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periodogram_Psat_alias_investigator.py
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periodogram_Psat_alias_investigator.py
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from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
import pandas
import os
import traceback
from astropy.timeseries import LombScargle
import matplotlib.cm as cm
#### this script will examine how the periodograms evolve as Psat -- > Pepoch (P_plan).
"""
That is, what is the effect of undersampling on the inferred period, or shape of the periodogram?
Try this: look at the evolution of the periodogram as you change the period of the moon.
"""
try:
ntrials = int(input('How many experiments you want to run? '))
for trial in np.arange(0,ntrials,1):
##### SEE HOW THE OBSERVATIONAL CADENCE PLAYS WITH THE SIGNAL
nsignals = np.random.choice(np.arange(1,5,1))
#amplitudes = np.random.random(size=nsignals)
amplitudes = np.linspace(1,1,nsignals)
periods = np.random.choice(np.arange(2,21,1), size=nsignals) + np.random.random(size=nsignals)
phases = np.random.choice(np.linspace(-2*np.pi, 2*np.pi, 100), size=nsignals)
periods_to_probe = np.linspace(2,40,1000)
freqs_to_probe = 1 / periods_to_probe
lc_time_array = np.arange(0,60,1)
hc_time_array = np.arange(0,60.01,0.01)
hc_delta_funcs = np.zeros(shape=((len(hc_time_array),)))
for nhcta, hcta in enumerate(hc_time_array):
if hcta % int(hcta) == 0.0:
hc_delta_funcs[nhcta] = 1.0
signal = np.zeros(shape=(len(lc_time_array),))
for amp,per,ph in zip(amplitudes, periods, phases):
signal += amp*np.sin((2*np.pi*(1/per)*lc_time_array) + ph)
signal_LS = LombScargle(lc_time_array, signal)
signal_LS_powers = signal_LS.power(freqs_to_probe)
cadence_LS = LombScargle(hc_time_array, hc_delta_funcs)
cadence_LS_powers = cadence_LS.power(freqs_to_probe)
signal_div_cadence_LS_powers = signal_LS_powers / cadence_LS_powers
fig, ax = plt.subplots(4, figsize=(6,8))
ax[0].plot(lc_time_array, signal, color='LightCoral', linewidth=2, alpha=0.7)
ax[1].plot(periods_to_probe, signal_LS_powers, c='k', alpha=0.7)
ax[2].plot(periods_to_probe, cadence_LS_powers, c='k', alpha=0.7)
ax[3].plot(periods_to_probe, signal_div_cadence_LS_powers, c='k', alpha=0.7)
ax[0].set_title('# signals = '+str(nsignals))
plt.show()
Pmoons = np.arange(2,21,1) #### days
colors = cm.viridis(np.linspace(0,1,len(Pmoons)))
baseline = 3650 ### days
Pplans = np.arange(50,1010,10)
ntransits = baseline // Pplans
periods_to_probe = np.logspace(np.log10(2),np.log10(np.nanmax(ntransits)),1000)
freqs_to_probe = 1 / periods_to_probe
master_GT_Psats_over_Ps = []
master_peak_powers = []
master_LS_Psats_over_Ps = []
for nt,Pp in zip(ntransits, Pplans):
print('Pplan = ', Pp)
time_array = np.arange(0,nt,1) #### each epoch is 1
time_array = np.sort(np.random.choice(time_array, size=int(0.6*len(time_array))))
Psats_over_Pp = Pmoons / Pp #### ratio of moon period to planet period (must be < 1!)
LS_Psats_over_Pp = []
fsats_over_fp = Pp / Pmoons #### equivalent to 1 / Psats_over_Pp
##### since in this context Pp = 1, the fraction above Psat_over_Pp is the period of the moon.
#sat_sines = np.sin(2*np.pi*fsats_over_fp*time_array + np.pi)
sat_sines = np.zeros(shape=(len(Pmoons), len(time_array)))
for nfsofp, fsofp in enumerate(fsats_over_fp):
sat_sines[nfsofp] = 5 * np.sin((2*np.pi*fsofp*time_array) + np.pi)
#### noise it up!
sat_sines[nfsofp] = np.random.normal(loc=sat_sines[nfsofp], scale=0.2*np.nanmax(sat_sines[nfsofp]))
#plt.scatter(time_array, sat_sines[nfsofp], facecolor='LightCoral', edgecolor='k', s=20, alpha=0.7)
#plt.plot(time_array, sat_sines[nfsofp], c='k', alpha=0.5, linestyle=':')
#plt.show()
#for nss, ss in enumerate(sat_sines):
for nss in np.arange(0,sat_sines.shape[0],1):
ss = sat_sines[nss]
#### run the periodogram
ss_LS = LombScargle(time_array, ss)
ss_LS_powers = ss_LS.power(freqs_to_probe)
##### TRY TO DIVIDE OUT THE OBSERVING CADENCE PERIODOGRAM!
hc_time_array = np.arange(0,nt,0.01)
hc_delta_funcs = np.zeros(shape=(len(hc_time_array),))
for nhcta, hcta in enumerate(hc_time_array):
if hcta % int(hcta) == 0.0:
hc_delta_funcs[nhcta] = 1.0
LS_obs_cadence = LombScargle(hc_time_array, hc_delta_funcs)
LS_obs_cadence_powers = LS_obs_cadence.power(freqs_to_probe)
fig, ax = plt.subplots(3, sharex=True)
ax[0].plot(periods_to_probe, ss_LS_powers)
ax[0].set_ylabel('signal')
ax[1].plot(periods_to_probe, LS_obs_cadence_powers)
ax[1].set_ylabel('cadence')
ax[2].plot(periods_to_probe, ss_LS_powers / LS_obs_cadence_powers)
ax[2].set_ylabel('signal / cadence')
plt.xscale('log')
plt.show()
master_GT_Psats_over_Ps.append(Psats_over_Pp[nss]) ### GROUND TRUTH!
master_peak_powers.append(np.nanmax(ss_LS_powers))
master_LS_Psats_over_Ps.append(periods_to_probe[np.argmax(ss_LS_powers)]) ##### number epochs == LS Psats / Pp.
LS_Psats_over_Pp.append(periods_to_probe[np.argmax(ss_LS_powers)])
#plt.plot(periods_to_probe, ss_LS_powers, color=colors[nss], alpha=0.5)
#plt.xscale('log')
#plt.title('Pp = '+str(Pp))
#plt.show()
plt.scatter(Psats_over_Pp, LS_Psats_over_Pp, c='LightCoral', edgecolor='k', s=20, alpha=0.7)
plt.xlabel(r'$P_S / P_P$ (ground truth)')
plt.ylabel(r'$P_S / P_P$ (Lomb-Scargle)')
plt.show()
plt.scatter(master_GT_Psats_over_Ps, master_LS_Psats_over_Ps, facecolor='LightCoral', edgecolor='k', s=20, alpha=0.5)
plt.xlabel(r'$P_S / P_P$ (ground truth)')
plt.ylabel(r'$P_S / P_P$ (Lomb-Scargle)')
plt.show()
good_idxs = np.where(np.array(master_LS_Psats_over_Ps) != 2.0)[0]
n, bins, edges = plt.hist(np.array(master_LS_Psats_over_Ps)[good_idxs], bins=np.arange(2,100,2), facecolor='DodgerBlue', edgecolor='k', alpha=0.7)
plt.xlabel('Peak power [epochs]')
plt.show()
except:
traceback.print_exc()