R, S, E)
with pytest.raises(ControlDimension):
cdare(A, B, Qfq, R, S, E)
with pytest.raises(ControlDimension):
cdare(A, Bf, Q, R, S, E)
with pytest.raises(ControlDimension):
cdare(A, B, Q, R, S, Ef)
with pytest.raises(ControlDimension):
cdare(A, B, Q, Rfq, S, E)
with pytest.raises(ControlDimension):
cdare(A, B, Q, R, Sf, E)
with pytest.raises(ControlArgument):
cdare(A, B, Qfs, R, S, E)
with pytest.raises(ControlArgument):
cdare(A, B, Q, Rfs, S, E)
