#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# saov.py - Waqas Bhatti (wbhatti@astro.princeton.edu) - Jan 2017
'''
Contains the Schwarzenberg-Czerny Analysis of Variance period-search algorithm
implementation for periodbase.
'''
#############
## LOGGING ##
#############
import logging
from astrobase import log_sub, log_fmt, log_date_fmt
DEBUG = False
if DEBUG:
level = logging.DEBUG
else:
level = logging.INFO
LOGGER = logging.getLogger(__name__)
logging.basicConfig(
level=level,
style=log_sub,
format=log_fmt,
datefmt=log_date_fmt,
)
LOGDEBUG = LOGGER.debug
LOGINFO = LOGGER.info
LOGWARNING = LOGGER.warning
LOGERROR = LOGGER.error
LOGEXCEPTION = LOGGER.exception
#############
## IMPORTS ##
#############
from multiprocessing import Pool, cpu_count
from numpy import (
nan as npnan, arange as nparange, array as nparray, isfinite as npisfinite,
argmax as npargmax, digitize as npdigitize, median as npmedian,
std as npstd, argsort as npargsort, unique as npunique, sum as npsum
)
###################
## LOCAL IMPORTS ##
###################
from ..lcmath import phase_magseries, sigclip_magseries
from .utils import get_frequency_grid, independent_freq_count, resort_by_time
############
## CONFIG ##
############
NCPUS = cpu_count()
#####################################################
## ANALYSIS of VARIANCE (Schwarzenberg-Czerny 1989) ##
#####################################################
[docs]def aov_theta(times, mags, errs, frequency,
binsize=0.05, minbin=9):
'''Calculates the Schwarzenberg-Czerny AoV statistic at a test frequency.
Parameters
----------
times,mags,errs : np.array
The input time-series and associated errors.
frequency : float
The test frequency to calculate the theta statistic at.
binsize : float
The phase bin size to use.
minbin : int
The minimum number of items in a phase bin to consider in the
calculation of the statistic.
Returns
-------
theta_aov : float
The value of the AoV statistic at the specified `frequency`.
'''
period = 1.0/frequency
fold_time = times[0]
phased = phase_magseries(times,
mags,
period,
fold_time,
wrap=False,
sort=True)
phases = phased['phase']
pmags = phased['mags']
bins = nparange(0.0, 1.0, binsize)
ndets = phases.size
binnedphaseinds = npdigitize(phases, bins)
bin_s1_tops = []
bin_s2_tops = []
binndets = []
goodbins = 0
all_xbar = npmedian(pmags)
for x in npunique(binnedphaseinds):
thisbin_inds = binnedphaseinds == x
thisbin_mags = pmags[thisbin_inds]
if thisbin_mags.size > minbin:
thisbin_ndet = thisbin_mags.size
thisbin_xbar = npmedian(thisbin_mags)
# get s1
thisbin_s1_top = (
thisbin_ndet *
(thisbin_xbar - all_xbar) *
(thisbin_xbar - all_xbar)
)
# get s2
thisbin_s2_top = npsum((thisbin_mags - all_xbar) *
(thisbin_mags - all_xbar))
bin_s1_tops.append(thisbin_s1_top)
bin_s2_tops.append(thisbin_s2_top)
binndets.append(thisbin_ndet)
goodbins = goodbins + 1
# turn the quantities into arrays
bin_s1_tops = nparray(bin_s1_tops)
bin_s2_tops = nparray(bin_s2_tops)
binndets = nparray(binndets)
# calculate s1 first
s1 = npsum(bin_s1_tops)/(goodbins - 1.0)
# then calculate s2
s2 = npsum(bin_s2_tops)/(ndets - goodbins)
theta_aov = s1/s2
return theta_aov
def _aov_worker(task):
'''This is a parallel worker for the function below.
Parameters
----------
task : tuple
This is of the form below::
task[0] = times
task[1] = mags
task[2] = errs
task[3] = frequency
task[4] = binsize
task[5] = minbin
Returns
-------
theta_aov : float
The theta value at the specified frequency. nan if the calculation
fails.
'''
times, mags, errs, frequency, binsize, minbin = task
try:
theta = aov_theta(times, mags, errs, frequency,
binsize=binsize, minbin=minbin)
return theta
except Exception:
return npnan
[docs]def aov_periodfind(times,
mags,
errs,
magsarefluxes=False,
startp=None,
endp=None,
stepsize=1.0e-4,
autofreq=True,
normalize=True,
phasebinsize=0.05,
mindetperbin=9,
nbestpeaks=5,
periodepsilon=0.1,
sigclip=10.0,
nworkers=None,
verbose=True):
'''This runs a parallelized Analysis-of-Variance (AoV) period search.
NOTE: `normalize = True` here as recommended by Schwarzenberg-Czerny 1996,
i.e. mags will be normalized to zero and rescaled so their variance = 1.0.
Parameters
----------
times,mags,errs : np.array
The mag/flux time-series with associated measurement errors to run the
period-finding on.
magsarefluxes : bool
If the input measurement values in `mags` and `errs` are in fluxes, set
this to True.
startp,endp : float or None
The minimum and maximum periods to consider for the transit search.
stepsize : float
The step-size in frequency to use when constructing a frequency grid for
the period search.
autofreq : bool
If this is True, the value of `stepsize` will be ignored and the
:py:func:`astrobase.periodbase.get_frequency_grid` function will be used
to generate a frequency grid based on `startp`, and `endp`. If these are
None as well, `startp` will be set to 0.1 and `endp` will be set to
`times.max() - times.min()`.
normalize : bool
This sets if the input time-series is normalized to 0.0 and rescaled
such that its variance = 1.0. This is the recommended procedure by
Schwarzenberg-Czerny 1996.
phasebinsize : float
The bin size in phase to use when calculating the AoV theta statistic at
a test frequency.
mindetperbin : int
The minimum number of elements in a phase bin to consider it valid when
calculating the AoV theta statistic at a test frequency.
nbestpeaks : int
The number of 'best' peaks to return from the periodogram results,
starting from the global maximum of the periodogram peak values.
periodepsilon : float
The fractional difference between successive values of 'best' periods
when sorting by periodogram power to consider them as separate periods
(as opposed to part of the same periodogram peak). This is used to avoid
broad peaks in the periodogram and make sure the 'best' periods returned
are all actually independent.
sigclip : float or int or sequence of two floats/ints or None
If a single float or int, a symmetric sigma-clip will be performed using
the number provided as the sigma-multiplier to cut out from the input
time-series.
If a list of two ints/floats is provided, the function will perform an
'asymmetric' sigma-clip. The first element in this list is the sigma
value to use for fainter flux/mag values; the second element in this
list is the sigma value to use for brighter flux/mag values. For
example, `sigclip=[10., 3.]`, will sigclip out greater than 10-sigma
dimmings and greater than 3-sigma brightenings. Here the meaning of
"dimming" and "brightening" is set by *physics* (not the magnitude
system), which is why the `magsarefluxes` kwarg must be correctly set.
If `sigclip` is None, no sigma-clipping will be performed, and the
time-series (with non-finite elems removed) will be passed through to
the output.
nworkers : int
The number of parallel workers to use when calculating the periodogram.
verbose : bool
If this is True, will indicate progress and details about the frequency
grid used for the period search.
Returns
-------
dict
This function returns a dict, referred to as an `lspinfo` dict in other
astrobase functions that operate on periodogram results. This is a
standardized format across all astrobase period-finders, and is of the
form below::
{'bestperiod': the best period value in the periodogram,
'bestlspval': the periodogram peak associated with the best period,
'nbestpeaks': the input value of nbestpeaks,
'nbestlspvals': nbestpeaks-size list of best period peak values,
'nbestperiods': nbestpeaks-size list of best periods,
'lspvals': the full array of periodogram powers,
'periods': the full array of periods considered,
'method':'aov' -> the name of the period-finder method,
'kwargs':{ dict of all of the input kwargs for record-keeping}}
'''
# get rid of nans first and sigclip
stimes, smags, serrs = sigclip_magseries(times,
mags,
errs,
magsarefluxes=magsarefluxes,
sigclip=sigclip)
stimes, smags, serrs = resort_by_time(stimes, smags, serrs)
# make sure there are enough points to calculate a spectrum
if len(stimes) > 9 and len(smags) > 9 and len(serrs) > 9:
# get the frequencies to use
if startp:
endf = 1.0/startp
else:
# default start period is 0.1 day
endf = 1.0/0.1
if endp:
startf = 1.0/endp
else:
# default end period is length of time series
startf = 1.0/(stimes.max() - stimes.min())
# if we're not using autofreq, then use the provided frequencies
if not autofreq:
frequencies = nparange(startf, endf, stepsize)
if verbose:
LOGINFO(
'using %s frequency points, start P = %.3f, end P = %.3f' %
(frequencies.size, 1.0/endf, 1.0/startf)
)
else:
# this gets an automatic grid of frequencies to use
frequencies = get_frequency_grid(stimes,
minfreq=startf,
maxfreq=endf)
if verbose:
LOGINFO(
'using autofreq with %s frequency points, '
'start P = %.3f, end P = %.3f' %
(frequencies.size,
1.0/frequencies.max(),
1.0/frequencies.min())
)
# map to parallel workers
if (not nworkers) or (nworkers > NCPUS):
nworkers = NCPUS
if verbose:
LOGINFO('using %s workers...' % nworkers)
pool = Pool(nworkers)
# renormalize the working mags to zero and scale them so that the
# variance = 1 for use with our LSP functions
if normalize:
nmags = (smags - npmedian(smags))/npstd(smags)
else:
nmags = smags
tasks = [(stimes, nmags, serrs, x, phasebinsize, mindetperbin)
for x in frequencies]
lsp = pool.map(_aov_worker, tasks)
pool.close()
pool.join()
del pool
lsp = nparray(lsp)
periods = 1.0/frequencies
# find the nbestpeaks for the periodogram: 1. sort the lsp array by
# highest value first 2. go down the values until we find five
# values that are separated by at least periodepsilon in period
# make sure to filter out non-finite values
finitepeakind = npisfinite(lsp)
finlsp = lsp[finitepeakind]
finperiods = periods[finitepeakind]
# make sure that finlsp has finite values before we work on it
try:
bestperiodind = npargmax(finlsp)
except ValueError:
LOGERROR('no finite periodogram values '
'for this mag series, skipping...')
return {'bestperiod':npnan,
'bestlspval':npnan,
'nbestpeaks':nbestpeaks,
'nbestlspvals':None,
'nbestperiods':None,
'lspvals':None,
'periods':None,
'method':'aov',
'kwargs':{'startp':startp,
'endp':endp,
'stepsize':stepsize,
'normalize':normalize,
'phasebinsize':phasebinsize,
'mindetperbin':mindetperbin,
'autofreq':autofreq,
'periodepsilon':periodepsilon,
'nbestpeaks':nbestpeaks,
'sigclip':sigclip}}
sortedlspind = npargsort(finlsp)[::-1]
sortedlspperiods = finperiods[sortedlspind]
sortedlspvals = finlsp[sortedlspind]
# now get the nbestpeaks
nbestperiods, nbestlspvals, peakcount = (
[finperiods[bestperiodind]],
[finlsp[bestperiodind]],
1
)
prevperiod = sortedlspperiods[0]
# find the best nbestpeaks in the lsp and their periods
for period, lspval in zip(sortedlspperiods, sortedlspvals):
if peakcount == nbestpeaks:
break
perioddiff = abs(period - prevperiod)
bestperiodsdiff = [abs(period - x) for x in nbestperiods]
# print('prevperiod = %s, thisperiod = %s, '
# 'perioddiff = %s, peakcount = %s' %
# (prevperiod, period, perioddiff, peakcount))
# this ensures that this period is different from the last
# period and from all the other existing best periods by
# periodepsilon to make sure we jump to an entire different peak
# in the periodogram
if (perioddiff > (periodepsilon*prevperiod) and
all(x > (periodepsilon*period) for x in bestperiodsdiff)):
nbestperiods.append(period)
nbestlspvals.append(lspval)
peakcount = peakcount + 1
prevperiod = period
return {'bestperiod':finperiods[bestperiodind],
'bestlspval':finlsp[bestperiodind],
'nbestpeaks':nbestpeaks,
'nbestlspvals':nbestlspvals,
'nbestperiods':nbestperiods,
'lspvals':lsp,
'periods':periods,
'method':'aov',
'kwargs':{'startp':startp,
'endp':endp,
'stepsize':stepsize,
'normalize':normalize,
'phasebinsize':phasebinsize,
'mindetperbin':mindetperbin,
'autofreq':autofreq,
'periodepsilon':periodepsilon,
'nbestpeaks':nbestpeaks,
'sigclip':sigclip}}
else:
LOGERROR('no good detections for these times and mags, skipping...')
return {'bestperiod':npnan,
'bestlspval':npnan,
'nbestpeaks':nbestpeaks,
'nbestlspvals':None,
'nbestperiods':None,
'lspvals':None,
'periods':None,
'method':'aov',
'kwargs':{'startp':startp,
'endp':endp,
'stepsize':stepsize,
'normalize':normalize,
'phasebinsize':phasebinsize,
'mindetperbin':mindetperbin,
'autofreq':autofreq,
'periodepsilon':periodepsilon,
'nbestpeaks':nbestpeaks,
'sigclip':sigclip}}
[docs]def analytic_false_alarm_probability(lspinfo,
times,
conservative_nfreq_eff=True,
peakvals=None,
inplace=True):
'''This returns the analytic false alarm probabilities for periodogram
peak values.
FIXME: this doesn't actually work. Fix later.
The calculation follows that on page 3 of Zechmeister & Kurster (2009)::
FAP = 1 − [1 − Prob(z > z0)]**M
where::
M is the number of independent frequencies
Prob(z > z0) is the probability of peak with value > z0
z0 is the peak value we're evaluating
For AoV and AoV-harmonic, the Prob(z > z0) is described by the F
distribution, according to:
- Schwarzenberg-Czerny (1997;
https://ui.adsabs.harvard.edu/#abs/1997ApJ...489..941S)
This is given by::
F( (B-1), (N-B); theta_aov )
Where::
N = number of observations
B = number of phase bins
This translates to a scipy.stats call to the F distribution CDF::
x = theta_aov_best
prob_exceeds_val = scipy.stats.f.cdf(x, (B-1.0), (N-B))
Which we can then plug into the false alarm prob eqn above with the
calculation of M.
Parameters
----------
lspinfo : dict
The dict returned by the
:py:func:`~astrobase.periodbase.spdm.aov_periodfind` function.
times : np.array
The times for which the periodogram result in ``lspinfo`` was
calculated.
conservative_nfreq_eff : bool
If True, will follow the prescription given in Schwarzenberg-Czerny
(2003):
http://adsabs.harvard.edu/abs/2003ASPC..292..383S
and estimate the effective number of independent frequences M_eff as::
min(N_obs, N_freq, DELTA_f/delta_f)
peakvals : sequence or None
The peak values for which to evaluate the false-alarm probability. If
None, will calculate this for each of the peak values in the
``nbestpeaks`` key of the ``lspinfo`` dict.
inplace : bool
If True, puts the results of the FAP calculation into the ``lspinfo``
dict as a list available as ``lspinfo['falsealarmprob']``.
Returns
-------
list
The calculated false alarm probabilities for each of the peak values in
``peakvals``.
'''
from scipy.stats import f
frequencies = 1.0/lspinfo['periods']
M = independent_freq_count(frequencies,
times,
conservative=conservative_nfreq_eff)
if peakvals is None:
peakvals = lspinfo['nbestlspvals']
nphasebins = nparange(0.0, 1.0, lspinfo['kwargs']['phasebinsize']).size
ndet = times.size
false_alarm_probs = []
for peakval in peakvals:
prob_xval = peakval
prob_exceeds_val = f.cdf(prob_xval,
nphasebins - 1.0,
ndet - nphasebins)
false_alarm_probs.append(1.0 - (1.0 - prob_exceeds_val)**M)
if inplace:
lspinfo['falsealarmprob'] = false_alarm_probs
return false_alarm_probs