def test_mapABCD_1(self):
"""Test function for mapABCD() 1/2"""
for f0 in self.f0s:
for form in self.forms:
for order in self.orders:
if f0 != 0. and order % 2 == 1:
# odd-order pass band modulator
continue
# Optimized zero placement
print("Testing form: %s, order: %d, f0: %f" % \
(form, order, f0))
ntf = synthesizeNTF(order, self.osr, 2, self.Hinf, f0)
a1, g1, b1, c1 = realizeNTF(ntf, form)
# we check realize NTF too
self.assertTrue(np.allclose(a1, self.res[f0][form][order]['a'],
atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(g1, self.res[f0][form][order]['g'],
atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(b1, self.res[f0][form][order]['b'],
atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(c1, self.res[f0][form][order]['c'],
atol=1e-4, rtol=1e-3))
ABCD = stuffABCD(a1, g1, b1, c1, form)
a, g, b, c = mapABCD(ABCD, form)
self.assertTrue(np.allclose(a1, a, atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(g1, g, atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(b1, b, atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(c1, c, atol=1e-4, rtol=1e-3))
def test_simulateSNR_2(self):
"""Test function for simulateSNR() 2/4"""
# next test: f0 = 0
# Load test references
fname = pkg_resources.resource_filename(__name__,
"test_data/test_snr_amp2.mat")
amp_ref = scipy.io.loadmat(fname)['amp'].reshape((-1, ))
snr_ref = scipy.io.loadmat(fname)['snr'].reshape((-1, ))
ABCD_ref = scipy.io.loadmat(fname)['ABCD'].reshape((4, 5))
order = 3
osr = 256
nlev = 2
f0 = 0.
Hinf = 1.25
form = 'CIFB'
ntf = ds.synthesizeNTF(order, osr, 2, Hinf, f0)
a1, g1, b1, c1 = ds.realizeNTF(ntf, form)
a1_ref = [0.008863535715733, 0.093216950269955, 0.444473912607388]
g1_ref = [9.035620546615189e-05]
b1_ref = [0.008863535715733, 0.093216950269955, 0.444473912607388, 1.]
c1_ref = [1., 1., 1.]
self.assertTrue(np.allclose(a1, a1_ref, atol=1e-9, rtol=5e-5))
self.assertTrue(np.allclose(g1, g1_ref, atol=1e-9, rtol=5e-5))
self.assertTrue(np.allclose(b1, b1_ref, atol=1e-9, rtol=1e-4))
self.assertTrue(np.allclose(c1, c1_ref, atol=1e-9, rtol=2e-5))
ABCD = ds.stuffABCD(a1, g1, b1, c1, form)
self.assertTrue(np.allclose(ABCD, ABCD_ref, atol=9e-5, rtol=1e-4))
snr, amp = ds.simulateSNR(ABCD, osr, None, f0, nlev)
self.assertTrue(np.allclose(snr, snr_ref, atol=1e-5, rtol=1e-5))
self.assertTrue(np.allclose(amp, amp_ref, atol=1e-5, rtol=1e-5))
def test_simulateSNR_2(self):
"""Test function for simulateSNR() 2/4"""
# next test: f0 = 0
# Load test references
fname = pkg_resources.resource_filename(__name__,
"test_data/test_snr_amp2.mat")
amp_ref = scipy.io.loadmat(fname)['amp'].reshape((-1,))
snr_ref = scipy.io.loadmat(fname)['snr'].reshape((-1,))
ABCD_ref = scipy.io.loadmat(fname)['ABCD'].reshape((4, 5))
order = 3
osr = 256
nlev = 2
f0 = 0.
Hinf = 1.25
form = 'CIFB'
ntf = ds.synthesizeNTF(order, osr, 2, Hinf, f0)
a1, g1, b1, c1 = ds.realizeNTF(ntf, form)
a1_ref = [0.008863535715733, 0.093216950269955, 0.444473912607388]
g1_ref = [9.035620546615189e-05]
b1_ref = [0.008863535715733, 0.093216950269955, 0.444473912607388, 1.]
c1_ref = [1., 1., 1.]
self.assertTrue(np.allclose(a1, a1_ref, atol=1e-9, rtol=5e-5))
self.assertTrue(np.allclose(g1, g1_ref, atol=1e-9, rtol=5e-5))
self.assertTrue(np.allclose(b1, b1_ref, atol=1e-9, rtol=1e-4))
self.assertTrue(np.allclose(c1, c1_ref, atol=1e-9, rtol=2e-5))
ABCD = ds.stuffABCD(a1, g1, b1, c1, form)
self.assertTrue(np.allclose(ABCD, ABCD_ref, atol=9e-5, rtol=1e-4))
snr, amp = ds.simulateSNR(ABCD, osr, None, f0, nlev)
self.assertTrue(np.allclose(snr, snr_ref, atol=1e-5, rtol=1e-5))
self.assertTrue(np.allclose(amp, amp_ref, atol=1e-5, rtol=1e-5))
def test_realizeNTF(self):
"""Test function for realizeNTF()"""
for f0 in self.f0s:
for form in self.forms:
for order in self.orders:
if f0 != 0. and order % 2 == 1:
# odd-order pass band modulator
continue
# Optimized zero placement
print("Testing form: %s, order: %d, f0: %f, OSR %d" % \
(form, order, f0, self.osr))
ntf = ds.synthesizeNTF(order,self. osr, 2, self.Hinf, f0)
a, g, b, c = ds.realizeNTF(ntf, form)
print(ntf)
print(a, g, b, c)
print(self.res[f0][form][order]['a'],
self.res[f0][form][order]['g'],
self.res[f0][form][order]['b'],
self.res[f0][form][order]['c'])
self.assertTrue(np.allclose(a, self.res[f0][form][order]['a'],
atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(g, self.res[f0][form][order]['g'],
atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(b, self.res[f0][form][order]['b'],
atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(c, self.res[f0][form][order]['c'],
atol=1e-4, rtol=1e-3))
return
def test_simulateSNR_1(self):
"""Test function for simulateSNR() 1/4"""
# first test: f0 = 0
# Load test references
fname = pkg_resources.resource_filename(__name__,
"test_data/test_snr_amp.mat")
amp_ref = scipy.io.loadmat(fname)['amp'].reshape((-1, ))
snr_ref = scipy.io.loadmat(fname)['snr'].reshape((-1, ))
amp_user_ref = scipy.io.loadmat(fname)['amp_user'].reshape((-1, ))
snr_user_ref = scipy.io.loadmat(fname)['snr_user'].reshape((-1, ))
order = 4
osr = 256
nlev = 2
f0 = 0.22
Hinf = 1.25
form = 'CRFB'
ntf = ds.synthesizeNTF(order, osr, 2, Hinf, f0)
a1, g1, b1, c1 = ds.realizeNTF(ntf, form)
ABCD = ds.stuffABCD(a1, g1, b1, c1, form)
ABCD_ref = np.array([[1., -1.6252, 0, 0, -0.0789, 0.0789],
[1., -0.6252, 0, 0, -0.0756, 0.0756],
[0, 1., 1., -1.6252, -0.2758, 0.2758],
[0, 1., 1., -0.6252, 0.0843, -0.0843],
[0, 0, 0, 1., 1., 0]])
self.assertTrue(np.allclose(ABCD, ABCD_ref, atol=9e-5, rtol=1e-4))
# bonus test, mapABCD - realizeNTF - stuffABCD
a2, g2, b2, c2 = ds.mapABCD(ABCD, form)
self.assertTrue(np.allclose(a1, a2, atol=1e-5, rtol=1e-5))
self.assertTrue(np.allclose(g1, g2, atol=1e-5, rtol=1e-5))
self.assertTrue(np.allclose(b1, b2, atol=1e-5, rtol=1e-5))
self.assertTrue(np.allclose(c1, c2, atol=1e-5, rtol=1e-5))
# We do three tests:
# SNR from ABCD matrix
# SNR from NTF
# SNR from LTI obj with user specified amplitudes
snr, amp = ds.simulateSNR(ABCD, osr, None, f0, nlev)
self.assertTrue(np.allclose(snr, snr_ref, atol=1, rtol=5e-2))
self.assertTrue(np.allclose(amp, amp_ref, atol=5e-1, rtol=1e-2))
snr2, amp2 = ds.simulateSNR(ntf, osr, None, f0, nlev)
self.assertTrue(np.allclose(snr2, snr_ref, atol=1e-5, rtol=1e-5))
self.assertTrue(np.allclose(amp2, amp_ref, atol=1e-5, rtol=1e-5))
amp_user = np.linspace(-100, 0, 200)[::10]
snr_user, amp_user = ds.simulateSNR(lti(*ntf),
osr=osr,
amp=amp_user,
f0=f0,
nlev=nlev)
self.assertTrue(
np.allclose(snr_user, snr_user_ref[::10], atol=1e-5, rtol=1e-5))
self.assertTrue(
np.allclose(amp_user, amp_user_ref[::10], atol=1e-5, rtol=1e-5))
def test_simulateSNR_1(self):
"""Test function for simulateSNR() 1/4"""
# first test: f0 = 0
# Load test references
fname = pkg_resources.resource_filename(__name__,
"test_data/test_snr_amp.mat")
amp_ref = scipy.io.loadmat(fname)['amp'].reshape((-1,))
snr_ref = scipy.io.loadmat(fname)['snr'].reshape((-1,))
amp_user_ref = scipy.io.loadmat(fname)['amp_user'].reshape((-1,))
snr_user_ref = scipy.io.loadmat(fname)['snr_user'].reshape((-1,))
order = 4
osr = 256
nlev = 2
f0 = 0.22
Hinf = 1.25
form = 'CRFB'
ntf = ds.synthesizeNTF(order, osr, 2, Hinf, f0)
a1, g1, b1, c1 = ds.realizeNTF(ntf, form)
ABCD = ds.stuffABCD(a1, g1, b1, c1, form)
ABCD_ref = np.array([[1., -1.6252, 0, 0, -0.0789, 0.0789],
[1., -0.6252, 0, 0, -0.0756, 0.0756],
[0, 1., 1., -1.6252, -0.2758, 0.2758],
[0, 1., 1., -0.6252, 0.0843, -0.0843],
[0, 0, 0, 1., 1., 0]])
self.assertTrue(np.allclose(ABCD, ABCD_ref, atol=9e-5, rtol=1e-4))
# bonus test, mapABCD - realizeNTF - stuffABCD
a2, g2, b2, c2 = ds.mapABCD(ABCD, form)
self.assertTrue(np.allclose(a1, a2, atol=1e-5, rtol=1e-5))
self.assertTrue(np.allclose(g1, g2, atol=1e-5, rtol=1e-5))
self.assertTrue(np.allclose(b1, b2, atol=1e-5, rtol=1e-5))
self.assertTrue(np.allclose(c1, c2, atol=1e-5, rtol=1e-5))
# We do three tests:
# SNR from ABCD matrix
# SNR from NTF
# SNR from LTI obj with user specified amplitudes
snr, amp = ds.simulateSNR(ABCD, osr, None, f0, nlev)
self.assertTrue(np.allclose(snr, snr_ref, atol=1, rtol=5e-2))
self.assertTrue(np.allclose(amp, amp_ref, atol=5e-1, rtol=1e-2))
snr2, amp2 = ds.simulateSNR(ntf, osr, None, f0, nlev)
self.assertTrue(np.allclose(snr2, snr_ref, atol=1e-5, rtol=1e-5))
self.assertTrue(np.allclose(amp2, amp_ref, atol=1e-5, rtol=1e-5))
amp_user = np.linspace(-100, 0, 200)[::10]
snr_user, amp_user = ds.simulateSNR(lti(*ntf), osr=osr, amp=amp_user,
f0=f0, nlev=nlev)
self.assertTrue(np.allclose(snr_user, snr_user_ref[::10], atol=1e-5,
rtol=1e-5))
self.assertTrue(np.allclose(amp_user, amp_user_ref[::10], atol=1e-5,
rtol=1e-5))
def setUp(self):
fname = pkg_resources.resource_filename(__name__, "test_data/test_simulateDSM.mat")
self.v_ref = scipy.io.loadmat(fname)['v']
self.xn_ref = scipy.io.loadmat(fname)['xn']
self.xmax_ref = scipy.io.loadmat(fname)['xmax']
self.y_ref = scipy.io.loadmat(fname)['y']
OSR = 32
self.H = synthesizeNTF(5, OSR, 1)
N = 8192
f = 85
self.u = 0.5*np.sin(2*np.pi*f/N*np.arange(N))
a, g, b, c = realizeNTF(self.H, 'CRFB')
self.ABCD = stuffABCD(a, g, b, c, form='CRFB')
def __init__(self, input: FixedPointValue, osr=32, order=4, n_lev=2):
self.input = input
self.fmt = input.fmt
self.h = synthesizeNTF(order, osr, 1)
a, g, b, c = realizeNTF(self.h, form='CIFB')
abcd = stuffABCD(a, g, b, c)
abcd_scaled, umax, s = scaleABCD(abcd, n_lev)
self.parameters = mapABCD(abcd_scaled)
print(umax)
self.order = order
self.osr = osr
assert n_lev > 1
self.n_lev = n_lev
self.quantization_values = [i * 2 - (n_lev / 2) for i in range(n_lev)]
self.output = Signal(range(0, len(self.quantization_values)))
def setUp(self):
order = 8
osr = 32
self.nlev = 2
self.f0 = 0.125
Hinf = 1.5
form = 'CRFB'
# Optimized zero placement
ntf = ds.synthesizeNTF(order, osr, 2, Hinf, self.f0)
a, g, b, c = ds.realizeNTF(ntf, form)
# we pass b = b[0]
# if you use a single feed-in for the input, b may be scalar too
ABCD = ds.stuffABCD(a, g, b[0], c, form)
# now we correct b for the assert
b = np.concatenate(( # Use a single feed-in for the input
np.atleast_1d(b[0]),
np.zeros((max(b.shape) - 1,))
))
self.ABCD0 = ABCD.copy()
# References
self.Sdiag_ref = np.array([71.9580, 51.9359, 8.2133, 6.5398,
1.9446, 1.2070, 0.4223, 0.3040])
self.umax_ref = 0.8667
ABCD_ref1 = np.array([[1., -0.7320, 0, 0, 0, 0],
[0.7218, 0.4717, 0, 0, 0, 0],
[0, 0.1581, 1., -0.7357, 0, 0],
[0, 0.1259, 0.7962, 0.4142, 0, 0],
[0, 0, 0, 0.2973, 1., -0.9437],
[0, 0, 0, 0.1846, 0.6207, 0.4142],
[0, 0, 0, 0, 0, 0.3499],
[0, 0, 0, 0, 0, 0.2518],
[0, 0, 0, 0, 0, 0]])
ABCD_ref2 = np.array([[0, 0, 0.0858, -0.0858],
[0, 0, 0.0619, 0.0428],
[0, 0, 0, 0.0642],
[0, 0, 0, 0.1835],
[0, 0, 0, 0.2447],
[0, 0, 0, 0.0581],
[1., -0.8971, 0, -0.0076],
[0.7197, 0.3543, 0, -0.1746],
[0, 3.29, 0, 0]])
self.ABCD_ref = np.hstack((ABCD_ref1, ABCD_ref2))
def setUp(self):
fname = pkg_resources.resource_filename(
__name__, "test_data/test_simulateDSM.mat")
self.v_ref = scipy.io.loadmat(fname)['v']
self.xn_ref = scipy.io.loadmat(fname)['xn']
self.xmax_ref = scipy.io.loadmat(fname)['xmax']
self.y_ref = scipy.io.loadmat(fname)['y']
self.u_ref = scipy.io.loadmat(fname)['u']
self.ABCD_ref = scipy.io.loadmat(fname)['ABCD']
self.zeros = cplxpair(scipy.io.loadmat(fname)['zeros'])
self.poles = cplxpair(scipy.io.loadmat(fname)['poles'])
self.v_ref = self.v_ref.reshape(-1)
self.y_ref = self.y_ref.reshape(-1)
OSR = 32
self.H = synthesizeNTF(5, OSR, 10)
N = 8192
f = 85
self.u = 0.5 * np.sin(2 * np.pi * f / N * np.arange(N))
a, g, b, c = realizeNTF(self.H, 'CRFB')
self.ABCD = stuffABCD(a, g, b, c, form='CRFB')
def test_mapABCD_1(self):
"""Test function for mapABCD() 1/2"""
for f0 in self.f0s:
for form in self.forms:
for order in self.orders:
if f0 != 0. and order % 2 == 1:
# odd-order pass band modulator
continue
# Optimized zero placement
print("Testing form: %s, order: %d, f0: %f" % \
(form, order, f0))
ntf = synthesizeNTF(order, self.osr, 2, self.Hinf, f0)
a1, g1, b1, c1 = realizeNTF(ntf, form)
# we check realize NTF too
self.assertTrue(
np.allclose(a1,
self.res[f0][form][order]['a'],
atol=1e-4,
rtol=1e-3))
self.assertTrue(
np.allclose(g1,
self.res[f0][form][order]['g'],
atol=1e-4,
rtol=1e-3))
self.assertTrue(
np.allclose(b1,
self.res[f0][form][order]['b'],
atol=1e-4,
rtol=1e-3))
self.assertTrue(
np.allclose(c1,
self.res[f0][form][order]['c'],
atol=1e-4,
rtol=1e-3))
ABCD = stuffABCD(a1, g1, b1, c1, form)
a, g, b, c = mapABCD(ABCD, form)
self.assertTrue(np.allclose(a1, a, atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(g1, g, atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(b1, b, atol=1e-4, rtol=1e-3))
self.assertTrue(np.allclose(c1, c, atol=1e-4, rtol=1e-3))
def test_realizeNTF(self):
"""Test function for realizeNTF()"""
for f0 in self.f0s:
for form in self.forms:
for order in self.orders:
if f0 != 0. and order % 2 == 1:
# odd-order pass band modulator
continue
# Optimized zero placement
print("Testing form: %s, order: %d, f0: %f, OSR %d" % \
(form, order, f0, self.osr))
ntf = ds.synthesizeNTF(order, self.osr, 2, self.Hinf, f0)
a, g, b, c = ds.realizeNTF(ntf, form)
print(ntf)
print(a, g, b, c)
print(self.res[f0][form][order]['a'],
self.res[f0][form][order]['g'],
self.res[f0][form][order]['b'],
self.res[f0][form][order]['c'])
self.assertTrue(
np.allclose(a,
self.res[f0][form][order]['a'],
atol=1e-4,
rtol=1e-3))
self.assertTrue(
np.allclose(g,
self.res[f0][form][order]['g'],
atol=1e-4,
rtol=1e-3))
self.assertTrue(
np.allclose(b,
self.res[f0][form][order]['b'],
atol=1e-4,
rtol=1e-3))
self.assertTrue(
np.allclose(c,
self.res[f0][form][order]['c'],
atol=1e-4,
rtol=1e-3))
return
def setUp(self):
order = 8
osr = 32
self.nlev = 2
self.f0 = 0.125
Hinf = 1.5
form = 'CRFB'
# Optimized zero placement
ntf = ds.synthesizeNTF(order, osr, 2, Hinf, self.f0)
a, g, b, c = ds.realizeNTF(ntf, form)
# we pass b = b[0]
# if you use a single feed-in for the input, b may be scalar too
ABCD = ds.stuffABCD(a, g, b[0], c, form)
# now we correct b for the assert
# Use a single feed-in for the input
b = np.concatenate((np.atleast_1d(b[0]), np.zeros(
(max(b.shape) - 1, ))))
self.ABCD0 = ABCD.copy()
# References
self.Sdiag_ref = np.array(
[71.9580, 51.9359, 8.2133, 6.5398, 1.9446, 1.2070, 0.4223, 0.3040])
self.umax_ref = 0.8667
ABCD_ref1 = np.array([[1., -0.7320, 0, 0, 0, 0],
[0.7218, 0.4717, 0, 0, 0, 0],
[0, 0.1581, 1., -0.7357, 0, 0],
[0, 0.1259, 0.7962, 0.4142, 0, 0],
[0, 0, 0, 0.2973, 1., -0.9437],
[0, 0, 0, 0.1846, 0.6207, 0.4142],
[0, 0, 0, 0, 0, 0.3499], [0, 0, 0, 0, 0, 0.2518],
[0, 0, 0, 0, 0, 0]])
ABCD_ref2 = np.array([[0, 0, 0.0858, -0.0858], [0, 0, 0.0619, 0.0428],
[0, 0, 0, 0.0642], [0, 0, 0, 0.1835],
[0, 0, 0, 0.2447], [0, 0, 0, 0.0581],
[1., -0.8971, 0, -0.0076],
[0.7197, 0.3543, 0, -0.1746], [0, 3.29, 0, 0]])
self.ABCD_ref = np.hstack((ABCD_ref1, ABCD_ref2))
def test_dsdemo3(self):
"""dsdemo3 test: Delta sigma modulator synthesis"""
order = 5
R = 42
opt = 1
H = ds.synthesizeNTF(order, R, opt)
# ## Evaluation of the coefficients for a CRFB topology
a, g, b, c = ds.realizeNTF(H)
# Use a single feed-in for the input
# Lets check that stuffABCD understands that if b is scalar it means 1 feed-in.
ABCD = ds.stuffABCD(a, g, b[0], c)
# for passing the assertion below, we need b to have the trailing zeros
b = np.concatenate((np.atleast_1d(b[0]), np.zeros((b.shape[0] - 1, ))))
u = np.linspace(0, 0.6, 30)
N = 1e4
T = np.ones((1, N))
maxima = np.zeros((order, len(u)))
for i in range(len(u)):
ui = u[i]
v, xn, xmax, _ = ds.simulateDSM(ui * T, ABCD)
maxima[:, i] = np.squeeze(xmax)
if any(xmax > 1e2):
umax = ui
u = u[:i + 1]
maxima = maxima[:, :i]
break
# save the maxima
prescale_maxima = np.copy(maxima)
# ## Scaled modulator
# ### Calculate the scaled coefficients
ABCDs, umax, _ = ds.scaleABCD(ABCD, N_sim=1e5)
as_, gs, bs, cs = ds.mapABCD(ABCDs)
# ### Calculate the state maxima
u = np.linspace(0, umax, 30)
N = 1e4
T = np.ones((N, ))
maxima = np.zeros((order, len(u)))
for i in range(len(u)):
ui = u[i]
v, xn, xmax, _ = ds.simulateDSM(ui * T, ABCDs)
maxima[:, i] = xmax.squeeze()
if any(xmax > 1e2):
umax = ui
u = u[:i]
maxima = maxima[:, :i]
break
self.assertTrue(np.allclose(ABCD, self.data['ABCD']))
self.assertTrue(
np.allclose(ABCDs, self.data['ABCDs'], atol=1e-2, rtol=5e-2))
self.assertTrue(np.allclose(a, self.data['a'], atol=1e-5, rtol=1e-3))
self.assertTrue(np.allclose(b, self.data['b'], atol=1e-5, rtol=1e-3))
self.assertTrue(np.allclose(g, self.data['g'], atol=1e-5, rtol=1e-3))
self.assertTrue(np.allclose(c, self.data['c'], atol=1e-5, rtol=1e-3))
self.assertTrue(np.allclose(as_, self.data['as'], atol=1e-2,
rtol=5e-3))
self.assertTrue(np.allclose(bs, self.data['bs'], atol=5e-3, rtol=5e-3))
self.assertTrue(np.allclose(gs, self.data['gs'], atol=5e-3, rtol=5e-3))
self.assertTrue(np.allclose(cs, self.data['cs'], atol=3e-2, rtol=3e-2))
self.assertTrue(
np.allclose(umax, self.data['umax'], atol=5e-3, rtol=5e-3))
self.assertTrue(
np.allclose(maxima, self.data['maxima'], atol=2e-2, rtol=5e-2))
def test_dsdemo3(self):
"""dsdemo3 test: Delta sigma modulator synthesis"""
order = 5
R = 42
opt = 1
H = ds.synthesizeNTF(order, R, opt)
# ## Evaluation of the coefficients for a CRFB topology
a, g, b, c = ds.realizeNTF(H)
# Use a single feed-in for the input
# Lets check that stuffABCD understands that if b is scalar it means 1 feed-in.
ABCD = ds.stuffABCD(a, g, b[0], c)
# for passing the assertion below, we need b to have the trailing zeros
b = np.concatenate((np.atleast_1d(b[0]),
np.zeros((b.shape[0] - 1,))))
u = np.linspace(0, 0.6, 30)
N = 1e4
T = np.ones((1, N))
maxima = np.zeros((order, len(u)))
for i in range(len(u)):
ui = u[i]
v, xn, xmax, _ = ds.simulateDSM(ui*T, ABCD);
maxima[:, i] = np.squeeze(xmax)
if any(xmax > 1e2):
umax = ui
u = u[:i+1]
maxima = maxima[:, :i]
break
# save the maxima
prescale_maxima = np.copy(maxima)
# ## Scaled modulator
# ### Calculate the scaled coefficients
ABCDs, umax, _ = ds.scaleABCD(ABCD, N_sim=1e5)
as_, gs, bs, cs = ds.mapABCD(ABCDs)
# ### Calculate the state maxima
u = np.linspace(0, umax, 30)
N = 1e4
T = np.ones((N,))
maxima = np.zeros((order, len(u)))
for i in range(len(u)):
ui = u[i]
v, xn, xmax, _ = ds.simulateDSM(ui*T, ABCDs)
maxima[:, i] = xmax.squeeze()
if any(xmax > 1e2):
umax = ui;
u = u[:i]
maxima = maxima[:, :i]
break
self.assertTrue(np.allclose(ABCD, self.data['ABCD']))
self.assertTrue(np.allclose(ABCDs, self.data['ABCDs'], atol=1e-2, rtol=5e-2))
self.assertTrue(np.allclose(a, self.data['a'], atol=1e-5, rtol=1e-3))
self.assertTrue(np.allclose(b, self.data['b'], atol=1e-5, rtol=1e-3))
self.assertTrue(np.allclose(g, self.data['g'], atol=1e-5, rtol=1e-3))
self.assertTrue(np.allclose(c, self.data['c'], atol=1e-5, rtol=1e-3))
self.assertTrue(np.allclose(as_, self.data['as'], atol=1e-2, rtol=5e-3))
self.assertTrue(np.allclose(bs, self.data['bs'], atol=5e-3, rtol=5e-3))
self.assertTrue(np.allclose(gs, self.data['gs'], atol=5e-3, rtol=5e-3))
self.assertTrue(np.allclose(cs, self.data['cs'], atol=3e-2, rtol=3e-2))
self.assertTrue(np.allclose(umax, self.data['umax'], atol=5e-3, rtol=5e-3))
self.assertTrue(np.allclose(maxima, self.data['maxima'], atol=2e-2, rtol=5e-2))