def _check(self, A, B, P, **kwargs):
"""
Perform the most common tests on the poles computed by place_poles
and return the Bunch object for further specific tests
"""
fsf = place_poles(A, B, P, **kwargs)
expected, _ = np.linalg.eig(A - np.dot(B, fsf.gain_matrix))
_assert_poles_close(expected,fsf.requested_poles)
_assert_poles_close(expected,fsf.computed_poles)
_assert_poles_close(P,fsf.requested_poles)
return fsf
def test_complex(self):
# Test complex pole placement on a linearized car model, taken from L.
# Jaulin, Automatique pour la robotique, Cours et Exercices, iSTE
# editions p 184/185
A = np.array([0,7,0,0,0,0,0,7/3.,0,0,0,0,0,0,0,0]).reshape(4,4)
B = np.array([0,0,0,0,1,0,0,1]).reshape(4,2)
# Test complex poles on YT
P = np.array([-3, -1, -2-1j, -2+1j])
self._check(A, B, P)
# Try to reach the specific case in _YT_complex where two singular
# values are almost equal. This is to improve code coverage but I
# have no way to be sure this code is really reached
P = [0-1e-6j,0+1e-6j,-10,10]
self._check(A, B, P, maxiter=1000)
# Try to reach the specific case in _YT_complex where the rank two
# update yields two null vectors. This test was found via Monte Carlo.
A = np.array(
[-2148,-2902, -2267, -598, -1722, -1829, -165, -283, -2546,
-167, -754, -2285, -543, -1700, -584, -2978, -925, -1300,
-1583, -984, -386, -2650, -764, -897, -517, -1598, 2, -1709,
-291, -338, -153, -1804, -1106, -1168, -867, -2297]
).reshape(6,6)
B = np.array(
[-108, -374, -524, -1285, -1232, -161, -1204, -672, -637,
-15, -483, -23, -931, -780, -1245, -1129, -1290, -1502,
-952, -1374, -62, -964, -930, -939, -792, -756, -1437,
-491, -1543, -686]
).reshape(6,5)
P = [-25.-29.j, -25.+29.j, 31.-42.j, 31.+42.j, 33.-41.j, 33.+41.j]
self._check(A, B, P)
# Use a lot of poles to go through all cases for update_order
# in _YT_loop
big_A = np.ones((11,11))-np.eye(11)
big_B = np.ones((11,10))-np.diag([1]*10,1)[:,1:]
big_A[:6,:6] = A
big_B[:6,:5] = B
P = [-10,-20,-30,40,50,60,70,-20-5j,-20+5j,5+3j,5-3j]
self._check(big_A, big_B, P)
#check with only complex poles and only real poles
P = [-10,-20,-30,-40,-50,-60,-70,-80,-90,-100]
self._check(big_A[:-1,:-1], big_B[:-1,:-1], P)
P = [-10+10j,-20+20j,-30+30j,-40+40j,-50+50j,
-10-10j,-20-20j,-30-30j,-40-40j,-50-50j]
self._check(big_A[:-1,:-1], big_B[:-1,:-1], P)
# need a 5x5 array to ensure YT handles properly when there
# is only one real pole and several complex
A = np.array([0,7,0,0,0,0,0,7/3.,0,0,0,0,0,0,0,0,
0,0,0,5,0,0,0,0,9]).reshape(5,5)
B = np.array([0,0,0,0,1,0,0,1,2,3]).reshape(5,2)
P = np.array([-2, -3+1j, -3-1j, -1+1j, -1-1j])
place_poles(A, B, P)
# same test with an odd number of real poles > 1
# this is another specific case of YT
P = np.array([-2, -3, -4, -1+1j, -1-1j])
self._check(A, B, P)
def test_errors(self):
# Test input mistakes from user
A = np.array([0,7,0,0,0,0,0,7/3.,0,0,0,0,0,0,0,0]).reshape(4,4)
B = np.array([0,0,0,0,1,0,0,1]).reshape(4,2)
#should fail as the method keyword is invalid
assert_raises(ValueError, place_poles, A, B, (-2.1,-2.2,-2.3,-2.4),
method="foo")
#should fail as poles are not 1D array
assert_raises(ValueError, place_poles, A, B,
np.array((-2.1,-2.2,-2.3,-2.4)).reshape(4,1))
#should fail as A is not a 2D array
assert_raises(ValueError, place_poles, A[:,:,np.newaxis], B,
(-2.1,-2.2,-2.3,-2.4))
#should fail as B is not a 2D array
assert_raises(ValueError, place_poles, A, B[:,:,np.newaxis],
(-2.1,-2.2,-2.3,-2.4))
#should fail as there are too many poles
assert_raises(ValueError, place_poles, A, B, (-2.1,-2.2,-2.3,-2.4,-3))
#should fail as there are not enough poles
assert_raises(ValueError, place_poles, A, B, (-2.1,-2.2,-2.3))
#should fail as the rtol is greater than 1
assert_raises(ValueError, place_poles, A, B, (-2.1,-2.2,-2.3,-2.4),
rtol=42)
#should fail as maxiter is smaller than 1
assert_raises(ValueError, place_poles, A, B, (-2.1,-2.2,-2.3,-2.4),
maxiter=-42)
# should fail as rank(B) is two
assert_raises(ValueError, place_poles, A, B, (-2,-2,-2,-2))
#unctrollable system
assert_raises(ValueError, place_poles, np.ones((4,4)),
np.ones((4,2)), (1,2,3,4))
# Should not raise ValueError as the poles can be placed but should
# raise a warning as the convergence is not reached
with warnings.catch_warnings(record=True) as w:
fsf = place_poles(A, B, (-1,-2,-3,-4), rtol=1e-16, maxiter=42)
assert_(len(w) == 1)
assert_(issubclass(w[-1].category, UserWarning))
assert_("Convergence was not reached after maxiter iterations"
in str(w[-1].message))
assert_equal(fsf.nb_iter, 42)
# should fail as a complex misses its conjugate
assert_raises(ValueError, place_poles, A, B, (-2+1j,-2-1j,-2+3j,-2))
# should fail as A is not square
assert_raises(ValueError, place_poles, A[:,:3], B, (-2,-3,-4,-5))
# should fail as B has not the same number of lines as A
assert_raises(ValueError, place_poles, A, B[:3,:], (-2,-3,-4,-5))
# should fail as KNV0 does not support complex poles
assert_raises(ValueError, place_poles, A, B,
(-2+1j,-2-1j,-2+3j,-2-3j), method="KNV0")