"""Struct of test system"""

def __init__(self, sys=None):

self.sys = sys

def __repr__(self):

"""Show system when debugging"""

@pytest.fixture

def siso_ss1(self):

A = np.array([[1., -2.], [3., -4.]])

B = np.array([[5.], [7.]])

C = np.array([[6., 8.]])

D = np.array([[9.]])

T = TSys(StateSpace(A, B, C, D, 0))

T.t = np.linspace(0, 1, 10)

T.ystep = np.array([9., 17.6457, 24.7072, 30.4855, 35.2234,

39.1165, 42.3227, 44.9694, 47.1599, 48.9776])

T.yinitial = np.array([11., 8.1494, 5.9361, 4.2258, 2.9118,

1.9092, 1.1508, 0.5833, 0.1645, -0.1391])

return T

@pytest.fixture

def siso_ss2(self, siso_ss1):

"""System siso_ss2 with D=0"""

ss1 = siso_ss1.sys

T = TSys(StateSpace(ss1.A, ss1.B, ss1.C, 0, 0))

T.t = siso_ss1.t

T.ystep = siso_ss1.ystep - 9

T.initial = siso_ss1.yinitial - 9

T.yimpulse = np.array([86., 70.1808, 57.3753, 46.9975, 38.5766,

31.7344, 26.1668, 21.6292, 17.9245, 14.8945])

return T

@pytest.fixture

def siso_tf1(self):

# Create some transfer functions

return TSys(TransferFunction([1], [1, 2, 1], 0))

@pytest.fixture

def siso_tf2(self, siso_ss1):

T = copy(siso_ss1)

T.sys = ss2tf(siso_ss1.sys)

return T

@pytest.fixture

def mimo_ss1(self, siso_ss1):

# Create MIMO system, contains ``siso_ss1`` twice

A = np.zeros((4, 4))

A[:2, :2] = siso_ss1.sys.A

A[2:, 2:] = siso_ss1.sys.A

B = np.zeros((4, 2))

B[:2, :1] = siso_ss1.sys.B

B[2:, 1:] = siso_ss1.sys.B

C = np.zeros((2, 4))

C[:1, :2] = siso_ss1.sys.C

C[1:, 2:] = siso_ss1.sys.C

D = np.zeros((2, 2))

D[:1, :1] = siso_ss1.sys.D

D[1:, 1:] = siso_ss1.sys.D

T = copy(siso_ss1)

T.sys = StateSpace(A, B, C, D)

return T

@pytest.fixture

def mimo_ss2(self, siso_ss2):

# Create MIMO system, contains ``siso_ss2`` twice

A = np.zeros((4, 4))

A[:2, :2] = siso_ss2.sys.A

A[2:, 2:] = siso_ss2.sys.A

B = np.zeros((4, 2))

B[:2, :1] = siso_ss2.sys.B

B[2:, 1:] = siso_ss2.sys.B

C = np.zeros((2, 4))

C[:1, :2] = siso_ss2.sys.C

C[1:, 2:] = siso_ss2.sys.C

D = np.zeros((2, 2))

T = copy(siso_ss2)

T.sys = StateSpace(A, B, C, D, 0)

return T

# Create discrete time systems

@pytest.fixture

def siso_dtf0(self):

T = TSys(TransferFunction([1.], [1., 0.], 1.))

T.t = np.arange(4)

T.yimpulse = [0., 1., 0., 0.]

return T

@pytest.fixture

def siso_dtf1(self):

T = TSys(TransferFunction([1], [1, 1, 0.25], True))

T.t = np.arange(0, 5, 1)

return T

@pytest.fixture

def siso_dtf2(self):

T = TSys(TransferFunction([1], [1, 1, 0.25], 0.2))

T.t = np.arange(0, 5, 0.2)

return T

@pytest.fixture

def siso_dss1(self, siso_dtf1):

T = copy(siso_dtf1)

T.sys = tf2ss(siso_dtf1.sys)

return T

@pytest.fixture

def siso_dss2(self, siso_dtf2):

T = copy(siso_dtf2)

T.sys = tf2ss(siso_dtf2.sys)

return T

@pytest.fixture

def mimo_dss1(self, mimo_ss1):

ss1 = mimo_ss1.sys

T = TSys(

StateSpace(ss1.A, ss1.B, ss1.C, ss1.D, True))

T.t = np.arange(0, 5, 0.2)

return T

@pytest.fixture

def mimo_dss2(self, mimo_ss1):

T = copy(mimo_ss1)

T.sys = c2d(mimo_ss1.sys, T.t[1]-T.t[0])

return T

@pytest.fixture

def mimo_tf2(self, siso_ss2, mimo_ss2):

T = copy(mimo_ss2)

# construct from siso to avoid slycot during fixture setup

tf_ = ss2tf(siso_ss2.sys)

T.sys = TransferFunction([[tf_.num[0][0], [0]], [[0], tf_.num[0][0]]],

[[tf_.den[0][0], [1]], [[1], tf_.den[0][0]]],

0)

return T

@pytest.fixture

def mimo_dtf1(self, siso_dtf1):

T = copy(siso_dtf1)

# construct from siso to avoid slycot during fixture setup

tf_ = siso_dtf1.sys

T.sys = TransferFunction([[tf_.num[0][0], [0]], [[0], tf_.num[0][0]]],

[[tf_.den[0][0], [1]], [[1], tf_.den[0][0]]],

True)

return T

@pytest.fixture

def pole_cancellation(self):

# for pole cancellation tests

return TransferFunction([1.067e+05, 5.791e+04],

[10.67, 1.067e+05, 5.791e+04])

@pytest.fixture

def no_pole_cancellation(self):

return TransferFunction([1.881e+06],

[188.1, 1.881e+06])

@pytest.fixture

def tsystem(self,

request,

siso_ss1, siso_ss2, siso_tf1, siso_tf2,

mimo_ss1, mimo_ss2, mimo_tf2,

siso_dtf0, siso_dtf1, siso_dtf2,

siso_dss1, siso_dss2,

mimo_dss1, mimo_dss2, mimo_dtf1,

pole_cancellation, no_pole_cancellation):

systems = {"siso_ss1": siso_ss1,

"siso_ss2": siso_ss2,

"siso_tf1": siso_tf1,

"siso_tf2": siso_tf2,

"mimo_ss1": mimo_ss1,

"mimo_ss2": mimo_ss2,

"mimo_tf2": mimo_tf2,

"siso_dtf0": siso_dtf0,

"siso_dtf1": siso_dtf1,

"siso_dtf2": siso_dtf2,

"siso_dss1": siso_dss1,

"siso_dss2": siso_dss2,

"mimo_dss1": mimo_dss1,

"mimo_dss2": mimo_dss2,

"mimo_dtf1": mimo_dtf1,

"pole_cancellation": pole_cancellation,

"no_pole_cancellation": no_pole_cancellation,

}

return systems[request.param]

@pytest.mark.parametrize(

def test_step_response_siso(self, siso_ss1, kwargs):

"""Test SISO system step response"""

sys = siso_ss1.sys

t = siso_ss1.t

yref = siso_ss1.ystep

# SISO call

out = step_response(sys, T=t, **kwargs)

tout, yout = out[:2]

assert len(out) == 3 if ('return_x', True) in kwargs.items() else 2

np.testing.assert_array_almost_equal(tout, t)

np.testing.assert_array_almost_equal(yout, yref, decimal=4)

def test_step_response_mimo(self, mimo_ss1):

"""Test MIMO system, which contains ``siso_ss1`` twice"""

sys = mimo_ss1.sys

t = mimo_ss1.t

yref = mimo_ss1.ystep

_t, y_00 = step_response(sys, T=t, input=0, output=0)

_t, y_11 = step_response(sys, T=t, input=1, output=1)

np.testing.assert_array_almost_equal(y_00, yref, decimal=4)

np.testing.assert_array_almost_equal(y_11, yref, decimal=4)

def test_step_response_return(self, mimo_ss1):

"""Verify continuous and discrete time use same return conventions"""

sysc = mimo_ss1.sys

sysd = c2d(sysc, 1) # discrete time system

Tvec = np.linspace(0, 10, 11) # make sure to use integer times 0..10

Tc, youtc = step_response(sysc, Tvec, input=0)

Td, youtd = step_response(sysd, Tvec, input=0)

np.testing.assert_array_equal(Tc.shape, Td.shape)

np.testing.assert_array_equal(youtc.shape, youtd.shape)

@pytest.mark.parametrize("dt", [0, 1], ids=["continuous", "discrete"])

def test_step_nostates(self, dt):

"""Constant system, continuous and discrete time

sys = TransferFunction([1], [1], dt)

t, y = step_response(sys)

np.testing.assert_array_equal(y, np.ones(len(t)))

def test_step_info(self):

# From matlab docs:

sys = TransferFunction([1, 5, 5], [1, 1.65, 5, 6.5, 2])

Strue = {

'RiseTime': 3.8456,

'SettlingTime': 27.9762,

'SettlingMin': 2.0689,

'SettlingMax': 2.6873,

'Overshoot': 7.4915,

'Undershoot': 0,

'Peak': 2.6873,

'PeakTime': 8.0530,

'SteadyStateValue': 2.50

}

S = step_info(sys)

Sk = sorted(S.keys())

Sktrue = sorted(Strue.keys())

assert Sk == Sktrue

# Very arbitrary tolerance because I don't know if the

# response from the MATLAB is really that accurate.

# maybe it is a good idea to change the Strue to match

# but I didn't do it because I don't know if it is

# accurate either...

rtol = 2e-2

np.testing.assert_allclose([S[k] for k in Sk],

[Strue[k] for k in Sktrue],

rtol=rtol)

def test_step_pole_cancellation(self, pole_cancellation,

no_pole_cancellation):

# confirm that pole-zero cancellation doesn't perturb results

# https://github.com/python-control/python-control/issues/440

step_info_no_cancellation = step_info(no_pole_cancellation)

step_info_cancellation = step_info(pole_cancellation)

for key in step_info_no_cancellation:

if key == 'Overshoot':

# skip this test because these systems have no overshoot

# => very sensitive to parameters

continue

np.testing.assert_allclose(step_info_no_cancellation[key],

step_info_cancellation[key], rtol=1e-4)

@pytest.mark.parametrize(

def test_impulse_response_siso(self, tsystem, kwargs):

"""Test impulse response of SISO systems"""

sys = tsystem.sys

t = tsystem.t

yref = tsystem.yimpulse

out = impulse_response(sys, T=t, **kwargs)

tout, yout = out[:2]

assert len(out) == 3 if ('return_x', True) in kwargs.items() else 2

np.testing.assert_array_almost_equal(tout, t)

np.testing.assert_array_almost_equal(yout, yref, decimal=4)

def test_impulse_response_mimo(self, mimo_ss2):

""""Test impulse response of MIMO systems"""

sys = mimo_ss2.sys

t = mimo_ss2.t

yref = mimo_ss2.yimpulse

_t, y_00 = impulse_response(sys, T=t, input=0, output=0)

np.testing.assert_array_almost_equal(y_00, yref, decimal=4)

_t, y_11 = impulse_response(sys, T=t, input=1, output=1)

np.testing.assert_array_almost_equal(y_11, yref, decimal=4)

yref_notrim = np.zeros((2, len(t)))

yref_notrim[:1, :] = yref

_t, yy = impulse_response(sys, T=t, input=0)

np.testing.assert_array_almost_equal(yy[:,0,:], yref_notrim, decimal=4)

@pytest.mark.skipif(StrictVersion(sp.__version__) < "1.3",

def test_discrete_time_impulse(self, siso_tf1):

# discrete time impulse sampled version should match cont time

dt = 0.1

t = np.arange(0, 3, dt)

sys = siso_tf1.sys

sysdt = sys.sample(dt, 'impulse')

np.testing.assert_array_almost_equal(impulse_response(sys, t)[1],

impulse_response(sysdt, t)[1])

def test_impulse_response_warnD(self, siso_ss1):

"""Test warning about direct feedthrough"""

with pytest.warns(UserWarning, match="System has direct feedthrough"):

_ = impulse_response(siso_ss1.sys, siso_ss1.t)

@pytest.mark.parametrize(

def test_initial_response(self, siso_ss1, kwargs):

"""Test initial response of SISO system"""

sys = siso_ss1.sys

t = siso_ss1.t

x0 = kwargs.get('X0', 0)

yref = siso_ss1.yinitial if np.any(x0) else np.zeros_like(t)

out = initial_response(sys, T=t, **kwargs)

tout, yout = out[:2]

assert len(out) == 3 if ('return_x', True) in kwargs.items() else 2

np.testing.assert_array_almost_equal(tout, t)

np.testing.assert_array_almost_equal(yout, yref, decimal=4)

def test_initial_response_mimo(self, mimo_ss1):

"""Test initial response of MIMO system"""

sys = mimo_ss1.sys

t = mimo_ss1.t

x0 = np.array([[.5], [1.], [.5], [1.]])

yref = mimo_ss1.yinitial

yref_notrim = np.broadcast_to(yref, (2, len(t)))

_t, y_00 = initial_response(sys, T=t, X0=x0, input=0, output=0)

np.testing.assert_array_almost_equal(y_00, yref, decimal=4)

_t, y_11 = initial_response(sys, T=t, X0=x0, input=0, output=1)

np.testing.assert_array_almost_equal(y_11, yref, decimal=4)

_t, yy = initial_response(sys, T=t, X0=x0)

np.testing.assert_array_almost_equal(yy, yref_notrim, decimal=4)

@pytest.mark.parametrize("tsystem",

def test_forced_response_step(self, tsystem):

"""Test forced response of SISO systems as step response"""

sys = tsystem.sys

t = tsystem.t

u = np.ones_like(t, dtype=float)

yref = tsystem.ystep

tout, yout = forced_response(sys, t, u)

np.testing.assert_array_almost_equal(tout, t)

np.testing.assert_array_almost_equal(yout, yref, decimal=4)

@pytest.mark.parametrize("u",

def test_forced_response_initial(self, siso_ss1, u):

"""Test forced response of SISO system as intitial response"""

sys = siso_ss1.sys

t = siso_ss1.t

x0 = np.array([[.5], [1.]])

yref = siso_ss1.yinitial

tout, yout = forced_response(sys, t, u, X0=x0)

np.testing.assert_array_almost_equal(tout, t)

np.testing.assert_array_almost_equal(yout, yref, decimal=4)

@pytest.mark.parametrize("tsystem, useT",

def test_forced_response_mimo(self, tsystem, useT):

"""Test forced response of MIMO system"""

# first system: initial value, second system: step response

sys = tsystem.sys

t = tsystem.t

u = np.array([[0., 0, 0, 0, 0, 0, 0, 0, 0, 0],

[1., 1, 1, 1, 1, 1, 1, 1, 1, 1]])

x0 = np.array([[.5], [1], [0], [0]])

yref = np.vstack([tsystem.yinitial, tsystem.ystep])

if useT:

_t, yout = forced_response(sys, t, u, x0)

else:

_t, yout = forced_response(sys, U=u, X0=x0)

np.testing.assert_array_almost_equal(yout, yref, decimal=4)

@pytest.mark.usefixtures("editsdefaults")

def test_forced_response_legacy(self):

# Define a system for testing

sys = ct.rss(2, 1, 1)

T = np.linspace(0, 10, 10)

U = np.sin(T)

"""Make sure that legacy version of forced_response works"""

ct.config.use_legacy_defaults("0.8.4")

# forced_response returns x by default

t, y = ct.step_response(sys, T)

t, y, x = ct.forced_response(sys, T, U)

ct.config.use_legacy_defaults("0.9.0")

# forced_response returns input/output by default

t, y = ct.step_response(sys, T)

t, y = ct.forced_response(sys, T, U)

t, y, x = ct.forced_response(sys, T, U, return_x=True)

@pytest.mark.parametrize("u, x0, xtrue",

def test_lsim_double_integrator(self, u, x0, xtrue):

"""Test forced response of double integrator"""

# Note: scipy.signal.lsim fails if A is not invertible

A = np.array([[0., 1.],

[0., 0.]])

B = np.array([[0.],

[1.]])

C = np.array([[1., 0.]])

D = 0.

sys = StateSpace(A, B, C, D)

t = np.linspace(0, 1, 10)

_t, yout, xout = forced_response(sys, t, u, x0, return_x=True)

np.testing.assert_array_almost_equal(xout, xtrue, decimal=6)

ytrue = np.squeeze(np.asarray(C.dot(xtrue)))

np.testing.assert_array_almost_equal(yout, ytrue, decimal=6)

@slycotonly

def test_step_robustness(self):

"Test robustness os step_response against denomiantors: gh-240"

# Create 2 input, 2 output system

num = [[[0], [1]], [[1], [0]]]

den1 = [[[1], [1,1]], [[1, 4], [1]]]

sys1 = TransferFunction(num, den1)

den2 = [[[1], [1e-10, 1, 1]], [[1, 4], [1]]] # slight perturbation

sys2 = TransferFunction(num, den2)

t1, y1 = step_response(sys1, input=0, T=2, T_num=100)

t2, y2 = step_response(sys2, input=0, T=2, T_num=100)

np.testing.assert_array_almost_equal(y1, y2)

@pytest.mark.parametrize(

def test_auto_generated_time_vector_tfinal(self, tfsys, tfinal):

"""Confirm a TF with a pole at p simulates for tfinal seconds"""

np.testing.assert_almost_equal(

_ideal_tfinal_and_dt(tfsys)[0], tfinal, decimal=4)

@pytest.mark.parametrize("wn, zeta", [(10, 0), (100, 0), (100, .1)])

def test_auto_generated_time_vector_dt_cont(self, wn, zeta):

"""Confirm a TF with a natural frequency of wn rad/s gets a

dtref = 0.25133 / wn

tfsys = TransferFunction(1, [1, 2*zeta*wn, wn**2])

np.testing.assert_almost_equal(_ideal_tfinal_and_dt(tfsys)[1], dtref)

def test_auto_generated_time_vector_dt_cont(self):

"""A sampled tf keeps its dt"""

wn = 100

zeta = .1

tfsys = TransferFunction(1, [1, 2*zeta*wn, wn**2]).sample(.1)

tfinal, dt = _ideal_tfinal_and_dt(tfsys)

np.testing.assert_almost_equal(dt, .1)

T, _ = initial_response(tfsys)

np.testing.assert_almost_equal(np.diff(T[:2]), [.1])

def test_default_timevector_long(self):

"""Test long time vector"""

# TF with fast oscillations simulates only 5000 time steps

# even with long tfinal

wn = 100

tfsys = TransferFunction(1, [1, 0, wn**2])

tout = _default_time_vector(tfsys, tfinal=100)

assert len(tout) == 5000

@pytest.mark.parametrize("fun", [step_response,

def test_default_timevector_functions_c(self, fun):

"""Test that functions can calculate the time vector automatically"""

sys = TransferFunction(1, [1, .5, 0])

# test impose number of time steps

tout, _ = fun(sys, T_num=10)

assert len(tout) == 10

# test impose final time

tout, _ = fun(sys, 100)

np.testing.assert_allclose(tout[-1], 100., atol=0.5)

@pytest.mark.parametrize("fun", [step_response,

def test_default_timevector_functions_d(self, fun):

"""Test that functions can calculate the time vector automatically"""

sys = TransferFunction(1, [1, .5, 0], 0.1)

# test impose number of time steps is ignored with dt given

tout, _ = fun(sys, T_num=15)

assert len(tout) != 15

# test impose final time

tout, _ = fun(sys, 100)

np.testing.assert_allclose(tout[-1], 100., atol=0.5)

@pytest.mark.parametrize("tsystem",

@pytest.mark.parametrize("fun", [step_response,

@pytest.mark.parametrize("squeeze", [None, True, False])

def test_time_vector(self, tsystem, fun, squeeze, matarrayout):

"""Test time vector handling and correct output convention

sys = tsystem.sys

kw = {}

if hasattr(tsystem, "t"):

t = tsystem.t

kw['T'] = t

if fun == forced_response:

kw['U'] = np.vstack([np.sin(t) for i in range(sys.ninputs)])

elif fun == forced_response and isctime(sys):

pytest.skip("No continuous forced_response without time vector.")

if hasattr(tsystem.sys, "nstates"):

kw['X0'] = np.arange(sys.nstates) + 1

if sys.ninputs > 1 and fun in [step_response, impulse_response]:

kw['input'] = 1

if squeeze is not None:

kw['squeeze'] = squeeze

out = fun(sys, **kw)

tout, yout = out[:2]

assert tout.ndim == 1

if hasattr(tsystem, 't'):

# tout should always match t, which has shape (n, )

np.testing.assert_allclose(tout, tsystem.t)

if squeeze is False or not sys.issiso():

assert yout.shape[0] == sys.noutputs

assert yout.shape[-1] == tout.shape[0]

else:

assert yout.shape == tout.shape

if sys.dt > 0 and sys.dt is not True and not np.isclose(sys.dt, 0.5):

kw['T'] = np.arange(0, 5, 0.5) # incompatible timebase

with pytest.raises(ValueError):

fun(sys, **kw)

@pytest.mark.parametrize("squeeze", [None, True, False])

def test_time_vector_interpolation(self, siso_dtf2, squeeze):

"""Test time vector handling in case of interpolation

sys = siso_dtf2.sys

t = np.arange(0, 10, 1.)

u = np.sin(t)

x0 = 0

squeezekw = {} if squeeze is None else {"squeeze": squeeze}

tout, yout = forced_response(sys, t, u, x0,

interpolate=True, **squeezekw)

if squeeze is False or sys.noutputs > 1:

assert yout.shape[0] == sys.noutputs

assert yout.shape[1] == tout.shape[0]

else:

assert yout.shape == tout.shape

assert np.allclose(tout[1:] - tout[:-1], sys.dt)

def test_discrete_time_steps(self, siso_dtf2):

"""Make sure rounding errors in sample time are handled properly

sys = siso_dtf2.sys

# Set up a time range and simulate

T = np.arange(0, 100, 0.2)

tout1, yout1 = step_response(sys, T)

# Simulate every other time step

T = np.arange(0, 100, 0.4)

tout2, yout2 = step_response(sys, T)

np.testing.assert_array_almost_equal(tout1[::2], tout2)

np.testing.assert_array_almost_equal(yout1[::2], yout2)

# Add a small error into some of the time steps

T = np.arange(0, 100, 0.2)

T[1:-2:2] -= 1e-12 # tweak second value and a few others

tout3, yout3 = step_response(sys, T)

np.testing.assert_array_almost_equal(tout1, tout3)

np.testing.assert_array_almost_equal(yout1, yout3)

# Add a small error into some of the time steps (w/ skipping)

T = np.arange(0, 100, 0.4)

T[1:-2:2] -= 1e-12 # tweak second value and a few others

tout4, yout4 = step_response(sys, T)

np.testing.assert_array_almost_equal(tout2, tout4)

np.testing.assert_array_almost_equal(yout2, yout4)

# Make sure larger errors *do* generate an error

T = np.arange(0, 100, 0.2)

T[1:-2:2] -= 1e-3 # change second value and a few others

with pytest.raises(ValueError):

step_response(sys, T)

def test_time_series_data_convention_2D(self, siso_ss1):

"""Allow input time as 2D array (output should be 1D)"""

tin = np.array(np.linspace(0, 10, 100), ndmin=2)

t, y = step_response(siso_ss1.sys, tin)

assert isinstance(t, np.ndarray) and not isinstance(t, np.matrix)

assert t.ndim == 1

assert y.ndim == 1 # SISO returns "scalar" output

assert t.shape == y.shape # Allows direct plotting of output

@pytest.mark.usefixtures("editsdefaults")

@pytest.mark.parametrize("fcn", [ct.ss, ct.tf, ct.ss2io])

@pytest.mark.parametrize("nstate, nout, ninp, squeeze, shape1, shape2", [

def test_squeeze(self, fcn, nstate, nout, ninp, squeeze, shape1, shape2):

# Figure out if we have SciPy 1+

scipy0 = StrictVersion(sp.__version__) < '1.0'

# Define the system

if 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, strictly_proper=True))

# Generate the time and input vectors

tvec = np.linspace(0, 1, 8)

uvec = np.dot(

np.ones((sys.ninputs, 1)),

np.reshape(np.sin(tvec), (1, 8)))

#

# Pass squeeze argument and make sure the shape is correct

#

# For responses that are indexed by the input, check against shape1

# For responses that have no/fixed input, check against shape2

#

# Impulse response

if isinstance(sys, StateSpace):

# Check the states as well

_, yvec, xvec = ct.impulse_response(

sys, tvec, squeeze=squeeze, return_x=True)

if sys.issiso():

assert xvec.shape == (sys.nstates, 8)

else:

assert xvec.shape == (sys.nstates, sys.ninputs, 8)

else:

_, yvec = ct.impulse_response(sys, tvec, squeeze=squeeze)

assert yvec.shape == shape1

# Step response

if isinstance(sys, StateSpace):

# Check the states as well

_, yvec, xvec = ct.step_response(

sys, tvec, squeeze=squeeze, return_x=True)

if sys.issiso():

assert xvec.shape == (sys.nstates, 8)

else:

assert xvec.shape == (sys.nstates, sys.ninputs, 8)

else:

_, yvec = ct.step_response(sys, tvec, squeeze=squeeze)

assert yvec.shape == shape1

# Initial response (only indexed by output)

if isinstance(sys, StateSpace):

# Check the states as well

_, yvec, xvec = ct.initial_response(

sys, tvec, 1, squeeze=squeeze, return_x=True)

assert xvec.shape == (sys.nstates, 8)

else:

_, yvec = ct.initial_response(sys, tvec, 1, squeeze=squeeze)

assert yvec.shape == shape2

# Forced response (only indexed by output)

if isinstance(sys, StateSpace):

# Check the states as well

_, yvec, xvec = ct.forced_response(

sys, tvec, uvec, 0, return_x=True, squeeze=squeeze)

assert xvec.shape == (sys.nstates, 8)

else:

# Just check the input/output response

_, yvec = ct.forced_response(sys, tvec, uvec, 0, squeeze=squeeze)

assert yvec.shape == shape2

# Test cases where we choose a subset of inputs and outputs

_, yvec = ct.step_response(

sys, tvec, input=ninp-1, output=nout-1, squeeze=squeeze)

if squeeze is False:

# Shape should be unsqueezed

assert yvec.shape == (1, 1, 8)

else:

# Shape should be squeezed

assert yvec.shape == (8, )

# For InputOutputSystems, also test input/output response

if isinstance(sys, ct.InputOutputSystem) and not scipy0:

_, yvec = ct.input_output_response(sys, tvec, uvec, squeeze=squeeze)

assert yvec.shape == shape2

#

# Changing config.default to False should return 3D frequency response

#

ct.config.set_defaults('control', squeeze_time_response=False)

_, yvec = ct.impulse_response(sys, tvec)

if squeeze is not True or sys.ninputs > 1 or sys.noutputs > 1:

assert yvec.shape == (sys.noutputs, sys.ninputs, 8)

_, yvec = ct.step_response(sys, tvec)

if squeeze is not True or sys.ninputs > 1 or sys.noutputs > 1:

assert yvec.shape == (sys.noutputs, sys.ninputs, 8)

_, yvec = ct.initial_response(sys, tvec, 1)

if squeeze is not True or sys.noutputs > 1:

assert yvec.shape == (sys.noutputs, 8)

if isinstance(sys, ct.StateSpace):

_, yvec, xvec = ct.forced_response(

sys, tvec, uvec, 0, return_x=True)

assert xvec.shape == (sys.nstates, 8)

else:

_, yvec = ct.forced_response(sys, tvec, uvec, 0)

if squeeze is not True or sys.noutputs > 1:

assert yvec.shape == (sys.noutputs, 8)

# For InputOutputSystems, also test input_output_response

if isinstance(sys, ct.InputOutputSystem) and not scipy0:

_, yvec = ct.input_output_response(sys, tvec, uvec)

if squeeze is not True or sys.noutputs > 1:

assert yvec.shape == (sys.noutputs, 8)

@pytest.mark.parametrize("fcn", [ct.ss, ct.tf, ct.ss2io])

def test_squeeze_exception(self, fcn):

sys = fcn(ct.rss(2, 1, 1))

with pytest.raises(ValueError, match="unknown squeeze value"):

step_response(sys, squeeze=1)

@pytest.mark.usefixtures("editsdefaults")

@pytest.mark.parametrize("nstate, nout, ninp, squeeze, shape", [

def test_squeeze_0_8_4(self, nstate, nout, ninp, squeeze, shape):

# Set defaults to match release 0.8.4

ct.config.use_legacy_defaults('0.8.4')

ct.config.use_numpy_matrix(False)

# Generate system, time, and input vectors

sys = ct.rss(nstate, nout, ninp, strictly_proper=True)

tvec = np.linspace(0, 1, 8)

uvec = np.dot(

np.ones((sys.ninputs, 1)),

np.reshape(np.sin(tvec), (1, 8)))

_, yvec = ct.initial_response(sys, tvec, 1, squeeze=squeeze)

assert yvec.shape == shape

@pytest.mark.parametrize(

def test_response_transpose(

self, nstate, nout, ninp, squeeze, ysh_in, ysh_no, xsh_in):

sys = ct.rss(nstate, nout, ninp)

T = np.linspace(0, 1, 8)

# Step response - input indexed

t, y, x = ct.step_response(

sys, T, transpose=True, return_x=True, squeeze=squeeze)

assert t.shape == (T.size, )

assert y.shape == ysh_in

assert x.shape == xsh_in

# Initial response - no input indexing

t, y, x = ct.initial_response(

sys, T, 1, transpose=True, return_x=True, squeeze=squeeze)

assert t.shape == (T.size, )

assert y.shape == ysh_no