def test_minimal_realization_State():
M = array([[-6.5, 0.5, 6.5, -6.5, 0., 1., 0.],
[-0.5, -5.5, -5.5, 5.5, 2., 1., 2.],
[-0.5, 0.5, 0.5, -6.5, 3., 4., 3.],
[-0.5, 0.5, -5.5, -0.5, 3., 2., 3.],
[1., 1., 0., 0., 0., 0., 0.]])
G = State(*matrix_slice(M, (1, 4), corner='sw'))
H = minimal_realization(G)
assert H.a.shape == (2, 2)
#
G = State(
array([[0., 1., 0., 0., 0.], [-0.1, -0.5, 1., -1., 0.],
[0., 0., 0., 1., 0.], [0., 0., 0., 0., 1.],
[0., 3.5, 1., -2., 2.]]), array([[0.], [1.], [0.], [0.], [1.]]),
array([[0., 3.5, 1., -1., 0.]]), array([[1.]]))
H = minimal_realization(G)
assert H.a.shape == (4, 4)
#
G = State(
array([[-2., 0., 0., 0.], [0., 0., 1., 0.], [0., 0., 0., 1.],
[0., -12., 4., 3.]]),
array([[1., 0.], [0., 0.], [0., 0.], [0., 1.]]),
array([[1., -9., 0., 0.], [0., -20., 0., 5.]]),
array([[0., 0.], [0., 1.]]))
H = minimal_realization(G)
assert H.a.shape == (3, 3)
def test_minimal_realization_State():
M = array([[-6.5, 0.5, 6.5, -6.5, 0., 1., 0.],
[-0.5, -5.5, -5.5, 5.5, 2., 1., 2.],
[-0.5, 0.5, 0.5, -6.5, 3., 4., 3.],
[-0.5, 0.5, -5.5, -0.5, 3., 2., 3.],
[1., 1., 0., 0., 0., 0., 0.]])
G = State(*matrix_slice(M, (1, 4), corner='sw'))
H = minimal_realization(G)
assert H.a.shape == (2, 2)
#
G = State(array([[0., 1., 0., 0., 0.],
[-0.1, -0.5, 1., -1., 0.],
[0., 0., 0., 1., 0.],
[0., 0., 0., 0., 1.],
[0., 3.5, 1., -2., 2.]]),
array([[0.], [1.], [0.], [0.], [1.]]),
array([[0., 3.5, 1., -1., 0.]]),
array([[1.]]))
H = minimal_realization(G)
assert H.a.shape == (4, 4)
#
G = State(array([[-2., 0., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.],
[0., -12., 4., 3.]]),
array([[1., 0.], [0., 0.], [0., 0.], [0., 1.]]),
array([[1., -9., 0., 0.], [0., -20., 0., 5.]]),
array([[0., 0.], [0., 1.]]))
H = minimal_realization(G)
assert H.a.shape == (3, 3)
def test_minimal_realization_Transfer():
G = Transfer(
[1., -8., 28., -58., 67., -30.],
poly([1, 2, 3., 2, 3., 4, 1 + (2 + 1e-6) * 1j, 1 - (2 + 1e-6) * 1j]))
H_f = minimal_realization(G)
assert_almost_equal(H_f.num, array([[1]]))
H_nf = minimal_realization(G, tol=1e-7)
assert_almost_equal(H_nf.num, array([[1., -7., 21., -37., 30.]]))
def test_minimal_realization_Transfer():
G = Transfer([1., -8., 28., -58., 67., -30.],
poly([1, 2, 3., 2, 3., 4, 1+(2+1e-6)*1j, 1-(2+1e-6)*1j]))
H_f = minimal_realization(G)
assert_almost_equal(H_f.num, array([[1]]))
H_nf = minimal_realization(G, tol=1e-7)
assert_almost_equal(H_nf.num, array([[1., -7., 21., -37., 30.]]))
H = minimal_realization(Transfer(eye(4)))
assert H._isgain
assert not H._isSISO
H = minimal_realization(State(eye(4)))
assert H._isgain
assert not H._isSISO
def test_minimal_realization_State():
M = array([[-6.5, 0.5, 6.5, -6.5, 0., 1., 0.],
[-0.5, -5.5, -5.5, 5.5, 2., 1., 2.],
[-0.5, 0.5, 0.5, -6.5, 3., 4., 3.],
[-0.5, 0.5, -5.5, -0.5, 3., 2., 3.],
[1., 1., 0., 0., 0., 0., 0.]])
G = State(*matrix_slice(M, (1, 4), corner='sw'))
H = minimal_realization(G)
assert_(H.a.shape, (2, 2))