def stellingwerf_pdm_theta(times, mags, errs, frequency,
binsize=0.05, minbin=9):
'''
This calculates the Stellingwerf PDM theta value at a test 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 = np.arange(0.0, 1.0, binsize)
nbins = bins.size
binnedphaseinds = npdigitize(phases, bins)
binvariances = []
binndets = []
goodbins = 0
for x in npunique(binnedphaseinds):
thisbin_inds = binnedphaseinds == x
thisbin_phases = phases[thisbin_inds]
thisbin_mags = pmags[thisbin_inds]
if thisbin_mags.size > minbin:
thisbin_variance = npvar(thisbin_mags,ddof=1)
binvariances.append(thisbin_variance)
binndets.append(thisbin_mags.size)
goodbins = goodbins + 1
# now calculate theta
binvariances = nparray(binvariances)
binndets = nparray(binndets)
theta_top = npsum(binvariances*(binndets - 1)) / (npsum(binndets) -
goodbins)
theta_bot = npvar(pmags,ddof=1)
theta = theta_top/theta_bot
return theta
def pwd_phasebin(phases, mags, binsize=0.002, minbin=9):
'''
This bins the phased mag series using the given binsize.
'''
bins = np.arange(0.0, 1.0, binsize)
binnedphaseinds = npdigitize(phases, bins)
binnedphases, binnedmags = [], []
for x in npunique(binnedphaseinds):
thisbin_inds = binnedphaseinds == x
thisbin_phases = phases[thisbin_inds]
thisbin_mags = mags[thisbin_inds]
if thisbin_inds.size > minbin:
binnedphases.append(npmedian(thisbin_phases))
binnedmags.append(npmedian(thisbin_mags))
return np.array(binnedphases), np.array(binnedmags)
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 stellingwerf_pdm_theta(times,
mags,
errs,
frequency,
binsize=0.05,
minbin=9):
'''
This calculates the Stellingwerf PDM theta value 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_pdm : float
The value of the theta 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)
binnedphaseinds = npdigitize(phases, bins)
binvariances = []
binndets = []
goodbins = 0
for x in npunique(binnedphaseinds):
thisbin_inds = binnedphaseinds == x
thisbin_mags = pmags[thisbin_inds]
if thisbin_mags.size > minbin:
thisbin_variance = npvar(thisbin_mags, ddof=1)
binvariances.append(thisbin_variance)
binndets.append(thisbin_mags.size)
goodbins = goodbins + 1
# now calculate theta
binvariances = nparray(binvariances)
binndets = nparray(binndets)
theta_top = npsum(binvariances *
(binndets - 1)) / (npsum(binndets) - goodbins)
theta_bot = npvar(pmags, ddof=1)
theta = theta_top / theta_bot
return theta
def aov_theta(times, mags, errs, frequency, binsize=0.05, minbin=9):
'''Calculates the Schwarzenberg-Czerny AoV statistic at a test 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 = np.arange(0.0, 1.0, binsize)
nbins = bins.size
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_phases = phases[thisbin_inds]
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