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"""lti_test.py"""
import re
import numpy as np
import pytest
import control as ct
from control import NonlinearIOSystem, c2d, common_timebase, isctime, \
isdtime, issiso, ss, tf, tf2ss
from control.lti import LTI, bandwidth, damp, dcgain, evalfr, poles, zeros
class TestLTI:
@pytest.mark.parametrize("fun, args", [
[tf, (126, [-1, 42])],
[ss, ([[42]], [[1]], [[1]], 0)]
])
def test_poles(self, fun, args):
sys = fun(*args)
np.testing.assert_allclose(sys.poles(), 42)
np.testing.assert_allclose(poles(sys), 42)
with pytest.raises(AttributeError, match="no attribute 'pole'"):
sys.pole()
with pytest.raises(AttributeError, match="no attribute 'pole'"):
ct.pole(sys)
@pytest.mark.parametrize("fun, args", [
[tf, (126, [-1, 42])],
[ss, ([[42]], [[1]], [[1]], 0)]
])
def test_zeros(self, fun, args):
sys = fun(*args)
np.testing.assert_allclose(sys.zeros(), 42)
np.testing.assert_allclose(zeros(sys), 42)
with pytest.raises(AttributeError, match="no attribute 'zero'"):
sys.zero()
with pytest.raises(AttributeError, match="no attribute 'zero'"):
ct.zero(sys)
def test_issiso(self):
assert issiso(1)
with pytest.raises(ValueError):
issiso(1, strict=True)
# SISO transfer function
sys = tf([-1, 42], [1, 10])
assert issiso(sys)
assert issiso(sys, strict=True)
# SISO state space system
sys = tf2ss(sys)
assert issiso(sys)
assert issiso(sys, strict=True)
@pytest.mark.slycot
def test_issiso_mimo(self):
# MIMO transfer function
sys = tf([[[-1, 41], [1]], [[1, 2], [3, 4]]],
[[[1, 10], [1, 20]], [[1, 30], [1, 40]]]);
assert not issiso(sys)
assert not issiso(sys, strict=True)
# MIMO state space system
sys = tf2ss(sys)
assert not issiso(sys)
assert not issiso(sys, strict=True)
def test_damp(self):
# Test the continuous-time case.
zeta = 0.1
wn = 42
p = -wn * zeta + 1j * wn * np.sqrt(1 - zeta**2)
sys = tf(1, [1, 2 * zeta * wn, wn**2])
expected = ([wn, wn], [zeta, zeta], [p, p.conjugate()])
np.testing.assert_allclose(sys.damp(), expected)
np.testing.assert_allclose(damp(sys), expected)
# Also test the discrete-time case.
dt = 0.001
sys_dt = c2d(sys, dt, method='matched')
p_zplane = np.exp(p*dt)
expected_dt = ([wn, wn], [zeta, zeta],
[p_zplane, p_zplane.conjugate()])
np.testing.assert_almost_equal(sys_dt.damp(), expected_dt)
np.testing.assert_almost_equal(damp(sys_dt), expected_dt)
# also check that for a discrete system with a negative real pole
# the damp function can extract wn and zeta.
p2_zplane = -0.2
sys_dt2 = tf(1, [1, -p2_zplane], dt)
wn2, zeta2, p2 = sys_dt2.damp()
p2_splane = -wn2 * zeta2 + 1j * wn2 * np.sqrt(1 - zeta2**2)
p2_zplane = np.exp(p2_splane * dt)
np.testing.assert_almost_equal(p2, p2_zplane)
def test_dcgain(self):
sys = tf(84, [1, 2])
np.testing.assert_allclose(sys.dcgain(), 42)
np.testing.assert_allclose(dcgain(sys), 42)
def test_bandwidth(self):
# test a first-order system, compared with matlab
sys1 = tf(0.1, [1, 0.1])
np.testing.assert_allclose(sys1.bandwidth(), 0.099762834511098)
np.testing.assert_allclose(bandwidth(sys1), 0.099762834511098)
# test a first-order discrete-time system, compared with matlab
sysd1 = tf([0.1, 0], [1, -0.9], 1)
np.testing.assert_allclose(sysd1.bandwidth(), 0.105207775532932)
np.testing.assert_allclose(bandwidth(sysd1), 0.105207775532932)
# test a second-order system, compared with matlab
wn2 = 1
zeta2 = 0.001
sys2 = sys1 * tf(wn2**2, [1, 2*zeta2*wn2, wn2**2])
np.testing.assert_allclose(sys2.bandwidth(), 0.101848388240241)
np.testing.assert_allclose(bandwidth(sys2), 0.101848388240241)
# test constant gain, bandwidth should be infinity
sysAP = tf(1,1)
np.testing.assert_allclose(bandwidth(sysAP), np.inf)
# test integrator, bandwidth should return np.nan
sysInt = tf(1, [1, 0])
np.testing.assert_allclose(bandwidth(sysInt), np.nan)
# test exception for system other than LTI
np.testing.assert_raises(TypeError, bandwidth, 1)
# test exception for system other than SISO system
sysMIMO = tf([[[-1, 41], [1]], [[1, 2], [3, 4]]],
[[[1, 10], [1, 20]], [[1, 30], [1, 40]]])
np.testing.assert_raises(TypeError, bandwidth, sysMIMO)
# test if raise exception if dbdrop is positive scalar
np.testing.assert_raises(ValueError, bandwidth, sys1, 3)
@pytest.mark.parametrize("dt1, dt2, expected",
[(None, None, None),
(None, 0, 0),
(None, 1, 1),
(None, True, True),
(True, True, True),
(True, 1, 1),
(1, 1, 1),
(0, 0, 0),
])
@pytest.mark.parametrize("sys1", [True, False])
@pytest.mark.parametrize("sys2", [True, False])
def test_common_timebase(self, dt1, dt2, expected, sys1, sys2):
"""Test that common_timbase adheres to :ref:`conventions-ref`"""
i1 = tf([1], [1, 2, 3], dt1) if sys1 else dt1
i2 = tf([1], [1, 4, 5], dt2) if sys2 else dt2
assert common_timebase(i1, i2) == expected
# Make sure behaviour is symmetric
assert common_timebase(i2, i1) == expected
@pytest.mark.parametrize("i1, i2",
[(True, 0),
(0, 1),
(1, 2)])
def test_common_timebase_errors(self, i1, i2):
"""Test that common_timbase raises errors on invalid combinations"""
with pytest.raises(ValueError):
common_timebase(i1, i2)
# Make sure behaviour is symmetric
with pytest.raises(ValueError):
common_timebase(i2, i1)
@pytest.mark.parametrize("dt, ref, strictref",
[(None, True, False),
(0, False, False),
(1, True, True),
(True, True, True)])
@pytest.mark.parametrize("objfun, arg",
[(LTI, ()),
(NonlinearIOSystem, (lambda x: x, ))])
def test_isdtime(self, objfun, arg, dt, ref, strictref):
"""Test isdtime and isctime functions to follow convention"""
obj = objfun(*arg, dt=dt)
assert isdtime(obj) == ref
assert isdtime(obj, strict=True) == strictref
if dt is not None:
ref = not ref
strictref = not strictref
assert isctime(obj) == ref
assert isctime(obj, strict=True) == strictref
def p(*args):
# convenience for parametrize below
return pytest.param(*args, marks=pytest.mark.slycot)
@pytest.mark.usefixtures("editsdefaults")
@pytest.mark.parametrize("fcn", [ct.ss, ct.tf, ct.frd])
@pytest.mark.parametrize("nstate, nout, ninp, omega, squeeze, shape", [
[1, 1, 1, 0.1, None, ()], # SISO
[1, 1, 1, [0.1], None, (1,)],
[1, 1, 1, [0.1, 1, 10], None, (3,)],
[2, 1, 1, 0.1, True, ()],
[2, 1, 1, [0.1], True, ()],
[2, 1, 1, [0.1, 1, 10], True, (3,)],
[3, 1, 1, 0.1, False, (1, 1)],
[3, 1, 1, [0.1], False, (1, 1, 1)],
[3, 1, 1, [0.1, 1, 10], False, (1, 1, 3)],
p(1, 2, 1, 0.1, None, (2, 1)),
p(1, 2, 1, [0.1], None, (2, 1, 1)),
p(1, 2, 1, [0.1, 1, 10], None, (2, 1, 3)),
p(2, 2, 1, 0.1, True, (2,)),
p(2, 2, 1, [0.1], True, (2,)),
p(3, 2, 1, 0.1, False, (2, 1)),
p(3, 2, 1, [0.1], False, (2, 1, 1)),
p(3, 2, 1, [0.1, 1, 10], False, (2, 1, 3)),
p(1, 1, 2, [0.1, 1, 10], None, (1, 2, 3)), # MISO
p(2, 1, 2, [0.1, 1, 10], True, (2, 3)),
p(3, 1, 2, [0.1, 1, 10], False, (1, 2, 3)),
p(1, 1, 2, 0.1, None, (1, 2)),
p(1, 1, 2, 0.1, True, (2,)),
p(1, 1, 2, 0.1, False, (1, 2)),
p(1, 2, 2, [0.1, 1, 10], None, (2, 2, 3)), # MIMO
p(2, 2, 2, [0.1, 1, 10], True, (2, 2, 3)),
p(3, 2, 2, [0.1, 1, 10], False, (2, 2, 3)),
p(1, 2, 2, 0.1, None, (2, 2)),
p(2, 2, 2, 0.1, True, (2, 2)),
p(3, 2, 2, 0.1, False, (2, 2)),
])
@pytest.mark.parametrize("omega_type", ["numpy", "native"])
def test_squeeze(self, fcn, nstate, nout, ninp, omega, squeeze, shape,
omega_type):
"""Test correct behavior of frequencey response squeeze parameter."""
# Create the system to be tested
if fcn == ct.frd:
sys = fcn(ct.rss(nstate, nout, ninp), [1e-2, 1e-1, 1, 1e1, 1e2])
else:
sys = fcn(ct.rss(nstate, nout, ninp))
if omega_type == "numpy":
omega = np.asarray(omega)
isscalar = omega.ndim == 0
# keep the ndarray type even for scalars
s = np.asarray(omega * 1j)
else:
isscalar = not hasattr(omega, '__len__')
if isscalar:
s = omega*1J
else:
s = [w*1J for w in omega]
# Call the transfer function directly and make sure shape is correct
assert sys(s, squeeze=squeeze).shape == shape
# Make sure that evalfr also works as expected
assert ct.evalfr(sys, s, squeeze=squeeze).shape == shape
# Check frequency response
mag, phase, _ = sys.frequency_response(omega, squeeze=squeeze)
if isscalar and squeeze is not True:
# sys.frequency_response() expects a list as an argument
# Add the shape of the input to the expected shape
assert mag.shape == shape + (1,)
assert phase.shape == shape + (1,)
else:
assert mag.shape == shape
assert phase.shape == shape
# Make sure the default shape lines up with squeeze=None case
if squeeze is None:
assert sys(s).shape == shape
# Changing config.default to False should return 3D frequency response
ct.config.set_defaults('control', squeeze_frequency_response=False)
mag, phase, _ = sys.frequency_response(omega)
if isscalar:
assert mag.shape == (sys.noutputs, sys.ninputs, 1)
assert phase.shape == (sys.noutputs, sys.ninputs, 1)
assert sys(s).shape == (sys.noutputs, sys.ninputs)
assert ct.evalfr(sys, s).shape == (sys.noutputs, sys.ninputs)
else:
assert mag.shape == (sys.noutputs, sys.ninputs, len(omega))
assert phase.shape == (sys.noutputs, sys.ninputs, len(omega))
assert sys(s).shape == \
(sys.noutputs, sys.ninputs, len(omega))
assert ct.evalfr(sys, s).shape == \
(sys.noutputs, sys.ninputs, len(omega))
@pytest.mark.parametrize("fcn", [ct.ss, ct.tf, ct.frd])
def test_squeeze_exceptions(self, fcn):
if fcn == ct.frd:
sys = fcn(ct.rss(2, 1, 1), [1e-2, 1e-1, 1, 1e1, 1e2])
else:
sys = fcn(ct.rss(2, 1, 1))
with pytest.raises(ValueError, match="unknown squeeze value"):
sys.frequency_response([1], squeeze='siso')
with pytest.raises(ValueError, match="unknown squeeze value"):
sys([1j], squeeze='siso')
with pytest.raises(ValueError, match="unknown squeeze value"):
evalfr(sys, [1j], squeeze='siso')
with pytest.raises(ValueError, match="must be 1D"):
sys.frequency_response([[0.1, 1], [1, 10]])
with pytest.raises(ValueError, match="must be 1D"):
sys([[0.1j, 1j], [1j, 10j]])
with pytest.raises(ValueError, match="must be 1D"):
evalfr(sys, [[0.1j, 1j], [1j, 10j]])
@pytest.mark.parametrize(
"outdx, inpdx, key",
[('y[0]', 'u[1]', (0, 1)),
(['y[0]'], ['u[1]'], (0, 1)),
(slice(0, 1, 1), slice(1, 2, 1), (0, 1)),
(['y[0]', 'y[1]'], ['u[1]', 'u[2]'], ([0, 1], [1, 2])),
([0, 'y[1]'], ['u[1]', 2], ([0, 1], [1, 2])),
(slice(0, 2, 1), slice(1, 3, 1), ([0, 1], [1, 2])),
(['y[2]', 'y[1]'], ['u[2]', 'u[0]'], ([2, 1], [2, 0])),
])
@pytest.mark.parametrize("fcn", [ct.ss, ct.tf, ct.frd])
def test_subsys_indexing(fcn, outdx, inpdx, key):
# Construct the base system and subsystem
sys = ct.rss(4, 3, 3)
subsys = sys[key]
# Construct the system to be tested
match fcn:
case ct.frd:
omega = np.logspace(-1, 1)
sys = fcn(sys, omega)
subsys_chk = fcn(subsys, omega)
case _:
sys = fcn(sys)
subsys_chk = fcn(subsys)
# Construct the subsystem
subsys_fcn = sys[outdx, inpdx]
# Check to make sure everythng matches up
match fcn:
case ct.frd:
np.testing.assert_almost_equal(
subsys_fcn.complex, subsys_chk.complex)
case ct.ss:
np.testing.assert_almost_equal(subsys_fcn.A, subsys_chk.A)
np.testing.assert_almost_equal(subsys_fcn.B, subsys_chk.B)
np.testing.assert_almost_equal(subsys_fcn.C, subsys_chk.C)
np.testing.assert_almost_equal(subsys_fcn.D, subsys_chk.D)
case ct.tf:
omega = np.logspace(-1, 1)
np.testing.assert_almost_equal(
subsys_fcn.frequency_response(omega).complex,
subsys_chk.frequency_response(omega).complex)
@pytest.mark.parametrize("op", [
'__mul__', '__rmul__', '__add__', '__radd__', '__sub__', '__rsub__'])
@pytest.mark.parametrize("fcn", [ct.ss, ct.tf, ct.frd])
def test_scalar_algebra(op, fcn):
sys_ss = ct.rss(4, 2, 2)
match fcn:
case ct.ss:
sys = sys_ss
case ct.tf:
sys = ct.tf(sys_ss)
case ct.frd:
sys = ct.frd(sys_ss, [0.1, 1, 10])
scaled = getattr(sys, op)(2)
np.testing.assert_almost_equal(getattr(sys(1j), op)(2), scaled(1j))
@pytest.mark.parametrize(
"fcn, args, kwargs, suppress, " +
"repr_expected, str_expected, latex_expected", [
(ct.ss, (-1e-12, 1, 2, 3), {}, False,
r"StateSpace\([\s]*array\(\[\[-1.e-12\]\]\).*",
None, # standard Numpy formatting
r"10\^\{-12\}"),
(ct.ss, (-1e-12, 1, 3, 3), {}, True,
r"StateSpace\([\s]*array\(\[\[-0\.\]\]\).*",
None, # standard Numpy formatting
r"-0"),
(ct.tf, ([1, 1e-12, 1], [1, 2, 1]), {}, False,
r"\[1\.e\+00, 1\.e-12, 1.e\+00\]",
r"s\^2 \+ 1e-12 s \+ 1",
r"1 \\times 10\^\{-12\}"),
(ct.tf, ([1, 1e-12, 1], [1, 2, 1]), {}, True,
r"\[1\., 0., 1.\]",
r"s\^2 \+ 1",
r"\{s\^2 \+ 1\}"),
])
@pytest.mark.usefixtures("editsdefaults")
def test_printoptions(
fcn, args, kwargs, suppress,
repr_expected, str_expected, latex_expected):
sys = fcn(*args, **kwargs)
with np.printoptions(suppress=suppress):
# Test loadable representation
assert re.search(repr_expected, ct.iosys_repr(sys, 'eval')) is not None
# Test string representation
if str_expected is not None:
assert re.search(str_expected, str(sys)) is not None
# Test LaTeX/HTML representation
assert re.search(latex_expected, sys._repr_html_()) is not None