https://github.com/gwastro/pycbc
Tip revision: b60402af9882b31236d79f93689d91f32c49bc42 authored by Ian Harry on 21 June 2017, 14:45:41 UTC
Remove unused import (#1754)
Remove unused import (#1754)
Tip revision: b60402a
autocorrelation.py
# Copyright (C) 2016 Christopher M. Biwer
# This program is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3 of the License, or (at your
# option) any later version.
#
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
# Public License for more details.
#
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
#
# =============================================================================
#
# Preamble
#
# =============================================================================
#
"""
This modules provides functions for calculating the autocorrelation function
and length of a data series.
"""
import numpy
from math import isnan
from pycbc.filter.matchedfilter import correlate
from pycbc.types import FrequencySeries, TimeSeries, zeros
def calculate_acf(data, delta_t=1.0, unbiased=False):
r"""Calculates the one-sided autocorrelation function.
Calculates the autocorrelation function (ACF) and returns the one-sided
ACF. The ACF is defined as the autocovariance divided by the variance. The
ACF can be estimated using
.. math::
\hat{R}(k) = \frac{1}{n \sigma^{2}} \sum_{t=1}^{n-k} \left( X_{t} - \mu \right) \left( X_{t+k} - \mu \right)
Where :math:`\hat{R}(k)` is the ACF, :math:`X_{t}` is the data series at
time t, :math:`\mu` is the mean of :math:`X_{t}`, and :math:`\sigma^{2}` is
the variance of :math:`X_{t}`.
Parameters
-----------
data : TimeSeries or numpy.array
A TimeSeries or numpy.array of data.
delta_t : float
The time step of the data series if it is not a TimeSeries instance.
unbiased : bool
If True the normalization of the autocovariance function is n-k
instead of n. This is called the unbiased estimation of the
autocovariance. Note that this does not mean the ACF is unbiased.
Returns
-------
acf : numpy.array
If data is a TimeSeries then acf will be a TimeSeries of the
one-sided ACF. Else acf is a numpy.array.
"""
# if given a TimeSeries instance then get numpy.array
if isinstance(data, TimeSeries):
y = data.numpy()
delta_t = data.delta_t
else:
y = data
# FFT data minus the mean
fdata = TimeSeries(y-y.mean(), delta_t=delta_t).to_frequencyseries()
# correlate
# do not need to give the congjugate since correlate function does it
cdata = FrequencySeries(zeros(len(fdata), dtype=numpy.complex64),
delta_f=fdata.delta_f, copy=False)
correlate(fdata, fdata, cdata)
# IFFT correlated data to get unnormalized autocovariance time series
acf = cdata.to_timeseries()
# normalize the autocovariance
# note that dividing by acf[0] is the same as ( y.var() * len(acf) )
if unbiased:
acf /= ( y.var() * numpy.arange(len(acf), 0, -1) )
else:
acf /= acf[0]
# return input datatype
if isinstance(data, TimeSeries):
return TimeSeries(acf, delta_t=delta_t)
else:
return acf
def calculate_acl(data, m=5, k=2, dtype=int):
""" Calculates the autocorrelation length (ACL).
ACL is estimated using
r = 1 + 2 \sum_{i=1}^{m*s} \hat{R}(i) < s
Where r is the ACL and \hat{R}(i) is the ACF that has been normalized so
that \hat{R}(0) is 1.0. And s is equal to i/m.
The parameter k sets the maximum samples to use in calculation of ACL. The
maximum number of samples will be the length of the ACL divided by k.
The parameter m controls the length of the window that is summed to
compute the ACL.
Parameters
-----------
data : {TimeSeries, numpy.array}
A TimeSeries or numpy.array of data.
dtype : {int, float}
The datatype of the output. If the dtype was set to int, then the
ceiling is returned.
Returns
-------
acl : {int, float}
The length s which is longer than the ACL. If ACL can not be estimated
then returns numpy.inf.
"""
# sanity check output data type
if dtype not in [int, float]:
raise ValueError("The dtype must be either int or float.")
# calculate ACF that is normalized by the zero-lag value
acf = calculate_acf(data)
# multiply all values beyond the zero-lag value by 2.0
acf[1:] *= 2.0
# sanity check ACF
if isnan(acf[0]):
return numpy.inf
assert acf[0] == 1.0
# the maximum index to calculate ACF
imax = int(len(acf)/k)
# calculate cumlative ACL until s is less than the cumulative ACL
cum_acl = 0.0
for i,val in enumerate(acf[:imax]):
s = float(i)/m
if cum_acl+val < s:
if dtype == int:
return numpy.ceil(s)
elif dtype == float:
return s
cum_acl += val
return numpy.inf