# Observation schedule
day = 23.934
cadence = 1.
nobs_per_epoch = 35 # number of observations per epochs of 35h
epoch_duration = nobs_per_epoch * cadence
epoch_starts = [50*day, 120*day, 210*day, 280*day] # 4 epochs of observation; total of 140 data points
times = np.array([]) # creating a time array for observations
for epoch_start in epoch_starts:
epoch_times = np.linspace(epoch_start, epoch_start + epoch_duration, nobs_per_epoch)
times = np.concatenate([times, epoch_times])
measurement_std = 0.001 # standard deviation of measurements from truth
# Posterior parameters
truth = IlluminationMapPosterior(times, np.zeros_like(times), measurement_std, nside=sim_nside)
# Parameters for the gaussian process and the maps; same as those used in sim_map.py
# We fix all parameters except for the rotation period, and assume other parameters are known
true_params = {
'log_orbital_period':np.log(p_orbit),
'logit_cos_inc':logit(np.cos(inclination)),
'logit_cos_obl':logit(np.cos(obliquity)),
'logit_phi_orb':logit(phi_orb, low=0, high=2*np.pi),
'logit_obl_orientation':logit(phi_rot, low=0, high=2*np.pi),
'mu':0.5,
'log_sigma':np.log(0.25),
'logit_wn_rel_amp':logit(0.02),
'logit_spatial_scale':logit(30. * np.pi/180),
'log_error_scale': np.log(1.)}
truth.fix_params(true_params) # fixing the parameters with the measurements
p = np.concatenate([[np.log(day)], sim_map]) # create an array with the map and the rotation period
# DO NOT CHANGE THIS.
phi_orb = abs(5 * (np.pi / 3) + sol_phase)
phi_rot = abs(2 * np.pi - sol_phase)
# NUMERIC
true_params = {
'log_orbital_period': np.log(p_orbit),
'log_rotation_period': np.log(p_rotation),
'logit_cos_inc': logit(np.cos(inclination)),
'logit_cos_obl': logit(np.cos(obliquity)),
'logit_phi_orb': logit(phi_orb, low=0, high=2 * np.pi),
'logit_obl_orientation': logit(phi_rot, low=0, high=2 * np.pi)
}
truth = IlluminationMapPosterior(times,
np.zeros_like(times),
measurement_std,
nside=nside)
truth.fix_params(true_params)
p = np.concatenate([np.zeros(truth.nparams), one_point_map])
numeric_lightcurve = truth.lightcurve(p)
run_times_analytic = np.array([])
run_times_numeric = np.array([])
nside_resolutions = np.array([1, 2, 4, 8])
print("Test:")
for i in np.nditer(nside_resolutions):
nside = i
whitenoise_relative_amp = 0.2
length_scale = 30 * np.pi / 2
albedo_mean = 0.5
albedo_std = 0.2
# setting the orbital properties
p_rotation = 23.934
p_orbit = 365.256363 * 24.0
phi_orb = np.pi
phi_rot = np.pi
inclination = 0
obliquity = 0
times = 7
# Measurement uncertainty
measurement_std = 0.001
# Using a posterior instance to generate a light-curve
truth = IlluminationMapPosterior(times,
np.zeros_like(times),
measurement_std,
nside=nside)
true_params = {
'log_orbital_period': np.log(p_orbit),
'log_rotation_period': np.log(p_rotation),
'logit_cos_inc': logit(np.cos(inclination)),
'logit_cos_obl': logit(np.cos(obliquity)),
'logit_phi_orb': logit(phi_orb, low=0, high=2 * np.pi),
'logit_obl_orientation': logit(phi_rot, low=0, high=2 * np.pi)
}
# truth.fix_params(true_params)
# p = np.concatenate([np.zeros(truth.nparams), simulated_map])
# kernel = truth.visibility_illumination_matrix(p)
# print(simulated_map)
def posterior_draw_4(draw):
draw_lightcurve = truth_4.lightcurve(np.concatenate([[draw], sim_map]))
return IlluminationMapPosterior(epoch_4,
draw_lightcurve,
measurement_std,
nside=sim_nside)
# Observation schedule
day = 23.934
cadence = 1.
nobs_per_epoch = 35
epoch_duration = nobs_per_epoch * cadence
epoch_1 = np.linspace(50 * day, 50 * day + epoch_duration, nobs_per_epoch)
epoch_2 = np.linspace(120 * day, 120 * day + epoch_duration, nobs_per_epoch)
epoch_3 = np.linspace(210 * day, 210 * day + epoch_duration, nobs_per_epoch)
epoch_4 = np.linspace(280 * day, 280 * day + epoch_duration, nobs_per_epoch)
measurement_std = 0.001 #to increase eventually
truth_1 = IlluminationMapPosterior(epoch_1,
np.zeros_like(epoch_1),
measurement_std,
nside=sim_nside)
truth_2 = IlluminationMapPosterior(epoch_2,
np.zeros_like(epoch_2),
measurement_std,
nside=sim_nside)
truth_3 = IlluminationMapPosterior(epoch_3,
np.zeros_like(epoch_3),
measurement_std,
nside=sim_nside)
truth_4 = IlluminationMapPosterior(epoch_4,
np.zeros_like(epoch_4),
measurement_std,
nside=sim_nside)
true_params = {
280 * day] # 4 epochs, total of 140 data points
times = np.array([])
for epoch_start in epoch_starts:
epoch_times = np.linspace(epoch_start, epoch_start + epoch_duration,
nobs_per_epoch)
times = np.concatenate([times, epoch_times])
# Experimental error, can be increased if the effect of the uncertainty is investigated
# Accurate results were recovered for uncertainties up to 0.01
measurement_std = 0.001
# Posterior parameters
# Identical to posterior parameters in fit_emcee.py
truth = IlluminationMapPosterior(times,
np.zeros_like(times),
measurement_std,
nside=sim_nside)
true_params = {
'log_orbital_period': np.log(p_orbit),
'logit_cos_inc': logit(np.cos(inclination)),
'logit_cos_obl': logit(np.cos(obliquity)),
'logit_phi_orb': logit(phi_orb, low=0, high=2 * np.pi),
'logit_obl_orientation': logit(phi_rot, low=0, high=2 * np.pi),
'mu': 0.5,
'log_sigma': np.log(0.25),
'logit_wn_rel_amp': logit(0.02),
'logit_spatial_scale': logit(30. * np.pi / 180),
'log_error_scale': np.log(1.)
}
truth.fix_params(true_params) # fix the known parameters
sol_phase=sol_phase,
times=times,
nside=nside)
analytic_5 = analytic_lightcurve_2(colat=colat_5,
lng=one_lng,
w_rot=w_rot,
w_orb=w_orb,
obq=obliquity,
i=inclination,
sol_phase=sol_phase,
times=times,
nside=nside)
# Numeric solution
truth = IlluminationMapPosterior(times,
np.zeros_like(times),
measurement_std,
nside=nside)
true_params = {
'log_orbital_period': np.log(p_orbit),
'log_rotation_period': np.log(p_rotation),
'logit_cos_inc': logit(np.cos(inclination)),
'logit_cos_obl': logit(np.cos(obliquity)),
'logit_phi_orb': logit(phi_orb, low=0, high=2 * np.pi),
'logit_obl_orientation': logit(obl_orientation, low=0, high=2 * np.pi)
}
truth.fix_params(true_params)
p_1 = np.concatenate([np.zeros(truth.nparams), sim_map_1])
p_2 = np.concatenate([np.zeros(truth.nparams), sim_map_2])
p_3 = np.concatenate([np.zeros(truth.nparams), sim_map_3])
p_4 = np.concatenate([np.zeros(truth.nparams), sim_map_4])