def test_simo_round_trip(self):
# See gh-5753
tf = ([[1, 2], [1, 1]], [1, 2])
A, B, C, D = tf2ss(*tf)
assert_allclose(A, [[-2]], rtol=1e-13)
assert_allclose(B, [[1]], rtol=1e-13)
assert_allclose(C, [[0], [-1]], rtol=1e-13)
assert_allclose(D, [[1], [1]], rtol=1e-13)
num, den = ss2tf(A, B, C, D)
assert_allclose(num, [[1, 2], [1, 1]], rtol=1e-13)
assert_allclose(den, [1, 2], rtol=1e-13)
tf = ([[1, 0, 1], [1, 1, 1]], [1, 1, 1])
A, B, C, D = tf2ss(*tf)
assert_allclose(A, [[-1, -1], [1, 0]], rtol=1e-13)
assert_allclose(B, [[1], [0]], rtol=1e-13)
assert_allclose(C, [[-1, 0], [0, 0]], rtol=1e-13)
assert_allclose(D, [[1], [1]], rtol=1e-13)
num, den = ss2tf(A, B, C, D)
assert_allclose(num, [[1, 0, 1], [1, 1, 1]], rtol=1e-13)
assert_allclose(den, [1, 1, 1], rtol=1e-13)
tf = ([[1, 2, 3], [1, 2, 3]], [1, 2, 3, 4])
A, B, C, D = tf2ss(*tf)
assert_allclose(A, [[-2, -3, -4], [1, 0, 0], [0, 1, 0]], rtol=1e-13)
assert_allclose(B, [[1], [0], [0]], rtol=1e-13)
assert_allclose(C, [[1, 2, 3], [1, 2, 3]], rtol=1e-13)
assert_allclose(D, [[0], [0]], rtol=1e-13)
num, den = ss2tf(A, B, C, D)
assert_allclose(num, [[0, 1, 2, 3], [0, 1, 2, 3]], rtol=1e-13)
assert_allclose(den, [1, 2, 3, 4], rtol=1e-13)
tf = ([1, [2, 3]], [1, 6])
A, B, C, D = tf2ss(*tf)
assert_allclose(A, [[-6]], rtol=1e-31)
assert_allclose(B, [[1]], rtol=1e-31)
assert_allclose(C, [[1], [-9]], rtol=1e-31)
assert_allclose(D, [[0], [2]], rtol=1e-31)
num, den = ss2tf(A, B, C, D)
assert_allclose(num, [[0, 1], [2, 3]], rtol=1e-13)
assert_allclose(den, [1, 6], rtol=1e-13)
tf = ([[1, -3], [1, 2, 3]], [1, 6, 5])
A, B, C, D = tf2ss(*tf)
assert_allclose(A, [[-6, -5], [1, 0]], rtol=1e-13)
assert_allclose(B, [[1], [0]], rtol=1e-13)
assert_allclose(C, [[1, -3], [-4, -2]], rtol=1e-13)
assert_allclose(D, [[0], [1]], rtol=1e-13)
num, den = ss2tf(A, B, C, D)
assert_allclose(num, [[0, 1, -3], [1, 2, 3]], rtol=1e-13)
assert_allclose(den, [1, 6, 5], rtol=1e-13)
def test_zero_order_round_trip(self):
# See Issue #5760
tf = (2, 1)
ss = tf2ss(*tf)
assert_equal(ss, [[0], [0], [0], [2]])
tf = ss2tf(*ss)
assert_equal(tf, [[[2, 0]], [1, 0]])
def test_zero_order_round_trip(self):
# See Issue #5760
tf = (2, 1)
ss = tf2ss(*tf)
assert_equal(ss, [[0], [0], [0], [2]])
tf = ss2tf(*ss)
assert_equal(tf, [[[2, 0]], [1, 0]])
def test_zero_order_round_trip(self):
# See gh-5760
tf = (2, 1)
A, B, C, D = tf2ss(*tf)
assert_allclose(A, [[0]], rtol=1e-13)
assert_allclose(B, [[0]], rtol=1e-13)
assert_allclose(C, [[0]], rtol=1e-13)
assert_allclose(D, [[2]], rtol=1e-13)
num, den = ss2tf(A, B, C, D)
assert_allclose(num, [[2, 0]], rtol=1e-13)
assert_allclose(den, [1, 0], rtol=1e-13)
tf = ([[5], [2]], 1)
A, B, C, D = tf2ss(*tf)
assert_allclose(A, [[0]], rtol=1e-13)
assert_allclose(B, [[0]], rtol=1e-13)
assert_allclose(C, [[0], [0]], rtol=1e-13)
assert_allclose(D, [[5], [2]], rtol=1e-13)
num, den = ss2tf(A, B, C, D)
assert_allclose(num, [[5, 0], [2, 0]], rtol=1e-13)
assert_allclose(den, [1, 0], rtol=1e-13)
def test_basic(self):
# Test a round trip through tf2ss and ss2tf.
b = np.array([1.0, 3.0, 5.0])
a = np.array([1.0, 2.0, 3.0])
A, B, C, D = tf2ss(b, a)
assert_allclose(A, [[-2, -3], [1, 0]], rtol=1e-13)
assert_allclose(B, [[1], [0]], rtol=1e-13)
assert_allclose(C, [[1, 2]], rtol=1e-13)
assert_allclose(D, [[1]], rtol=1e-14)
bb, aa = ss2tf(A, B, C, D)
assert_allclose(bb[0], b, rtol=1e-13)
assert_allclose(aa, a, rtol=1e-13)
def test_basic(self):
# Test a round trip through tf2ss and sst2f.
b = np.array([1.0, 3.0, 5.0])
a = np.array([1.0, 2.0, 3.0])
A, B, C, D = tf2ss(b, a)
assert_allclose(A, [[-2, -3], [1, 0]], rtol=1e-13)
assert_allclose(B, [[1], [0]], rtol=1e-13)
assert_allclose(C, [[1, 2]], rtol=1e-13)
# N.b. the shape of D returned by tf2ss is (1,), not (1, 1). Sigh.
assert_allclose(D, [1], rtol=1e-14)
bb, aa = ss2tf(A, B, C, D)
assert_allclose(bb[0], b, rtol=1e-13)
assert_allclose(aa, a, rtol=1e-13)
