def estimate_good_plot_length(xx, chrono=None, mult=100):
"""
Estimate good length for plotting stuff
from the time scale of the system.
Provide sensible fall-backs (better if chrono is supplied).
"""
if xx.ndim == 2:
# If mult-dim, then average over dims (by ravel)....
# But for inhomogeneous variables, it is important
# to subtract the mean first!
xx = xx - np.mean(xx, axis=0)
xx = xx.ravel(order='F')
try:
K = mult * series.estimate_corr_length(xx)
except ValueError:
K = 0
if chrono is not None:
t = chrono
K = int(min(max(K, t.dkObs), t.K))
T = round2(t.tt[K], 2) # Could return T; T>tt[-1]
K = utils.find_1st_ind(t.tt >= T)
if K:
return K
else:
return t.K
else:
K = int(min(max(K, 1), len(xx)))
T = round2(K, 2)
return K
def assimilate(self, HMM, xx, yy):
Dyn, Obs, chrono, stats = HMM.Dyn, HMM.Obs, HMM.t, self.stats
# Compute "climatological" Kalman gain
muC = np.mean(xx, 0)
AC = xx - muC
PC = (AC.T @ AC) / (xx.shape[0] - 1)
# Setup scalar "time-series" covariance dynamics.
# ONLY USED FOR DIAGNOSTICS, not to affect the Kalman gain.
L = series.estimate_corr_length(AC.ravel(order='F'))
SM = fit_sigmoid(1/2, L, 0)
# Init
mu = muC
stats.assess(0, mu=mu, Cov=PC)
for k, kObs, t, dt in progbar(chrono.ticker):
# Forecast
mu = Dyn(mu, t-dt, dt)
if kObs is not None:
stats.assess(k, kObs, 'f', mu=muC, Cov=PC)
# Analysis
H = Obs.linear(muC, t)
KG = mtools.mrdiv([email protected], H@[email protected] + Obs.noise.C.full)
mu = muC + KG@(yy[kObs] - Obs(muC, t))
P = (np.eye(Dyn.M) - KG@H) @ PC
SM = fit_sigmoid(P.trace()/PC.trace(), L, k)
stats.assess(k, kObs, mu=mu, Cov=2*PC*SM(k))
def estimate_good_plot_length(xx, chrono=None, mult=100):
"""Estimate the range of the xx slices for plotting.
The length is based on the estimated time scale (wavelength)
of the system.
Provide sensible fall-backs (better if chrono is supplied).
Parameters
----------
xx: ndarray
Plotted array
chrono: `dapper.tools.chronos.Chronology`, optional
object with property dkObS. Defaults: None
mult: int, optional
Number of waves for plotting. Defaults: 100
Returns
-------
K: int
length for plotting
Example
-------
>>> K_lag = estimate_good_plot_length(stats.xx, chrono, mult=80) # doctest: +SKIP
"""
if xx.ndim == 2:
# If mult-dim, then average over dims (by ravel)....
# But for inhomogeneous variables, it is important
# to subtract the mean first!
xx = xx - np.mean(xx, axis=0)
xx = xx.ravel(order='F')
try:
K = mult * series.estimate_corr_length(xx)
except ValueError:
K = 0
if chrono is not None:
t = chrono
K = int(min(max(K, t.dkObs), t.K))
T = round2sigfig(t.tt[K], 2) # Could return T; T>tt[-1]
K = find_1st_ind(t.tt >= T)
if K:
return K
else:
return t.K
else:
K = int(min(max(K, 1), len(xx)))
T = round2sigfig(K, 2)
return K
def assimilate(self, HMM, xx, yy):
Dyn, Obs, chrono, X0, stats = HMM.Dyn, HMM.Obs, HMM.t, HMM.X0, self.stats
if isinstance(self.B, np.ndarray):
# compare ndarray 1st to avoid == error for ndarray
B = self.B.astype(float)
elif self.B in (None, 'clim'):
# Use climatological cov, estimated from truth
B = np.cov(xx.T)
elif self.B == 'eye':
B = np.eye(HMM.Nx)
else:
raise ValueError("Bad input B.")
B *= self.xB
# ONLY USED FOR DIAGNOSTICS, not to change the Kalman gain.
CC = 2 * np.cov(xx.T)
L = series.estimate_corr_length(center(xx)[0].ravel(order='F'))
P = X0.C.full
SM = fit_sigmoid(P.trace() / CC.trace(), L, 0)
# Init
mu = X0.mu
stats.assess(0, mu=mu, Cov=P)
for k, kObs, t, dt in progbar(chrono.ticker):
# Forecast
mu = Dyn(mu, t - dt, dt)
P = CC * SM(k)
if kObs is not None:
stats.assess(k, kObs, 'f', mu=mu, Cov=P)
# Analysis
H = Obs.linear(mu, t)
KG = mrdiv(B @ H.T, H @ B @ H.T + Obs.noise.C.full)
mu = mu + KG @ (yy[kObs] - Obs(mu, t))
# Re-calibrate fit_sigmoid with new W0 = Pa/B
P = (np.eye(Dyn.M) - KG @ H) @ B
SM = fit_sigmoid(P.trace() / CC.trace(), L, k)
stats.assess(k, kObs, mu=mu, Cov=P)