def test_for_constant_signal():
size = 1000
Ts = 0.1
coef = np.ones(size) * 0.7
vector = np.array([1., 0, 0])
inp = system.Input(Ts, coefficients=coef, steeringVector=vector)
A = np.eye(3, k=-1)
c = np.eye(3)
sys = system.System(A, c)
mixingMatrix = -1e1 * np.eye(3)
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys, ctrl)
t = np.linspace(0., 99., size)
res = sim.simulate(t, (inp, ))
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(3)])
recon = reconstruction.WienerFilter(t, sys, (inp, ))
u_hat, log = recon.filter(ctrl)
plt.figure()
plt.plot(t, coef, label="u")
plt.plot(t, u_hat, label="u_hat")
plt.legend()
def test_postFiltering():
size = 10000
order = 4
Ts = 0.1
amplitude = 0.35
frequency = 1e-2
phase = np.pi * 7. / 8.
vector = np.zeros(order)
vector[0] = 1.
inp = system.Sin(Ts,
amplitude=amplitude,
frequency=frequency,
phase=phase,
steeringVector=vector)
A = np.eye(order, k=-1)
c = np.eye(order)
sys = system.System(A, c)
mixingMatrix = -1e0 * np.eye(order)
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys, ctrl)
t = np.linspace(0., Ts * (size - 1), size)
res = sim.simulate(t, [inp])
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(order)])
bandwith = 2 * np.pi * frequency * 1e-2
print("Bandwith = %s" % bandwith)
postFilterTF = filters.TransferFunction()
postFilterTF.butterWorth(2, (bandwith, ))
print(postFilterTF.a, postFilterTF.b)
postFilter = filters.Filter()
postFilter.tf2lssObservableForm(postFilterTF.b, postFilterTF.a)
print("Filter A = \n%s" % postFilter.A)
print(postFilter.b)
print(postFilter.c)
recon = reconstruction.WienerFilterWithPostFiltering(
t, sys, (inp, ), postFilter)
u_hat, log = recon.filter(ctrl)
plt.figure()
plt.plot(t, inp.scalarFunction(t), label="u")
plt.plot(t, u_hat, label="u_hat")
plt.legend()
def testSystem():
A = np.array([[1., 0], [2., 1.]])
c = np.array([[1., 0], [0, 1]])
sys = system.System(A, c)
# Test str function
print(sys)
f = sys.frequencyResponse(0.)
state = np.array([3, 2])
output = sys.output(state)
np.testing.assert_array_equal(state, output)
def test_lowering_order():
size = 1000
order = 8
Ts = 0.1
amplitude = 0.35
frequency = 1e-2
phase = np.pi * 7. / 8.
vector = np.zeros(order)
vector[0] = 1.
inp = system.Sin(Ts,
amplitude=amplitude,
frequency=frequency,
phase=phase,
steeringVector=vector)
A = np.eye(order, k=-1)
c = np.eye(order)
sys = system.System(A, c)
mixingMatrix = -1e0 * np.eye(order)
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys, ctrl)
t = np.linspace(0., 99., size)
res = sim.simulate(t, (inp, ))
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(order)])
u_hats = []
for index in range(1, order + 1):
newSystem, newControl, newInput = system.LowerOrderSystem(
sys, ctrl, inp, index)
recon = reconstruction.WienerFilter(t, newSystem, (newInput, ))
u_hat, log = recon.filter(newControl)
u_hats.append(u_hat)
plt.figure()
plt.plot(t, inp.scalarFunction(t), label="u")
for index in range(order):
plt.plot(t, u_hats[index], label="u_hat_%i" % (index + 1))
plt.legend()
def test_evaluate_PlotTransferFunctions():
size = 10000
order = 7
Ts = 0.1
beta = 5.
coef = np.random.rand(size) * 2. - 1.
vector = np.zeros(order)
vector[0] = 2.
inp = system.FirstOrderHold(Ts, coefficients=coef, steeringVector=vector)
T = 40
t = 10 ** (T/10.)
rho = np.power(t, 1./order)/beta * np.sqrt(2)
A = beta * np.eye(order, k=-1) - rho * np.eye(order, k=0)
c = np.eye(order)
sys = system.System(A, c)
mixingMatrix = - 1e1 * np.eye(order)
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys, ctrl)
t = np.linspace(0., 99., size)
res = sim.simulate(t, (inp,))
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(order)])
recon = reconstruction.WienerFilter(t, sys, (inp,))
u_hat, log = recon.filter(ctrl)
ev = evaluation.Evaluation(sys, u_hat, (inp,))
freqsLim = [1e-2, 1e2]
figure1 = ev.PlotTransferFunctions(freqsLim)
figure2 = ev.PlotPowerSpectralDensity(t)
def test_for_sinusodial_signal():
size = 1000
order = 8
Ts = 0.1
amplitude = 0.35
frequency = 1e-2
phase = np.pi * 7. / 8.
vector = np.zeros(order)
vector[0] = 1.
inp = system.Sin(Ts,
amplitude=amplitude,
frequency=frequency,
phase=phase,
steeringVector=vector)
A = np.eye(order, k=-1)
c = np.eye(order)
sys = system.System(A, c)
mixingMatrix = -1e0 * np.eye(order)
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys, ctrl)
t = np.linspace(0., 99., size)
res = sim.simulate(t, (inp, ))
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(order)])
recon = reconstruction.WienerFilter(t, sys, (inp, ))
u_hat, log = recon.filter(ctrl)
plt.figure()
plt.plot(t, inp.scalarFunction(t), label="u")
plt.plot(t, u_hat, label="u_hat")
plt.legend()
def test_integratorChain():
size = 1000
Ts = 0.1
coef = np.ones(size)
vector = np.array([1., 0, 0])
inp = system.Input(Ts, coefficients=coef, steeringVector=vector)
A = np.eye(3, k=-1)
c = np.eye(3)
sys = system.System(A, c)
mixingMatrix = -1e1 * np.eye(3)
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys, ctrl)
t = np.linspace(0., 99., size)
res = sim.simulate(t, (inp, ))
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(3)])
def testSystemSetup():
size = 1000
Ts = 0.1
coef = np.random.rand(size)
vector = np.array([1., 0, 0])
inp = system.Input(Ts, coefficients=coef, steeringVector=vector)
A = np.random.rand(3, 3)
c = np.eye(3)
sys = system.System(A, c)
mixingMatrix = -np.eye(3)
ctrl = system.Control(mixingMatrix, size)
return {
'size': size,
'Ts': Ts,
'inp': inp,
'sys': sys,
'ctrl': ctrl,
}
def test_for_first_order_filter_signal():
size = 10000
order = 7
Ts = 0.1
coef = np.random.rand(size) * 2. - 1.
vector = np.zeros(order)
vector[0] = 1.
inp = system.FirstOrderHold(Ts, coefficients=coef, steeringVector=vector)
A = np.eye(order, k=-1)
c = np.eye(order)
sys = system.System(A, c)
mixingMatrix = -1e1 * np.eye(order)
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys, ctrl)
t = np.linspace(0., 99., size)
res = sim.simulate(t, (inp, ))
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(order)])
recon = reconstruction.WienerFilter(t, sys, (inp, ))
reconP = reconstruction.ParallelWienerFilter(t, sys, (inp, ))
u_hat, log = recon.filter(ctrl)
u_hatP = reconP.filter(ctrl)
plt.figure()
plt.plot(t, coef, label="coef")
plt.plot(t, inp.scalarFunction(t), label="u")
plt.plot(t, u_hat, label="u_hat")
plt.plot(t, u_hatP, label="u_hatP")
plt.legend()
def test_noisy_integratorChain():
size = 1000
Ts = 0.1
order = 3
coef = np.ones(size)
vector = np.array([1., 0, 0])
inp = system.Input(Ts, coefficients=coef, steeringVector=vector)
A = np.eye(3, k=-1)
c = np.eye(3)
noiseVariance = np.ones(3) * 1e-4
noiseSources = []
for index in range(order):
if noiseVariance[index] > 0:
vector = np.zeros(order)
vector[index] = 1
noiseSources.append({
"std": np.sqrt(noiseVariance[index]),
"steeringVector": vector,
"name": "Noise Source %s" % index
})
options = {'noise': noiseSources}
sys = system.System(A, c)
mixingMatrix = -1e1 * np.eye(3)
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys, ctrl, options=options)
t = np.linspace(0., 99., size)
res = sim.simulate(t, (inp, ))
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(3)])
def test_for_noise_simulation():
size = 1000
order = 8
Ts = 0.1
amplitude = 0.35
frequency = 1e-2
phase = np.pi * 7. / 8.
vector = np.zeros(order)
vector[0] = 1.
inp = system.Sin(Ts,
amplitude=amplitude,
frequency=frequency,
phase=phase,
steeringVector=vector)
A = np.eye(order, k=-1)
c = np.eye(order)
sys = system.System(A, c)
mixingMatrix = -1e0 * np.eye(order)
ctrl = system.Control(mixingMatrix, size)
noiseVariance = np.ones(order) * 1e-4
noiseSources = []
for index in range(order):
if noiseVariance[index] > 0:
vector = np.zeros(order)
vector[index] = 1
noiseSources.append({
"std": np.sqrt(noiseVariance[index]),
"steeringVector": vector,
"name": "Noise Source %s" % index
})
options = {'noise': noiseSources}
sim = simulator.Simulator(sys, ctrl, options=options)
t = np.linspace(0., 99., size)
res = sim.simulate(t, [inp])
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(order)])
recon = reconstruction.WienerFilter(t, sys, (inp, ))
recon_with_noise = reconstruction.WienerFilter(t,
sys, [inp],
options=options)
recon_with_noise_Parallel = reconstruction.ParallelWienerFilter(
t, sys, [inp], options=options)
u_hat, log = recon.filter(ctrl)
u_hat_with_noise, log_with_noise = recon_with_noise.filter(ctrl)
u_hat_with_noise_Parallel = recon_with_noise_Parallel.filter(ctrl)
plt.figure()
plt.plot(t, inp.scalarFunction(t), label="u")
plt.plot(t, u_hat, label="u_hat")
plt.plot(t, u_hat_with_noise, label="u_hat_with_noise")
plt.plot(t, u_hat_with_noise_Parallel, label="u_hat_with_noise_Parallel")
plt.legend()
def piBlockSystem1():
start_time = time.time()
size = 20000 # Number of samples in the simulation
M = (1 << 0) # Number of parallel controlnverters
N = 2 # Number of PI mixing submatrices
Ts = 8e-5 # Sampling period
num_inputs = 1
t = np.linspace(0, (size - 1) * Ts, size) # Time grid for control updates
beta = 6250
kappa = 1
stability = Ts * beta * (1 / np.sqrt(M) + kappa) <= 1
print("Stability margin: {}".format(1. - Ts * beta *
(1 / np.sqrt(M) + kappa)))
print("Stability criterion: {}".format(stability))
H = hadamardMatrix(M)
L = 1
A = np.zeros(((N + 1) * M, (N + 1) * M))
MixingPi = np.empty((N, M, M))
for k in range(N):
MixingPi[k] = beta * np.outer(H[:, 0], H[:, 0])
# (beta)*(0.2*np.outer(H[:,0],H[:,0])
# + 0.1*np.outer(H[:,1],H[:,1])
# + 0.3*np.outer(H[:,2],H[:,2])
# + 0.4*np.outer(H[:,3],H[:,3])) # Index set = {0,0}
A[(k + 1) * M:(k + 2) * M, (k) * M:(k + 1) * M] = MixingPi[k]
nperseg = (1 << 16)
selected_FFT_bin = 250.
input_signals = []
frequencies = []
# sins = np.empty((M,size))
for i in range(num_inputs):
amplitude = 1
frequency = (i + 1) * (selected_FFT_bin / (nperseg * Ts))
print("{} Hz".format(frequency))
# size =
frequencies.append(frequency)
phase = 0
vector = np.zeros((N + 1) * M)
vector[0:M] = beta * (H[:, i])
input_signals.append(
system.Sin(Ts,
amplitude=amplitude,
frequency=frequency,
phase=phase,
steeringVector=vector))
input_signals = tuple(input_signals)
print("A = \n%s\nb = \n%s" % (A, vector))
checkCovarianceMatrixConvergence(A, vector)
checkCovarianceMatrixConvergence(-A, vector)
c = np.eye((N + 1) * M)
sys = system.System(A, c)
mixingMatrix = -kappa * beta * np.eye((N + 1) * M)
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys,
ctrl,
options={
'stateBound':
(Ts * beta * kappa) / (1. - Ts * beta) + 1.,
'noise': [{
'std':
1e-6,
'steeringVector':
beta * np.eye((N + 1) * M)[:, i],
'name':
'Bastard'
} for i in range((N + 1) * M)]
})
res = sim.simulate(t, input_signals)
# plt.figure()
# plt.plot(res['t'], res['output'])
# plt.legend(["%s" % x for x in range(res['output'].shape[0])])
# plt.show()
eta2 = np.ones((N + 1) * M) * 1e5
options = {
'eta2':
eta2,
'sigmaU2': [1.],
'noise': [{
'std': 1e-6,
'steeringVector': beta * np.eye((N + 1) * M)[:, i],
'name': 'Bastard'
} for i in range((N + 1) * M)]
}
recon = reconstruction.WienerFilter(t, sys, input_signals, options)
input_estimates, recon_log = recon.filter(ctrl)
print("Run Time: {} seconds".format(time.time() - start_time))
nfft = (1 << 16)
spectrums = np.empty((num_inputs, nfft // 2 + 1))
for i in range(num_inputs):
freq, spec = signal.welch(input_estimates[:, i],
1. / Ts,
axis=0,
nperseg=nperseg,
nfft=nfft,
scaling='density')
spectrums[i, :] = spec
plt.figure()
[
plt.semilogx(freq, 10 * np.log10(np.abs(spec)), label="")
for spec in spectrums
]
plt.grid()
plt.title("Block diagonal Pi System")
def test_evaluate_PlotTransferFunctions_For_PostFiltering():
size = 10000
order = 2
postFilterOrder = 2
Ts = 0.1
eta2 = 1e-6
filterEta2 = 1e-0
amplitude = 1.
frequency = 1e-1
phase = np.pi * 7. / 8.
vector = np.zeros(order)
vector[0] = 1.
inp = system.Sin(Ts, amplitude=amplitude, frequency=frequency, phase=phase, steeringVector=vector)
# coef = np.random.rand(size) * 2. - 1.
# vector = np.zeros(order)
# vector[0] = 2.
# inp = system.FirstOrderHold(Ts, coefficients=coef, steeringVector=vector)
A = 2 * np.eye(order, k=-1, dtype=np.float)
# make causal filter
A += 0. * np.eye(order, k=0)
c = np.eye(order, dtype=np.float)
sys = system.System(A, c)
mixingMatrix = - 1e1 * np.eye(order)
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys, ctrl)
t = np.linspace(0., 99., size)
res = sim.simulate(t, (inp,))
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(order)])
# System 1
recon = reconstruction.WienerFilter(t, sys, (inp,), {"eta2":eta2*np.ones(order)})
u_hat, log = recon.filter(ctrl)
ev = evaluation.Evaluation(sys, u_hat, (inp,))
# Post Filtering
bandwith = 2 * np.pi * 1e-1
print("Bandwith = %s" % bandwith)
postFilterTF = filters.TransferFunction()
postFilterTF.butterWorth(postFilterOrder, (bandwith))
postFilterElliptic = filters.TransferFunction()
postFilterElliptic.iirFilter(postFilterOrder, (bandwith,), 'ellip')
postFilterCheby1 = filters.TransferFunction()
postFilterCheby1.iirFilter(postFilterOrder, (bandwith,), 'cheby1')
postFilterCheby2 = filters.TransferFunction()
postFilterCheby2.iirFilter(postFilterOrder, (bandwith,), 'cheby2')
postFilterBessel = filters.TransferFunction()
postFilterBessel.iirFilter(postFilterOrder, (bandwith,), 'bessel')
plt.figure()
w1, h1 = postFilterTF.frequencyResponse()
w2, h2 = postFilterElliptic.frequencyResponse()
w3, h3 = postFilterCheby1.frequencyResponse()
w4, h4 = postFilterCheby2.frequencyResponse()
w5, h5 = postFilterBessel.frequencyResponse()
plt.semilogx(w1/np.pi/2., 20 * np.log10(abs(h1)), label="Butterworth")
plt.semilogx(w2/np.pi/2., 20 * np.log10(abs(h2)), label="Elliptic")
plt.semilogx(w3/np.pi/2., 20 * np.log10(abs(h3)), label="Cheby 1")
plt.semilogx(w4/np.pi/2., 20 * np.log10(abs(h4)), label="Cheby 2")
plt.semilogx(w5/np.pi/2., 20 * np.log10(abs(h5)), label="Bessel")
plt.legend()
plt.xlabel('Frequency [Hz]')
plt.ylabel('Amplitude response [dB]')
plt.grid()
# plt.show()
# print(postFilterTF.a, postFilterTF.b)
postFilter1 = filters.Filter()
postFilter2 = filters.Filter()
postFilter3 = filters.Filter()
postFilter4 = filters.Filter()
postFilter5 = filters.Filter()
postFilter1.tf2lssObservableForm(postFilterTF.b, postFilterTF.a)
postFilter2.tf2lssObservableForm(postFilterElliptic.b, postFilterElliptic.a)
postFilter3.tf2lssObservableForm(postFilterCheby1.b, postFilterCheby1.a)
postFilter4.tf2lssObservableForm(postFilterCheby2.b, postFilterCheby2.a)
postFilter5.tf2lssObservableForm(postFilterBessel.b, postFilterBessel.a)
# eta2PostFilter = np.concatenate((eta2 * np.ones(order), filterEta2 * np.ones(postFilter.c.shape[1])))
eta2PostFilter = eta2 * np.ones(order)
reconstructionFiltered1 = reconstruction.WienerFilterWithPostFiltering(t, sys, (inp,), postFilter1, {"eta2":eta2PostFilter})
reconstructionFiltered2 = reconstruction.WienerFilterWithPostFiltering(t, sys, (inp,), postFilter2, {"eta2":eta2PostFilter})
reconstructionFiltered3 = reconstruction.WienerFilterWithPostFiltering(t, sys, (inp,), postFilter3, {"eta2":eta2PostFilter})
reconstructionFiltered4 = reconstruction.WienerFilterWithPostFiltering(t, sys, (inp,), postFilter4, {"eta2":eta2PostFilter})
reconstructionFiltered5 = reconstruction.WienerFilterWithPostFiltering(t, sys, (inp,), postFilter5, {"eta2":eta2PostFilter})
print(ctrl.mixingMatrix)
u_hatP_1, log_1 = reconstructionFiltered1.filter(ctrl)
print(ctrl.mixingMatrix)
print(postFilter2)
u_hatP_2, log_2 = reconstructionFiltered2.filter(ctrl)
u_hatP_3, log_3 = reconstructionFiltered3.filter(ctrl)
u_hatP_4, log_4 = reconstructionFiltered4.filter(ctrl)
u_hatP_5, log_5 = reconstructionFiltered5.filter(ctrl)
evP1 = evaluation.Evaluation(sys, u_hatP_1, (inp,))
evP2 = evaluation.Evaluation(sys, u_hatP_2, (inp,))
evP3 = evaluation.Evaluation(sys, u_hatP_3, (inp,))
evP4 = evaluation.Evaluation(sys, u_hatP_4, (inp,))
evP5 = evaluation.Evaluation(sys, u_hatP_5, (inp,))
freqsLim = [1e-2, 1e2]
# figure1 = ev.PlotTransferFunctions(freqsLim)
figure2 = ev.PlotPowerSpectralDensity(t)
# figure3 = ev2.PlotTransferFunctions(freqsLim)
figure4 = evP1.PlotPowerSpectralDensity(t)
figure5 = evP2.PlotPowerSpectralDensity(t)
figure6 = evP3.PlotPowerSpectralDensity(t)
figure7 = evP4.PlotPowerSpectralDensity(t)
figure8 = evP5.PlotPowerSpectralDensity(t)
plt.figure()
plt.plot(u_hat, label="u_hat")
# plt.plot(u_hatP_1, label="Butter")
# plt.plot(u_hatP_2, label="Elliptic")
plt.plot(u_hatP_3, label="Chebyshev 1")
# plt.plot(u_hatP_4, label="Chebychev 2")
plt.plot(u_hatP_5, label="Bessel")
# plt.plot(u_hat - u_hat2, label="diff")
plt.legend()
def test_evaluate_WithNoise():
size = 10000
order = 5
Ts = 0.0001
eta2 = 1e-4
beta = 1000.
noiseVariance = np.ones(order) * 1e-12
noiseSources = []
for index in range(order):
if noiseVariance[index]>0:
vector = np.zeros(order)
vector[index] = beta
noiseSources.append(
{
"std": np.sqrt(noiseVariance[index]),
"steeringVector": vector,
"name": "Noise Source %s" % index
}
)
options = {
'noise': noiseSources,
'eta2': eta2 * np.ones(order)
}
# options = {}
# options2 = {
# # 'noise': {"standardDeviation": np.sqrt(noiseVariance) * np.array([1./(order - x)**3 for x in range(order)])},
# 'noise': {"standardDeviation": 1e-4 * np.array([1. for x in range(order)])},
# 'eta2': eta2 * np.ones(order)
# }
# options['noise']['standardDeviation'][5] = 1e-1
amplitude = 1. * 1e-6
frequency = 1e2 / (2. * np.pi)
phase = np.pi * 7. / 8.
vector = np.ones(order) * beta / 2.
# vector = np.zeros(order)
vector[0] = beta
inp = system.Sin(Ts, amplitude=amplitude, frequency=frequency, phase=phase, steeringVector=vector)
# coef = np.random.rand(size) * 2. - 1.
# vector = np.zeros(order)
# vector[0] = beta
# inp = system.FirstOrderHold(Ts, coefficients=coef, steeringVector=vector)
# T = 120
# t = 10 ** (T/10.)
# rho = np.power(t, 1./order)/beta * np.sqrt(2)
rho = 0.
A = beta/2. * np.eye(order, k=-1) - rho * np.eye(order, k=0)
# A[0, :] =-np.ones(order) * beta/2.
print(A)
# A = 1e-2 * np.eye(order, k=-1) - rho * np.eye(order, k=0)
# A = np.zeros((order, order))
# A = np.random.randn(order, order)
# A = np.dot(A, np.linalg.inv(np.diag(np.sum(np.abs(A), axis=1))))
# print(A)
# A = 9. * np.eye(order, k=-1, dtype=np.float)
# make causal filter
# A += 0. * np.eye(order, k=0)
c0 = np.zeros(order, dtype=np.float).reshape((order,1))
c0[-1] = 1.
c = np.eye(order, dtype=np.float)
sys0 = system.System(A, c0)
sys = system.System(A, c)
mixingMatrix = - 10.5 * np.eye(order)
ctrl = system.Control(mixingMatrix, size)
ctrl0 = system.Control(mixingMatrix, size)
sim0 = simulator.Simulator(sys0, ctrl0, options=options)
sim = simulator.Simulator(sys, ctrl, options=options)
t = np.linspace(0., Ts * (size - 1) , size)
u = inp.scalarFunction(t)
# res2 = sim0.simulate(t, (inp,))
res = sim.simulate(t, (inp,))
plt.figure()
plt.plot(res['t'], res['output'])
plt.legend(["%s" % x for x in range(order)])
# System 1
reconSISO = reconstruction.WienerFilter(t, sys0, (inp,), {"eta2":np.array(eta2)})
reconSIMO = reconstruction.WienerFilter(t, sys, (inp,), {"eta2":eta2 * np.ones(order)})
reconMIMO = reconstruction.WienerFilter(t, sys, [inp], options)
u_hatSISO, log_SISO = reconSISO.filter(ctrl)
u_hatSIMO, log_SIMO = reconSIMO.filter(ctrl)
u_hatMIMO, log_MIMO = reconMIMO.filter(ctrl)
print(reconSISO)
ev_SISO = evaluation.Evaluation(sys, u_hatSISO, (inp,))
ev_SIMO = evaluation.Evaluation(sys, u_hatSIMO, (inp,))
ev_MIMO = evaluation.Evaluation(sys, u_hatMIMO, (inp,))
freqsLim = [1e-2, 1e2]
freq, SISOSPECTRUM, SIGNALSPECTRUM = ev_SISO.PowerSpectralDensity(t)
_, SIMOSPECTRUM, _ = ev_SIMO.PowerSpectralDensity(t)
_, MIMOSPECTRUM, _ = ev_MIMO.PowerSpectralDensity(t)
plt.figure()
plt.semilogx(freq, 10 * np.log10(np.abs(SIGNALSPECTRUM[0].flatten())), label="u_hatSISO")
plt.semilogx(freq, 10 * np.log10(np.abs(SISOSPECTRUM.flatten())), label="u_hatSISO")
plt.semilogx(freq, 10 * np.log10(np.abs(SIMOSPECTRUM.flatten())), label="u_hatSIMO")
plt.semilogx(freq, 10 * np.log10(np.abs(MIMOSPECTRUM[:, 0].flatten())), label="u_hatMIMO")
plt.legend()
plt.figure()
plt.plot(u, label="u")
plt.plot(u_hatSISO, label="u_hatSISO")
plt.plot(u_hatSIMO, label="u_hatSIMO")
plt.plot(u_hatMIMO, label="u_hatMIMO")
plt.legend()
plt.figure()
plt.plot(u_hatSISO.flatten() - u.flatten(), label="u_hatSISO")
plt.plot(u_hatSIMO.flatten() - u.flatten(), label="u_hatSIMO")
plt.plot(u_hatMIMO[:,0] - u.flatten(), label="u_hatMIMO")
plt.legend()
plt.figure()
freq, u_hatSISOSP = signal.welch(u_hatSISO.flatten() - u.flatten(), 1./Ts)
_, u_hatSIMOSP = signal.welch(u_hatSIMO.flatten() - u.flatten(), 1./Ts)
_, u_hatMIMOSP = signal.welch(u_hatMIMO[:,0] - u.flatten(), 1./Ts)
plt.semilogx(freq, 10 * np.log10(np.abs(u_hatSISOSP)), label="u_hatSISO")
plt.semilogx(freq, 10 * np.log10(np.abs(u_hatSIMOSP)), label="u_hatSIMO")
plt.semilogx(freq, 10 * np.log10(np.abs(u_hatMIMOSP)), label="u_hatMIMO")
plt.legend()
figure1 = ev_SISO.PlotTransferFunctions(freqsLim)
def __init__(self,
experiment_id,
data_dir,
M,
N,
L,
input_phase,
input_amplitude,
input_frequency=None,
beta=6250,
sampling_period=8e-5,
primary_signal_dimension=0,
systemtype='ParallelIntegratorChain',
OSR=16,
eta2_magnitude=1,
kappa=1,
sigma2_thermal=1e-6,
sigma2_reconst=1e-6,
num_periods_in_simulation=100,
controller='subspaceController',
bitsPerControl=1):
print("Initializing Experiment | ID: %s" % experiment_id)
self.experiment_id = experiment_id
self.data_dir = Path(data_dir)
self.M = M
self.N = N
self.L = L
self.input_phase = input_phase
self.input_amplitude = input_amplitude
self.input_frequency = input_frequency
self.beta = beta
self.sampling_period = sampling_period
self.primary_signal_dimension = primary_signal_dimension
self.systemtype = systemtype
self.OSR = OSR
self.kappa = kappa
self.sigma2_thermal = sigma2_thermal
self.sigma2_reconst = sigma2_reconst
self.num_periods_in_simulation = num_periods_in_simulation
self.size = round(num_periods_in_simulation / sampling_period)
self.controller = controller
self.bitsPerControl = bitsPerControl
self.border = np.int(self.size // 100)
self.all_input_signal_amplitudes = np.zeros(L)
self.all_input_signal_amplitudes[
primary_signal_dimension] = input_amplitude
self.logstr = ("{0}: EXPERIMENT LOG\n{0}: Experiment ID: {1}\n".format(
time.strftime("%d/%m/%Y %H:%M:%S"), experiment_id))
self.finished_simulation = False
self.finished_reconstruction = False
if not self.data_dir.exists():
self.data_dir.mkdir(parents=True)
#################################################
# System and input signal specifications #
#################################################
if self.primary_signal_dimension > self.M:
self.log(
"Primary Signal Dimension cannot be larger than M, setting to 0 (first dim)"
)
self.primary_signal_dimension = 0
if self.input_frequency == None:
self.input_frequency = 1. / (self.sampling_period * 2 * self.OSR)
self.log(f'Setting f_sig = f_s/(2*OSR) = {self.input_frequency}')
if self.systemtype == "ParallelIntegratorChain":
self.A = np.zeros((self.N * self.M, self.N * self.M))
mixingPi = np.zeros((self.N - 1, self.M, self.M))
H = hadamardMatrix(self.M)
if N > 1:
# L=1 means just one of M dimensions is used and there is
# only one input signal => We scale up the input vector by sqrt(M)
if L == 1:
for k in range(N - 1):
mixingPi[k] = beta * np.sqrt(M) * (
np.outer(H[:, 0], H[:, 0])
) # + beta * np.sqrt(M) * sum(np.outer(H[:,i],H[:,i]) for i in range(1,self.M)) * 1e-3
self.A[(k + 1) * self.M:(k + 2) * self.M,
(k) * self.M:(k + 1) * self.M] = mixingPi[k]
# L=M means M input signals
elif L == M:
for k in range(N - 1):
mixingPi[k] = self.beta * np.sqrt(M) * np.eye(
M
) #(sum(np.outer(H[:,i],H[:,i]) for i in range(self.M)))
self.A[(k + 1) * self.M:(k + 2) * self.M,
(k) * self.M:(k + 1) * self.M] = mixingPi[k]
else:
for k in range(N - 1):
mixingPi[k] = self.beta * np.sqrt(M / L) * (sum(
np.outer(H[:, i], H[:, i]) for i in range(self.L)))
self.A[(k + 1) * self.M:(k + 2) * self.M,
(k) * self.M:(k + 1) * self.M] = mixingPi[k]
# raise NotImplemented
print("A = {}".format(self.A))
else:
mixingPi = [np.zeros((M, M))]
# Limit the low frequency gain of the filter
# at approximately the thermal noise level
LeakyIntegrators = True
if LeakyIntegrators == True:
self.rho = beta / ((sigma2_thermal)**(-1 / N))
self.A -= np.eye(N * M) * self.rho
# Define input signals:
self.input_signals = []
self.all_input_signal_frequencies = np.zeros(L)
self.all_input_signal_frequencies[
self.primary_signal_dimension] = self.input_frequency
allowed_signal_frequencies = self.input_frequency * (
0.5**np.arange(1, 3 * M))
for i in range(self.L):
if i == self.primary_signal_dimension: continue
k = np.random.randint(0, L - 1)
self.all_input_signal_frequencies[
i] = allowed_signal_frequencies[i]
self.all_input_signal_amplitudes[i] = input_amplitude
# Define input steeringVectors
if L == 1:
inputVectorMatrix = beta * np.sqrt(M) * H
elif L == 2:
# The outer product sum results in a checkerboard matrix with 1/0 entries.
# We pick input vectors from there and scale up by M (undoing the attenuation from the outer products)
inputVectorMatrix = beta * (M / 2) * (np.outer(
H[:, 0], H[:, 0]) + np.outer(H[:, 1], H[:, 1])) * 2
elif L == M:
inputVectorMatrix = beta * np.sqrt(M) * (np.hstack(
(np.outer(H[:, i], H[:, i])[:, 0].reshape(-1, 1)
for i in range(L))))
else:
inputVectorMatrix = beta * np.sqrt(M / L) * H
for i in range(self.L):
vector = np.zeros(self.M * self.N)
vector[0:self.M] = inputVectorMatrix[:, i]
self.input_signals.append(
system.Sin(
self.sampling_period,
amplitude=self.all_input_signal_amplitudes[i],
frequency=self.all_input_signal_frequencies[i],
phase=self.input_phase, #+ (np.pi/2)*i,
steeringVector=vector))
print(f'b_{i} = {self.input_signals[i].steeringVector}')
self.input_signals = tuple(self.input_signals)
elif self.systemtype == "CyclicIntegratorChain":
self.A = np.zeros((self.N * self.M, self.N * self.M))
mixingPi = np.zeros((self.N, self.M, self.M))
H = hadamardMatrix(self.M)
self.all_input_signal_frequencies = np.zeros(L)
self.all_input_signal_frequencies[
self.primary_signal_dimension] = self.input_frequency
self.all_input_signal_amplitudes[
self.primary_signal_dimension] = self.input_amplitude
if N > 1:
if L == 1:
# Start with the Pi_N, in the top right corner
mixingPi[-1] = beta * np.sqrt(M) * sum(
np.outer(H[:, i], H[:, i]) for i in range(self.N - 1))
self.A[0:self.M, -self.M:self.M * self.N] = mixingPi[-1]
# Iterate just like before, down the first sub-diagonal, always summing over all but the k'th pi vector
for k in range(N - 1):
mixingPi[k] = beta * np.sqrt(M) * sum(
np.outer(H[:, i], H[:, i])
for i in range(self.N) if i != k)
self.A[(k + 1) * self.M:(k + 2) * self.M,
(k) * self.M:(k + 1) * self.M] = mixingPi[k]
else:
raise NotImplemented
else:
mixingPi = [np.zeros((M, M))]
# Define input signals:
self.input_signals = []
if self.L == 1:
selector = np.zeros(self.M)
selector[0] = 1
vector = np.zeros(self.M * self.N)
vector[0:self.M * self.N] = beta * np.sqrt(M) * np.dot(
np.vstack(
(np.outer(H[:, i], H[:, i]) for i in range(self.N))),
selector.reshape(-1, 1)).flatten()
self.input_signals.append(
system.Sin(self.sampling_period,
amplitude=self.input_amplitude,
frequency=self.input_frequency,
phase=self.input_phase,
steeringVector=vector))
else:
raise NotImplemented
else:
raise NotImplemented
# pd.DataFrame(self.A).to_csv('A_matrix.csv')
# print("A = \n%s\nb = \n%s" % (self.A, self.input_signals[self.primary_signal_dimension].steeringVector))
self.c = np.eye(self.N * self.M)
self.sys = system.System(
A=self.A,
c=self.c,
b=self.input_signals[primary_signal_dimension].steeringVector)
systemResponse = lambda f: np.dot(self.sys.frequencyResponse(f), self.
sys.b)
self.eta2_magnitude = np.max(
np.abs(systemResponse(1. / (2. * sampling_period * OSR)))**2)
self.log("eta2_magnitude set to max(|G(s)b|^2) = {:.5e}".format(
self.eta2_magnitude))
print("eta2_magnitude set to max(|G(s)b|^2) = {:.5e}".format(
self.eta2_magnitude))
#################################################
# Controller specification #
#################################################
dither = True
"""
The subspace controller is only implemented for L=1 signal right now.
"""
if controller == 'subspaceController':
self.ctrlMixingMatrix = np.zeros((self.N * self.M, self.N))
# if L>1:
# raise "Multi-Bit controller not implemented for L>1 input signals"
if dither:
self.ctrlMixingMatrix = (
np.random.randint(2, size=(N * M, N)) * 2 -
1) * beta * 1e-3
if L == 1:
for i in range(N):
self.ctrlMixingMatrix[
i * M:(i + 1) * M,
i] = -np.sqrt(self.M) * self.beta * H[:, 0]
else:
raise NotImplemented
# self.ctrlMixingMatrix = np.zeros((N*M,N*M))
# for i in range(N):
# self.ctrlMixingMatrix[i*M:(i+1)*M,i*M:(i+1)*M] = -np.sqrt(self.M) * self.beta * H #
elif controller == 'diagonalController':
self.ctrlMixingMatrix = np.zeros((N * M, N * M))
if dither:
self.ctrlMixingMatrix = (np.random.randint(
2, size=(self.N * self.M, self.N * self.M)) * 2 -
1) * beta * 0.05 / (self.M * self.N)
self.ctrlMixingMatrix += -self.kappa * self.beta * np.sqrt(
M) * np.eye(self.N * self.M)
# elif controller == 'blockDiagonalController:
# for k in range(N):
# self.ctrlMixingMatrix[k * self.M: (k+1) * self.M,
# k * self.M:(k+1) * self.M] = (-self.beta
# * np.outer(H[:,0],H[:,0]))
self.ctrlOptions = {
'bitsPerControl': bitsPerControl,
'bound': 1,
}
self.ctrl = system.Control(self.ctrlMixingMatrix,
self.size,
options=self.ctrlOptions)
print("ctrlMixingMatrix: %s\n" % (self.ctrlMixingMatrix, ))
'std': sigma2_thermal,
'steeringVector': beta * np.eye(N)[:, i]
} for i in range(N)]
}
mixingMatrix = -kappa * beta * np.eye(N)
ctrl = system.Control(mixingMatrix, size)
input_signal = system.Sin(Ts,
amplitude=amplitude,
frequency=frequency,
phase=phase,
steeringVector=input_vector)
all_inputs = [input_signal]
order = N
sys = system.System(A=A, c=c, b=input_vector)
systemResponse = lambda f: np.dot(sys.frequencyResponse(f), sys.b)
eta2_magnitude = np.max(
np.abs(systemResponse(1. / (2. * Ts * osr)))**2)
print("Eta2 = %d" % eta2_magnitude)
eta2 = np.ones(order) * eta2_magnitude
ctrl = system.Control(mixingMatrix, size)
sim = simulator.Simulator(sys, ctrl, options=simulationOptions)
res = sim.simulate(t, (input_signal, ))
reconstructionOptions = {
'eta2':
eta2,
'sigmaU2':
sigmaU2,