def fit_acf_by_AR1(acf_empir, nlags=None):
"""Fit an empirical auto cov function (ACF) by that of an AR1 process.
- `acf_empir`: auto-corr/cov-function.
- `nlags`: length of ACF to use in AR(1) fitting
"""
if nlags is None:
nlags = len(acf_empir)
# geometric_mean = ss.mstats.gmean
def geometric_mean(xx):
return np.exp(np.mean(np.log(xx)))
def mean_ratio(xx):
return geometric_mean([xx[i] / xx[i - 1] for i in range(1, len(xx))])
# Negative correlation => Truncate ACF
neg_ind = find_1st_ind(np.array(acf_empir) <= 0)
acf_empir = acf_empir[:neg_ind]
if len(acf_empir) == 0:
return 0
elif len(acf_empir) == 1:
return 0.01
else:
return mean_ratio(acf_empir)
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