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"""lti_test.py"""
import numpy as np
import pytest
from .conftest import editsdefaults
import control as ct
from control import c2d, tf, tf2ss, NonlinearIOSystem
from control.lti import (LTI, common_timebase, evalfr, damp, dcgain, isctime,
isdtime, issiso, pole, timebaseEqual, zero)
from control.tests.conftest import slycotonly
from control.exception import slycot_check
class TestLTI:
def test_pole(self):
sys = tf(126, [-1, 42])
np.testing.assert_allclose(sys.pole(), 42)
np.testing.assert_allclose(pole(sys), 42)
def test_zero(self):
sys = tf([-1, 42], [1, 10])
np.testing.assert_allclose(sys.zero(), 42)
np.testing.assert_allclose(zero(sys), 42)
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)
@slycotonly
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)
def test_dcgain(self):
sys = tf(84, [1, 2])
np.testing.assert_allclose(sys.dcgain(), 42)
np.testing.assert_allclose(dcgain(sys), 42)
@pytest.mark.parametrize("dt1, dt2, expected",
[(None, None, True),
(None, 0, True),
(None, 1, True),
pytest.param(None, True, True,
marks=pytest.mark.xfail(
reason="returns false")),
(0, 0, True),
(0, 1, False),
(0, True, False),
(1, 1, True),
(1, 2, False),
(1, True, False),
(True, True, True)])
def test_timebaseEqual_deprecated(self, dt1, dt2, expected):
"""Test that timbaseEqual throws a warning and returns as documented"""
sys1 = tf([1], [1, 2, 3], dt1)
sys2 = tf([1], [1, 4, 5], dt2)
print(sys1.dt)
print(sys2.dt)
with pytest.deprecated_call():
assert timebaseEqual(sys1, sys2) is expected
# Make sure behaviour is symmetric
with pytest.deprecated_call():
assert timebaseEqual(sys2, sys1) is expected
@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 throws 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
@pytest.mark.usefixtures("editsdefaults")
@pytest.mark.parametrize("fcn", [ct.ss, ct.tf, ct.frd, ct.ss2io])
@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)],
[1, 2, 1, 0.1, None, (2, 1)], # SIMO
[1, 2, 1, [0.1], None, (2, 1, 1)],
[1, 2, 1, [0.1, 1, 10], None, (2, 1, 3)],
[2, 2, 1, 0.1, True, (2,)],
[2, 2, 1, [0.1], True, (2,)],
[3, 2, 1, 0.1, False, (2, 1)],
[3, 2, 1, [0.1], False, (2, 1, 1)],
[3, 2, 1, [0.1, 1, 10], False, (2, 1, 3)],
[1, 1, 2, [0.1, 1, 10], None, (1, 2, 3)], # MISO
[2, 1, 2, [0.1, 1, 10], True, (2, 3)],
[3, 1, 2, [0.1, 1, 10], False, (1, 2, 3)],
[1, 1, 2, 0.1, None, (1, 2)],
[1, 1, 2, 0.1, True, (2,)],
[1, 1, 2, 0.1, False, (1, 2)],
[1, 2, 2, [0.1, 1, 10], None, (2, 2, 3)], # MIMO
[2, 2, 2, [0.1, 1, 10], True, (2, 2, 3)],
[3, 2, 2, [0.1, 1, 10], False, (2, 2, 3)],
[1, 2, 2, 0.1, None, (2, 2)],
[2, 2, 2, 0.1, True, (2, 2)],
[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])
elif fcn == ct.tf and (nout > 1 or ninp > 1) and not slycot_check():
pytest.skip("Conversion of MIMO systems to transfer functions "
"requires slycot.")
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, ct.ss2io])
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=1)
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]])
with pytest.warns(DeprecationWarning, match="LTI `inputs`"):
ninputs = sys.inputs
assert ninputs == sys.ninputs
with pytest.warns(DeprecationWarning, match="LTI `outputs`"):
noutputs = sys.outputs
assert noutputs == sys.noutputs
if isinstance(sys, ct.StateSpace):
with pytest.warns(
DeprecationWarning, match="StateSpace `states`"):
nstates = sys.states
assert nstates == sys.nstates