def acf(times, yvals):
"""
computes the autocorrelation function for an evenly-sampled time-series
"""
cadence = np.median(np.diff(times))
N = len(yvals)
max_lag = N / 2
median_yval = np.median(yvals)
norm_term = np.sum((yvals - median_yval)**2)
lags = np.arange(max_lag)
#print median_yval,norm_term,max_lag
ACF0 = [
np.sum((yvals[:N - j] - median_yval) * (yvals[j:] - median_yval))
for j in lags
]
ACF1 = ACF0 / norm_term
# smooth the ACF
gauss_kernel = Gaussian1DKernel(18, x_size=55)
ACF = ap_convolve(ACF1, gauss_kernel, boundary="extend")
#ACF = ACF1
periods = cadence * lags
return periods, ACF
def acf(times,yvals):
"""
computes the autocorrelation function for an evenly-sampled time-series
"""
cadence = np.median(np.diff(times))
N = len(yvals)
max_lag = N/2
median_yval = np.median(yvals)
norm_term = np.sum((yvals - median_yval)**2)
lags = np.arange(max_lag)
#print median_yval,norm_term,max_lag
ACF0 = [np.sum((yvals[:N-j] - median_yval)*(yvals[j:] - median_yval)) for j in lags]
ACF1 = ACF0/norm_term
# smooth the ACF
gauss_kernel = Gaussian1DKernel(18,x_size=55)
ACF = ap_convolve(ACF1, gauss_kernel,boundary="extend")
#ACF = ACF1
periods = cadence*lags
return periods,ACF
def calc_sigma(time,flux,flux_err):
"""
Following McQuillan et al. (2013), determines the standard deviation
of the flux by iteratively smoothing the flux and removing outliers,
then calculating the standard deviation of the residuals between the
smoothed flux and the original flux.
"""
x,y,yerr = np.float64(time),np.float64(flux),np.float64(flux_err)
#print len(x),len(y),len(yerr)
bad = (np.isnan(y) | np.isnan(yerr) | np.isnan(x))
good = np.where(bad==False)[0]
x,y,yerr = x[good],y[good],yerr[good]
#print len(x),len(y),len(yerr)
x1,y1,yerr1 = np.copy(x),np.copy(y),np.copy(yerr)
# Loop three times, applying a median filter then a boxcar filter before clipping 3-sigma outliers
for i in range(1):
y_med = medfilt(y1,11)
y_boxed = ap_convolve(y_med, Box1DKernel(11),boundary="extend")
residuals = y_med - y1
sigma_residuals = np.std(residuals)
to_clip = (abs(residuals)>(3*sigma_residuals))
to_keep = np.where(to_clip==False)[0]
x1,y1,yerr1 = x1[to_keep],y1[to_keep],yerr1[to_keep]
#print len(x1),len(y1),len(yerr1)
# After outliers have been removed, apply the smoothing one last time
# then determine the residuals from this smoothed curve.
y_smoothed1 = medfilt(y1,11)
y_smoothed = ap_convolve(y_smoothed1, Box1DKernel(11))
# smoothing screws up the endpoints, which screws up the std(residuals)
residuals = (y_smoothed - y1)[10:-10]
sigma_res = np.std(residuals)
return x,y,yerr,sigma_res
def acf(times,yvals):
"""
Compute the autocorrelation function for an evenly-sampled time-series
Inputs:
-------
times: array of epochs/time points
yvals: array of fluxes corresponding to times
Returns:
--------
periods: array of lag times
ACF: autocorrelation function corresponding to the lags
"""
# And the number of observations
# (the maximum lag that will be tested is half the number of observations)
N = len(yvals)
max_lag = N//2
lags = np.arange(max_lag)
# Calculate values for normalizing the ACF
median_yval = np.median(yvals)
norm_term = np.sum((yvals - median_yval)**2)
#print median_yval,norm_term,max_lag
# Compute the ACF following McQuillan+2013
ACF0 = [np.sum((yvals[:N-j] - median_yval)*(yvals[j:] - median_yval)) for j in lags]
ACF1 = ACF0/norm_term
# smooth the ACF
gauss_kernel = Gaussian1DKernel(18,x_size=55)
ACF = ap_convolve(ACF1, gauss_kernel,boundary="extend")
#ACF = ACF1
# Compute the lags in index-space to time-space
cadence = np.median(np.diff(times))
periods = cadence*lags
return periods,ACF
from astropy.convolution import convolve as ap_convolve
from astropy.convolution import Box2DKernel
box_2D_kernel = Box2DKernel(9)
nan = float('nan')
data = np.where(data == 0, nan, data)
data[:, 0] = nan
data[:, -1] = nan
data[0, :] = nan
data[-1, :] = nan
data2 = ap_convolve(data, box_2D_kernel, normalize_kernel=True)
plt.clf()
dd = data - data2
dd = np.ma.masked_invalid(dd)
ddmean = np.mean(dd)
ddstd = np.std(dd)
dd = dd - ddmean
ddcvlo = -ddstd * 2.
ddcvhi = +ddstd * 2.
ddcvin = (ddcvhi - ddcvlo) / 100.
plt.pcolor(dd[:, 0:2500].T,
np.arange(ddcvlo, ddcvhi, ddcvin),
cmap=plt.cm.get_cmap('Blues'))