Source code for lenstronomy.Sampling.Likelihoods.time_delay_likelihood
import numpy as np
import lenstronomy.Util.constants as const
__all__ = ['TimeDelayLikelihood']
[docs]class TimeDelayLikelihood(object):
"""
class to compute the likelihood of a model given a measurement of time delays
"""
def __init__(self, time_delays_measured, time_delays_uncertainties, lens_model_class, point_source_class):
"""
:param time_delays_measured: relative time delays (in days) in respect to the first image of the point source
:param time_delays_uncertainties: time-delay uncertainties in same order as time_delay_measured. Alternatively
a full covariance matrix that describes the likelihood.
:param lens_model_class: instance of the LensModel() class
:param point_source_class: instance of the PointSource() class, note: the first point source type is the one the
time delays are imposed on
"""
if time_delays_measured is None:
raise ValueError("time_delay_measured need to be specified to evaluate the time-delay likelihood.")
if time_delays_uncertainties is None:
raise ValueError("time_delay_uncertainties need to be specified to evaluate the time-delay likelihood.")
self._delays_measured = np.array(time_delays_measured)
self._delays_errors = np.array(time_delays_uncertainties)
self._lensModel = lens_model_class
self._pointSource = point_source_class
[docs] def logL(self, kwargs_lens, kwargs_ps, kwargs_cosmo):
"""
routine to compute the log likelihood of the time delay distance
:param kwargs_lens: lens model kwargs list
:param kwargs_ps: point source kwargs list
:param kwargs_cosmo: cosmology and other kwargs
:return: log likelihood of the model given the time delay data
"""
x_pos, y_pos = self._pointSource.image_position(kwargs_ps=kwargs_ps, kwargs_lens=kwargs_lens, original_position=True)
x_pos, y_pos = x_pos[0], y_pos[0]
delay_arcsec = self._lensModel.fermat_potential(x_pos, y_pos, kwargs_lens)
D_dt_model = kwargs_cosmo['D_dt']
delay_days = const.delay_arcsec2days(delay_arcsec, D_dt_model)
logL = self._logL_delays(delay_days, self._delays_measured, self._delays_errors)
return logL
@staticmethod
def _logL_delays(delays_model, delays_measured, delays_errors):
"""
log likelihood of modeled delays vs measured time delays under considerations of errors
:param delays_model: n delays of the model (not relative delays)
:param delays_measured: relative delays (1-2,1-3,1-4) relative to the first in the list
:param delays_errors: gaussian errors on the measured delays
:return: log likelihood of data given model
"""
if len(delays_model)-1 != len(delays_measured):
return -10**15
delta_t_model = np.array(delays_model[1:]) - delays_model[0]
if delays_errors.ndim <= 1:
logL = np.sum(-(delta_t_model - delays_measured) ** 2 / (2 * delays_errors ** 2))
elif delays_errors.ndim == 2:
D = delta_t_model - delays_measured
logL = -1/2 * D @ np.linalg.inv(delays_errors) @ D # TODO: only calculate the inverse once
else:
raise ValueError('Dimension of time delay error needs to be either one- or two-dimensional, not %s'
% delays_errors.ndim)
return logL
@property
def num_data(self):
"""
:return: number of time delay measurements
"""
return len(self._delays_measured)