def _conduct_FIRuncFilter_and_MonteCarlo(Ub, b1, blow, kind, runs, sigma_noise,
x):
y, Uy = FIRuncFilter(x, sigma_noise, b1, Ub, blow=blow,
kind=kind) # apply uncertain FIR filter (GUM formula)
yMC, UyMC = MC(x, sigma_noise, b1, np.ones(1), Ub, runs=runs,
blow=blow) # apply uncertain FIR filter (Monte Carlo)
return Uy, UyMC, y, yMC
def test_FIRuncFilter_MC_uncertainty_comparison(filters, signals, lowpasses):
# Check output for thinkable permutations of input parameters against a Monte Carlo approach.
# run method
y_fir, Uy_fir = FIRuncFilter(**filters,
**signals,
**lowpasses,
return_full_covariance=True)
# run Monte Carlo simulation of an FIR
## adjust input to match conventions of MC
x = signals["y"]
ux = signals["sigma_noise"]
b = filters["theta"]
a = [1.0]
if isinstance(filters["Utheta"], np.ndarray):
Uab = filters["Utheta"]
else: # Utheta == None
Uab = np.zeros(
(len(b), len(b))) # MC-method cant deal with Utheta = None
blow = lowpasses["blow"]
if isinstance(blow, np.ndarray):
n_blow = len(blow)
else:
n_blow = 0
## run FIR with MC and extract diagonal of returned covariance
y_mc, Uy_mc = MC(x, ux, b, a, Uab, blow=blow, runs=2000)
# HACK for visualization during debugging
# import matplotlib.pyplot as plt
# fig, ax = plt.subplots(nrows=1, ncols=3)
# ax[0].plot(y_fir, label="fir")
# ax[0].plot(y_mc, label="mc")
# ax[0].set_title("filter: {0}, signal: {1}".format(len(b), len(x)))
# ax[0].legend()
# ax[1].imshow(Uy_fir)
# ax[1].set_title("FIR")
# ax[2].imshow(Uy_mc)
# ax[2].set_title("MC")
# plt.show()
# /HACK
# check basic properties
assert np.all(np.diag(Uy_fir) >= 0)
assert np.all(np.diag(Uy_mc) >= 0)
assert Uy_fir.shape == Uy_mc.shape
# approximative comparison after swing-in of MC-result
# (which is after the combined length of blow and b)
assert np.allclose(
Uy_fir[len(b) + n_blow:, len(b) + n_blow:],
Uy_mc[len(b) + n_blow:, len(b) + n_blow:],
atol=2e-1 *
Uy_fir.max(), # very broad check, increase runs for better fit
rtol=1e-1,
)
def test_FIRuncFilter_float():
# input signal + run methods
x = rect(time,100*Ts,250*Ts,1.0,noise=sigma_noise)
# apply uncertain FIR filter (GUM formula)
for blow in [None, b2]:
y, Uy = FIRuncFilter(x, sigma_noise, b1, Ub, blow=blow, kind="float")
assert len(y) == len(x)
assert len(Uy) == len(x)
def test_FIRuncFilter_diag():
sigma_diag = sigma_noise * ( 1 + np.heaviside(np.arange(len(time)) - len(time)//2,0) ) # std doubles after half of the time
noise = sigma_diag * white_gaussian(len(time))
# input signal + run methods
x = rect(time,100*Ts,250*Ts,1.0,noise=noise)
# apply uncertain FIR filter (GUM formula)
for blow in [None, b2]:
y, Uy = FIRuncFilter(x, sigma_diag, b1, Ub, blow=blow, kind="diag")
assert len(y) == len(x)
assert len(Uy) == len(x)
def test_FIRuncFilter_legacy_comparison(filters, signals, lowpasses):
# Compare output of both functions for thinkable permutations of input parameters.
y, Uy = legacy_FIRuncFilter(**filters, **signals, **lowpasses)
y2, Uy2 = FIRuncFilter(**filters, **signals, **lowpasses)
# check output dimensions
assert len(y2) == len(signals["y"])
assert Uy2.shape == (len(signals["y"]), )
# check value identity
assert np.allclose(y, y2)
assert np.allclose(Uy, Uy2)
def test_FIR_IIR_identity(kind, fir_filter, input_signal):
# run signal through both implementations
y_iir, Uy_iir, _ = IIRuncFilter(*input_signal.values(), **fir_filter, kind=kind)
y_fir, Uy_fir = FIRuncFilter(
*input_signal.values(),
theta=fir_filter["b"],
Utheta=fir_filter["Uab"],
kind=kind,
)
assert_allclose(y_fir, y_iir)
assert_allclose(Uy_fir, Uy_iir)
def test_FIRuncFilter_corr():
# get an instance of noise, the covariance and the covariance-matrix with the specified color
color = "white"
noise = power_law_noise(N=nTime, color_value=color, std=sigma_noise)
Ux = power_law_acf(nTime, color_value=color, std=sigma_noise)
# input signal
x = rect(time,100*Ts,250*Ts,1.0,noise=noise)
# apply uncertain FIR filter (GUM formula)
for blow in [None, b2]:
y, Uy = FIRuncFilter(x, Ux, b1, Ub, blow=blow, kind="corr")
assert len(y) == len(x)
assert len(Uy) == len(x)
def test_FIRuncFilter_equality(equal_filters, equal_signals):
# Check expected output for being identical across different equivalent input
# parameter cases.
all_y = []
all_uy = []
# run all combinations of filter and signals
for (f, s) in itertools.product(equal_filters, equal_signals):
y, uy = FIRuncFilter(**f, **s)
all_y.append(y)
all_uy.append(uy)
# check that all have the same output, as they are supposed to represent equal cases
for a, b in itertools.combinations(all_y, 2):
assert np.allclose(a, b)
for a, b in itertools.combinations(all_uy, 2):
assert np.allclose(a, b)
def evaluate():
if covariance_case == "full":
U_theta = np.diag(np.full_like(theta, sigma_noise))
elif covariance_case == "zero":
len_theta = len(theta)
U_theta = np.zeros((len_theta, len_theta))
elif covariance_case == "none":
U_theta = None
else:
raise NotImplementedError
# measure runtime (timeit.timeit is unable to use both local+global variables)
start_time = time.time()
current_y, current_Uy = FIRuncFilter(signal,
sigma_noise,
theta,
U_theta,
blow=None)
end_time = time.time()
return end_time - start_time, current_y, current_Uy
def apply_filter(self,
b,
a=1,
filter_uncertainty=None,
MonteCarloRuns=None):
"""Apply digital filter (b,a) to the signal values and propagate the uncertainty associated with the signal
Parameters
----------
b: np.ndarray
filter numerator coefficients
a: np.ndarray
filter denominator coefficients, use a=1 for FIR-type filter
filter_uncertainty: np.ndarray
covariance matrix associated with filter coefficients, Uab=None if no uncertainty associated with filter
MonteCarloRuns: int
number of Monte Carlo runs, if `None` then GUM linearization will be used
Returns
-------
no return variables
"""
if isinstance(a, list):
a = np.array(a)
if not (isinstance(a, np.ndarray)): # FIR type filter
if len(self.uncertainty.shape) == 1:
if not isinstance(MonteCarloRuns, int):
self.values, self.uncertainty = \
FIRuncFilter(self.values, self.uncertainty, b, Utheta = filter_uncertainty)
else:
self.values, self.uncertainty = \
MC(self.values, self.uncertainty, b, a, filter_uncertainty, runs=MonteCarloRuns)
else:
if not isinstance(MonteCarloRuns, int):
MonteCarloRuns = 10000
self.values, self.uncertainty = \
MC(self.values, self.uncertainty, b, a, filter_uncertainty, runs=MonteCarloRuns)
else: # IIR-type filter
if not isinstance(MonteCarloRuns, int):
MonteCarloRuns = 10000
self.values, self.uncertainty = \
MC(self.values, self.uncertainty, b, a, filter_uncertainty, runs=MonteCarloRuns)
# uncertain knowledge: cutoff between 19.5kHz and 20.5kHz
runs = 1000
FC = fcut + (2 * np.random.rand(runs) - 1) * 0.5e3
B = np.zeros((runs, L + 1))
for k in range(runs):
B[k, :] = kaiser_lowpass(L, FC[k], Fs)[0]
Ub = make_semiposdef(np.cov(B, rowvar=0))
# simulate input and output signals
time = np.arange(0, 499 * Ts, Ts)
noise = 1e-3
x = rect(time, 100 * Ts, 250 * Ts, 1.0, noise=noise)
y, Uy = FIRuncFilter(x, noise, b, Ub)
yMC, UyMC = MC.MC(x, noise, b, [1.0], Ub, runs=10000)
yMC2, UyMC2 = MC.SMC(x, noise, b, [1.0], Ub, runs=10000)
plt.figure(1)
plt.cla()
plt.plot(time, col_hstack([x, y]))
plt.legend(('input', 'output'))
plt.figure(3)
plt.cla()
plt.plot(time, col_hstack([Uy, UyMC, UyMC2]))
plt.title('Uncertainty of filter output signal')
plt.legend(('FIR formula', 'Monte Carlo', 'Sequential Monte Carlo'))
plt.show()
bF, UbF = model_est.invLSFIR_unc(
H, UH, N, tau, f,
Fs) # Calculation of FIR deconvolution filter and its assoc. unc.
CbF = UbF / (np.tile(np.sqrt(np.diag(UbF))[:, np.newaxis], (1, N + 1)) *
np.tile(np.sqrt(np.diag(UbF))[:, np.newaxis].T,
(N + 1, 1))) # correlation of filter coefficients
# Deconvolution Step1: lowpass filter for noise attenuation
fcut = f0 + 20e3
low_order = 100 # cut-off frequency and filter order
blow, lshift = kaiser_lowpass(low_order, fcut,
Fs) # FIR low pass filter coefficients
shift = tau + lshift # delay of low-pass plus that of the FIR deconv filter
# Deconvolution Step2: Application of deconvolution filter
xhat, Uxhat = FIRuncFilter(yn, noise, bF, UbF, shift,
blow) # apply low-pass and FIR deconv filter
# Plot of results
fplot = np.linspace(0, 80e3, 1000)
Hc = dsp.freqz(b, a, 2 * np.pi * fplot / Fs)[1]
Hif = dsp.freqz(bF, 1.0, 2 * np.pi * fplot / Fs)[1]
Hl = dsp.freqz(blow, 1.0, 2 * np.pi * fplot / Fs)[1]
plt.figure(1)
plt.clf()
plt.plot(fplot * 1e-3, db(Hc), fplot * 1e-3, db(Hif * Hl), fplot * 1e-3,
db(Hc * Hif * Hl))
plt.legend(
('System freq. resp.', 'compensation filter', 'compensation result'))
# plt.title('Amplitude of frequency responses')
plt.xlabel('frequency / kHz', fontsize=22)
# uncertain knowledge: cutoff between 19.5kHz and 20.5kHz
runs = 1000
FC = fcut + (2 * np.random.rand(runs) - 1) * 0.5e3
B = np.zeros((runs, L + 1))
for k in range(runs): # Monte Carlo for filter coefficients of low-pass filter
B[k, :] = kaiser_lowpass(L, FC[k], Fs)[0]
Ub = make_semiposdef(np.cov(B, rowvar=False)) # covariance matrix of MC result
# simulate input and output signals
time = np.arange(0, 499 * Ts, Ts) # time values
noise = 1e-5 # std of white noise
x = rect(time, 100 * Ts, 250 * Ts, 1.0, noise=noise) # input signal
y, Uy = FIRuncFilter(x, noise, b, Ub,
blow=b) # apply uncertain FIR filter (GUM formula)
yMC, UyMC = MC(x, noise, b, np.ones(1), Ub, runs=1000,
blow=b) # apply uncertain FIR filter (Monte Carlo)
plt.figure(1)
plt.cla()
plt.plot(time, x, label="input")
plt.plot(time, y, label="output")
plt.xlabel("time / au")
plt.ylabel("signal amplitude / au")
plt.legend()
plt.figure(2)
plt.cla()
plt.plot(time, Uy, label="FIR formula")
plt.plot(time, np.sqrt(np.diag(UyMC)), label="Monte Carlo")
# different cases
sigma_noise = 1e-2 # 1e-5
for kind in ["float", "corr", "diag"]:
for blow in [None, b2]:
print(kind, type(blow))
if kind == "float":
# input signal + run methods
x = rect(time, 100 * Ts, 250 * Ts, 1.0, noise=sigma_noise)
y, Uy = FIRuncFilter(
x, sigma_noise, b1, Ub, blow=blow,
kind=kind) # apply uncertain FIR filter (GUM formula)
yMC, UyMC = MC(
x, sigma_noise, b1, [1.0], Ub, runs=runs,
blow=blow) # apply uncertain FIR filter (Monte Carlo)
elif kind == "corr":
# get an instance of noise, the covariance and the covariance-matrix with the specified color
color = "red"
noise = power_law_noise(N=nTime,
color_value=color,
std=sigma_noise)
Ux = power_law_acf(nTime, color_value=color, std=sigma_noise)
UH = np.cov(np.c_[np.real(HMC), np.imag(HMC)], rowvar=0)
UH = make_semiposdef(UH)
# Calculation of FIR deconvolution filter and its assoc. unc.
bF, UbF = deconv.LSFIR_unc(H, UH, N, tau, f, Fs)
# correlation of filter coefficients
CbF = UbF / (np.tile(np.sqrt(np.diag(UbF))[:, np.newaxis], (1, N + 1)) *
np.tile(np.sqrt(np.diag(UbF))[:, np.newaxis].T, (N + 1, 1)))
# Deconvolution Step1: lowpass filter for noise attenuation
fcut = f0 + 20e3
low_order = 100
blow, lshift = kaiser_lowpass(low_order, fcut, Fs)
shift = -tau - lshift
# Deconvolution Step2: Application of deconvolution filter
xhat, Uxhat = FIRuncFilter(yn, noise, bF, UbF, shift, blow)
# Plot of results
fplot = np.linspace(0, 80e3, 1000)
Hc = dsp.freqz(b, a, 2 * np.pi * fplot / Fs)[1]
Hif = dsp.freqz(bF, 1.0, 2 * np.pi * fplot / Fs)[1]
Hl = dsp.freqz(blow, 1.0, 2 * np.pi * fplot / Fs)[1]
plt.figure(1)
plt.clf()
plt.plot(fplot * 1e-3, db(Hc), fplot * 1e-3, db(Hif * Hl), fplot * 1e-3,
db(Hc * Hif * Hl))
plt.legend(
('System freq. resp.', 'compensation filter', 'compensation result'))
# plt.title('Amplitude of frequency responses')
plt.xlabel('frequency / kHz', fontsize=22)
def conduct_validation_of_FIRuncFilter():
# parameters of simulated measurement
Fs = 100e3 # sampling frequency (in Hz)
Ts = 1 / Fs # sampling interval length (in s)
# nominal system parameters
fcut = 20e3 # low-pass filter cut-off frequency (6 dB)
L = 100 # filter order
b1 = kaiser_lowpass(L, fcut, Fs)[0]
b2 = kaiser_lowpass(L - 20, fcut, Fs)[0]
# uncertain knowledge: cutoff between 19.5kHz and 20.5kHz
runs = 1000
FC = fcut + (2 * np.random.rand(runs) - 1) * 0.5e3
B = np.zeros((runs, L + 1))
for k in range(
runs): # Monte Carlo for filter coefficients of low-pass filter
B[k, :] = kaiser_lowpass(L, FC[k], Fs)[0]
Ub = make_semiposdef(np.cov(
B, rowvar=False)) # covariance matrix of MC result
# simulate input and output signals
nTime = 500
time = np.arange(nTime) * Ts # time values
# different cases
sigma_noise = 1e-2 # 1e-5
for kind in ["float", "corr", "diag"]:
for blow in [None, b2]:
print(kind, type(blow))
if kind == "float":
# input signal + run methods
x = rect(time, 100 * Ts, 250 * Ts, 1.0, noise=sigma_noise)
Uy, UyMC, y, yMC = _conduct_FIRuncFilter_and_MonteCarlo(
Ub, b1, blow, kind, runs, sigma_noise, x)
elif kind == "corr":
# get an instance of noise, the covariance and the covariance-matrix
# with
# the specified color
color = "red"
noise = power_law_noise(N=nTime,
color_value=color,
std=sigma_noise)
Ux = power_law_acf(nTime, color_value=color, std=sigma_noise)
# input signal
x = rect(time, 100 * Ts, 250 * Ts, 1.0, noise=noise)
# build Ux_matrix from autocorrelation Ux
Ux_matrix = toeplitz(trimOrPad(Ux, nTime))
# run methods
y, Uy = FIRuncFilter(
x, Ux, b1, Ub, blow=blow,
kind=kind) # apply uncertain FIR filter (GUM formula)
yMC, UyMC = MC(
x, Ux_matrix, b1, np.ones(1), Ub, runs=runs,
blow=blow) # apply uncertain FIR filter (Monte Carlo)
elif kind == "diag":
sigma_diag = sigma_noise * (
1 +
np.heaviside(np.arange(len(time)) - len(time) // 2.5, 0)
) # std doubles after half of the time
noise = sigma_diag * white_gaussian(len(time))
# input signal + run methods
x = rect(time, 100 * Ts, 250 * Ts, 1.0, noise=noise)
Uy, UyMC, y, yMC = _conduct_FIRuncFilter_and_MonteCarlo(
Ub, b1, blow, kind, runs, sigma_diag, x)
# compare FIR and MC results
plt.figure(1)
plt.cla()
plt.plot(time, x, label="input")
plt.plot(time, y, label="output FIR direct")
plt.plot(time, yMC, label="output FIR MC")
plt.xlabel("time [s]")
plt.ylabel("signal amplitude [1]")
plt.legend()
plt.figure(2)
plt.cla()
plt.plot(time, Uy, label="FIR formula")
plt.plot(time, np.sqrt(np.diag(UyMC)), label="Monte Carlo")
plt.xlabel("time [s]")
plt.ylabel("signal uncertainty [1]")
plt.legend()
plt.show()
from PyDynamic.uncertainty.propagate_filter import FIRuncFilter
def evaluate(signal, filter, case="full/zero/none"):
# different covariance matrices
if case == "full":
U_theta = 1e-2 * np.eye(filter_length)
elif case == "zero":
U_theta = np.zeros((filter_length, filter_length))
elif case == "none":
U_theta = None
else:
raise NotImplementedError
# measure runtime (timeit.timeit is unable to use both local+global variables)
start = time.time()
y, Uy = FIRuncFilter(signal, sigma_noise, theta, U_theta, blow=None)
end = time.time()
runtime = end - start
return runtime, y, Uy
filter_lengths = [10, 50, 100, 200, 500, 1000]
cases = ["full", "zero", "none"]
results = pd.DataFrame(index=filter_lengths, columns=cases)
# prepare signal
signal_length = 2000
sigma_noise = 1e-2 # 1e-5
signal = sigma_noise * np.random.randn(signal_length)
def test(fir_unc_filter_input):
def legacy_FIRuncFilter(y,
sigma_noise,
theta,
Utheta=None,
shift=0,
blow=None,
kind="corr"):
"""Uncertainty propagation for signal y and uncertain FIR filter theta
A preceding FIR low-pass filter with coefficients `blow` can be provided
optionally.
Parameters
----------
y : np.ndarray
filter input signal
sigma_noise : float or np.ndarray
float: standard deviation of white noise in y
1D-array: interpretation depends on kind
theta : np.ndarray
FIR filter coefficients
Utheta : np.ndarray, optional
covariance matrix associated with theta
if the filter is fully certain, use `Utheta = None` (default) to make use of
more efficient calculations. See also the comparison given in
<examples/Digital filtering/FIRuncFilter_runtime_comparison.py>
shift : int, optional
time delay of filter output signal (in samples) (defaults to 0)
blow : np.ndarray, optional
optional FIR low-pass filter
kind : string
only meaningful in combination with sigma_noise a 1D numpy array
"diag": point-wise standard uncertainties of non-stationary white noise
"corr": single sided autocovariance of stationary (colored/correlated)
noise (default)
Returns
-------
x : np.ndarray
FIR filter output signal
ux : np.ndarray
point-wise standard uncertainties associated with x
References
----------
* Elster and Link 2008 [Elster2008]_
.. seealso:: :mod:`PyDynamic.deconvolution.fit_filter`
"""
Ntheta = len(theta) # FIR filter size
# check which case of sigma_noise is necessary
if isinstance(sigma_noise, float):
sigma2 = sigma_noise**2
elif isinstance(sigma_noise, np.ndarray) and len(
sigma_noise.shape) == 1:
if kind == "diag":
sigma2 = sigma_noise**2
elif kind == "corr":
sigma2 = sigma_noise
else:
raise ValueError("unknown kind of sigma_noise")
else:
raise ValueError(
f"FIRuncFilter: Uncertainty sigma_noise associated "
f"with input signal is expected to be either a float or a 1D array but "
f"is of shape {sigma_noise.shape}. Please check documentation for "
f"input "
f"parameters sigma_noise and kind for more information.")
if isinstance(
blow, np.ndarray
): # calculate low-pass filtered signal and propagate noise
if isinstance(sigma2, float):
Bcorr = np.correlate(blow, blow,
"full") # len(Bcorr) == 2*Ntheta - 1
ycorr = (sigma2 * Bcorr[len(blow) - 1:]
) # only the upper half of the correlation is needed
# trim / pad to length Ntheta
ycorr = trimOrPad(ycorr, Ntheta)
Ulow = toeplitz(ycorr)
elif isinstance(sigma2, np.ndarray):
if kind == "diag":
# [Leeuw1994](Covariance matrix of ARMA errors in closed form)
# can be
# used, to derive this formula
# The given "blow" corresponds to a MA(q)-process.
# Going through the calculations of Leeuw, but assuming
# that E(vv^T) is a diagonal matrix with non-identical elements,
# the covariance matrix V becomes (see Leeuw:corollary1)
# V = N * SP * N^T + M * S * M^T
# N, M are defined as in the paper
# and SP is the covariance of input-noise prior to the observed
# time-interval (SP needs be available len(blow)-time steps into the
# past. Here it is assumed, that SP is constant with the first value
# of sigma2)
# V needs to be extended to cover Ntheta-1 time steps more into
# the past
sigma2_extended = np.append(
sigma2[0] * np.ones((Ntheta - 1)), sigma2)
N = toeplitz(blow[1:][::-1],
np.zeros_like(sigma2_extended)).T
M = toeplitz(
trimOrPad(blow, len(sigma2_extended)),
np.zeros_like(sigma2_extended),
)
SP = np.diag(sigma2[0] * np.ones_like(blow[1:]))
S = np.diag(sigma2_extended)
# Ulow is to be sliced from V, see below
V = N.dot(SP).dot(N.T) + M.dot(S).dot(M.T)
elif kind == "corr":
# adjust the lengths sigma2 to fit blow and theta
# this either crops (unused) information or appends zero-information
# note1: this is the reason, why Ulow will have dimension
# (Ntheta x Ntheta) without further ado
# calculate Bcorr
Bcorr = np.correlate(blow, blow, "full")
# pad or crop length of sigma2, then reflect some part to the
# left and
# invert the order
# [0 1 2 3 4 5 6 7] --> [0 0 0 7 6 5 4 3 2 1 0 1 2 3]
sigma2 = trimOrPad(sigma2, len(blow) + Ntheta - 1)
sigma2_reflect = np.pad(sigma2, (len(blow) - 1, 0),
mode="reflect")
ycorr = np.correlate(
sigma2_reflect, Bcorr, mode="valid"
) # used convolve in a earlier version, should make no
# difference as
# Bcorr is symmetric
Ulow = toeplitz(ycorr)
xlow, _ = lfilter(blow, 1.0, y, zi=y[0] * lfilter_zi(blow, 1.0))
else: # if blow is not provided
if isinstance(sigma2, float):
Ulow = np.eye(Ntheta) * sigma2
elif isinstance(sigma2, np.ndarray):
if kind == "diag":
# V needs to be extended to cover Ntheta time steps more into the
# past
sigma2_extended = np.append(
sigma2[0] * np.ones((Ntheta - 1)), sigma2)
# Ulow is to be sliced from V, see below
V = np.diag(
sigma2_extended
) # this is not Ulow, same thing as in the case of a provided blow
# (see above)
elif kind == "corr":
Ulow = toeplitz(trimOrPad(sigma2, Ntheta))
xlow = y
# apply FIR filter to calculate best estimate in accordance with GUM
x, _ = lfilter(theta, 1.0, xlow, zi=xlow[0] * lfilter_zi(theta, 1.0))
x = np.roll(x, -int(shift))
# add dimension to theta, otherwise transpose won't work
if len(theta.shape) == 1:
theta = theta[:, np.newaxis]
# NOTE: In the code below wherever `theta` or `Utheta` get used, they need to be
# flipped. This is necessary to take the time-order of both variables into
# account. (Which is descending for `theta` and `Utheta` but ascending for
# `Ulow`.)
#
# Further details and illustrations showing the effect of not-flipping
# can be found at https://github.com/PTB-M4D/PyDynamic/issues/183
# handle diag-case, where Ulow needs to be sliced from V
if kind == "diag":
# UncCov needs to be calculated inside in its own for-loop
# V has dimension (len(sigma2) + Ntheta) * (len(sigma2) + Ntheta) -->
# slice a
# fitting Ulow of dimension (Ntheta x Ntheta)
UncCov = np.zeros((len(sigma2)))
if isinstance(Utheta, np.ndarray):
for k in range(len(sigma2)):
Ulow = V[k:k + Ntheta, k:k + Ntheta]
UncCov[k] = np.squeeze(
np.flip(theta).T.dot(Ulow.dot(np.flip(theta))) +
np.abs(np.trace(Ulow.dot(
np.flip(Utheta))))) # static part of uncertainty
else:
for k in range(len(sigma2)):
Ulow = V[k:k + Ntheta, k:k + Ntheta]
UncCov[k] = np.squeeze(
np.flip(theta).T.dot(Ulow.dot(
np.flip(theta)))) # static part of uncertainty
else:
if isinstance(Utheta, np.ndarray):
UncCov = np.flip(theta).T.dot(Ulow.dot(
np.flip(theta))) + np.abs(
np.trace(Ulow.dot(
np.flip(Utheta)))) # static part of uncertainty
else:
UncCov = np.flip(theta).T.dot(Ulow.dot(
np.flip(theta))) # static part of uncertainty
if isinstance(Utheta, np.ndarray):
unc = np.empty_like(y)
# use extended signal to match assumption of stationary signal prior to
# first
# entry
xlow_extended = np.append(np.full(Ntheta - 1, xlow[0]), xlow)
for m in range(len(xlow)):
# extract necessary part from input signal
XL = xlow_extended[m:m + Ntheta, np.newaxis]
unc[m] = XL.T.dot(
np.flip(Utheta).dot(XL)) # apply formula from paper
else:
unc = np.zeros_like(y)
ux = np.sqrt(np.abs(UncCov + unc))
ux = np.roll(ux, -int(shift)) # correct for delay
return x, ux.flatten() # flatten in case that we still have 2D array
legacy_y, legacy_Uy = legacy_FIRuncFilter(**fir_unc_filter_input)
current_y, current_Uy = FIRuncFilter(**fir_unc_filter_input)
assert_allclose(
legacy_y,
current_y,
atol=1e-15,
)
assert_allclose(
legacy_Uy,
current_Uy,
atol=np.max((np.max(current_Uy) * 1e-7, 1e-7)),
rtol=3e-6,
)
def test_FIRuncFilter(filters, signals, lowpasses):
# Check expected output for thinkable permutations of input parameters.
y, Uy = FIRuncFilter(**filters, **signals, **lowpasses)
assert len(y) == len(signals["y"])
assert len(Uy) == len(signals["y"])