def test_sg03ad_ex1d(self):
""" Example 1 discrete case"""
n = 100
Xref = np.ones((n, n))
U = np.tril(Xref)
for t in range(0, 50, 10):
A = 2**(-t) * np.eye(n) + np.diag(np.arange(1., n + 1.)) + U.T
E = np.eye(n) + 2**(-t) * U
Y = A.T.dot(Xref).dot(A) - E.T.dot(Xref).dot(E)
Q = np.zeros((n, n))
Z = np.zeros((n, n))
A, E, Q, Z, X, scale, sep, ferr, alphar, alphai, beta = \
synthesis.sg03ad('D', 'B', 'N', 'N', 'L', n, A, E, Q, Z, Y)
assert_almost_equal(X, Xref)
def test_sg03ad_a(self):
# Example 1
n = 100
Xref = np.ones((n,n))
U = np.tril(Xref)
for t in range(0, 50, 10):
A = 2.0**(-t) - np.eye(n) + np.diag(range(1,n+1)) + U.T
E = np.eye(n) + 2**(-t)*U
Y = A.T.dot(Xref).dot(E) + E.T.dot(Xref).dot(A)
Q = np.zeros((n,n))
Z = np.zeros((n,n))
A, E, Q, Z, X, scale, sep, ferr, alphar, alphai, beta = \
synthesis.sg03ad('C', 'B', 'N', 'N', 'L', n, A, E, Q, Z, Y)
assert_almost_equal(Xref, X)
def test_sg03ad_3(self):
n = 3
A = np.matrix([[3.0, 1.0, 1.0], [1.0, 3.0, 0.0], [1.0, 0.0, 2.0]])
E = np.matrix([[1.0, 3.0, 0.0], [3.0, 2.0, 1.0], [1.0, 0.0, 1.0]])
Y = np.matrix([[64.0, 73.0, 28.0], [73.0, 70.0, 25.0],
[28.0, 25.0, 18.0]])
Xref = np.array([[-2.0000, -1.0000,
0.0000], [-1.0000, -3.0000, -1.0000],
[0.0000, -1.0000, -3.0000]])
Q = np.matrix(np.zeros((3, 3)))
Z = np.matrix(np.zeros((3, 3)))
A, E, Q, Z, X, scale, sep, ferr, alphar, alphai, beta = \
synthesis.sg03ad('C', 'B', 'N', 'N', 'L', n, A, E, Q, Z, -Y)
#print(A, E, Q, Z, X, scale, sep)
assert_almost_equal(X, Xref)