def test_29(self):
alpha = np.random.randn()
N = 7
M = 10
X0 = np.random.randn(N, M)
A = np.random.randn(N, 1)
Bg = np.random.randn(M, 4)
B = Bg.dot(Bg.T)
C = A * X0.dot(B) + alpha * X0
X1 = linalg.solve_symmetric_sylvester(A, B, C, alpha)
assert mse(X0, X1) < 1e-12
Lambda, Q = np.linalg.eigh(B)
X1 = linalg.solve_symmetric_sylvester(A, (Lambda, Q), C, alpha)
assert mse(X0, X1) < 1e-12
def test_30(self):
alpha = np.random.randn()
N = 7
M = 10
X0 = np.random.randn(N, M)
Ag = np.random.randn(4, N)
A = Ag.T.dot(Ag)
B = np.random.randn(1, M)
C = A.dot(X0) * B + alpha * X0
X1 = linalg.solve_symmetric_sylvester(A, B, C, alpha)
assert mse(X0, X1) < 1e-12
Lambda, Q = np.linalg.eigh(A)
X1 = linalg.solve_symmetric_sylvester((Lambda, Q), B, C, alpha)
assert mse(X0, X1) < 1e-12
def test_28(self):
alpha = np.random.randn()
N = 7
M = 10
X0 = np.random.randn(N, M)
A = np.random.randn(N, 1)
B = np.random.randn(1, M)
C = A * X0 * B + alpha * X0
X1 = linalg.solve_symmetric_sylvester(A, B, C, alpha)
assert mse(X0, X1) < 1e-14
A = A[:, 0]
B = B[0]
X1 = linalg.solve_symmetric_sylvester(A, B, C, alpha)
assert mse(X0, X1) < 1e-14
def test_31(self):
alpha = np.random.randn()
N = 8
M = 11
X0 = np.random.randn(N, M)
Ag = np.random.randn(4, N)
A = Ag.T.dot(Ag)
Bg = np.random.randn(M, 4)
B = Bg.dot(Bg.T)
C = A.dot(X0).dot(B) + alpha * X0
X1 = linalg.solve_symmetric_sylvester(A, B, C, alpha)
assert mse(X0, X1) < 1e-12
LambdaA, QA = np.linalg.eigh(A)
LambdaB, QB = np.linalg.eigh(B)
X1 = linalg.solve_symmetric_sylvester((LambdaA, QA), (LambdaB, QB), C,
alpha)
assert mse(X0, X1) < 1e-12