def test_log_likelihood(self):
likelihood = DdtGaussianLikelihood(**self.kwargs_lens)
lnlog = likelihood.log_likelihood(ddt=self.ddt_mean, dd=None)
npt.assert_almost_equal(lnlog, 0, decimal=5)
lnlog = likelihood.log_likelihood(ddt=self.ddt_mean + self.ddt_sigma, dd=None)
npt.assert_almost_equal(lnlog, -0.5, decimal=5)
def __init__(self, z_lens, z_source, ddt_mean, ddt_sigma, dd_mean, dd_sigma):
"""
:param z_lens: lens redshift
:param z_source: source redshift
:param ddt_mean: mean of Ddt distance
:param ddt_sigma: 1-sigma uncertainty in the Ddt distance
:param dd_mean: mean of Dd distance ratio
:param dd_sigma: 1-sigma uncertainty in the Dd distance
"""
self._dd_mean = dd_mean
self._dd_sigma2 = dd_sigma ** 2
self._tdLikelihood = DdtGaussianLikelihood(z_lens, z_source, ddt_mean=ddt_mean, ddt_sigma=ddt_sigma)
self.num_data = 2
def setup(self):
self.z_lens = 0.8
self.z_source = 3.0
self.ddt_mean = 10
self.ddt_sigma = 0.1
self.dd_mean = 1.
kwargs_ddt_gauss = {
'z_lens': self.z_lens,
'z_source': self.z_source,
'ddt_mean': self.ddt_mean,
'ddt_sigma': self.ddt_sigma
}
ds_dds = self.ddt_mean / self.dd_mean / (1 + self.z_lens)
j_mean_list = np.ones(1)
scaling_ifu = 1
sigma_v_measurement = np.sqrt(
ds_dds * scaling_ifu * j_mean_list) * const.c / 1000
sigma_v_sigma = sigma_v_measurement / 10.
error_cov_measurement = np.diag(sigma_v_sigma**2)
error_cov_j_sqrt = np.diag(np.zeros_like(sigma_v_measurement))
self.kin_likelihood = KinLikelihood(self.z_lens,
self.z_source,
sigma_v_measurement,
j_mean_list,
error_cov_measurement,
error_cov_j_sqrt,
normalized=True)
self.ddt_gauss_likelihood = DdtGaussianLikelihood(**kwargs_ddt_gauss)
self.ddt_gauss_kin_likelihood = DdtGaussKinLikelihood(
self.z_lens,
self.z_source,
self.ddt_mean,
self.ddt_sigma,
sigma_v_measurement,
j_mean_list,
error_cov_measurement,
error_cov_j_sqrt,
sigma_sys_error_include=False)
self.sigma_v_measurement = sigma_v_measurement
self.error_cov_measurement = error_cov_measurement
class DdtDdGaussian(object):
"""
class for joint kinematics and time delay likelihood assuming independent Gaussian likelihoods in Ddt and Dd.
Attention: Gaussian errors in the velocity dispersion do not translate into Gaussian uncertainties in Dd.
"""
def __init__(self, z_lens, z_source, ddt_mean, ddt_sigma, dd_mean, dd_sigma):
"""
:param z_lens: lens redshift
:param z_source: source redshift
:param ddt_mean: mean of Ddt distance
:param ddt_sigma: 1-sigma uncertainty in the Ddt distance
:param dd_mean: mean of Dd distance ratio
:param dd_sigma: 1-sigma uncertainty in the Dd distance
"""
self._dd_mean = dd_mean
self._dd_sigma2 = dd_sigma ** 2
self._tdLikelihood = DdtGaussianLikelihood(z_lens, z_source, ddt_mean=ddt_mean, ddt_sigma=ddt_sigma)
self.num_data = 2
def log_likelihood(self, ddt, dd, aniso_scaling=None):
"""
:param ddt: time-delay distance
:param dd: angular diameter distance to the deflector
:param aniso_scaling: array of size of the velocity dispersion measurement or None, scaling of the predicted
dimensionless quantity J (proportional to sigma_v^2) of the anisotropy model in the sampling relative to the
anisotropy model used to derive the prediction and covariance matrix in the init of this class.
:return: log likelihood given the single lens analysis
"""
if aniso_scaling is not None:
dd_ = dd * aniso_scaling[0]
else:
dd_ = dd
lnlikelihood = self._tdLikelihood.log_likelihood(ddt, dd_) - (dd_ - self._dd_mean) ** 2 / self._dd_sigma2 / 2
return lnlikelihood
def ddt_measurement(self):
"""
:return: mean, 1-sigma of the ddt inference/model measurement
"""
return self._tdLikelihood.ddt_measurement()
def __init__(self,
z_lens,
z_source,
ddt_mean,
ddt_sigma,
sigma_v_measurement,
j_model,
error_cov_measurement,
error_cov_j_sqrt,
sigma_sys_error_include=False,
normalized=True):
"""
:param z_lens: lens redshift
:param z_source: source redshift
:param ddt_mean: mean Ddt [Mpc] of time-delay and lens model likelihood
:param ddt_sigma: 1-sigma uncertainty in Ddt
:param sigma_v_measurement: numpy array, velocity dispersion measured
:param j_model: numpy array of the predicted dimensionless dispersion on the IFU's
:param error_cov_measurement: covariance matrix of the measured velocity dispersions in the IFU's
:param error_cov_j_sqrt: covariance matrix of sqrt(J) of the model predicted dimensionless dispersion on the IFU's
:param sigma_sys_error_include: bool, if True will include a systematic error in the velocity dispersion
measurement (if sampled from), otherwise this sampled value is ignored.
:param normalized: bool, if True, returns the normalized likelihood, if False, separates the constant prefactor
(in case of a Gaussian 1/(sigma sqrt(2 pi)) ) to compute the reduced chi2 statistics
"""
self._ddt_gauss_likelihood = DdtGaussianLikelihood(z_lens,
z_source,
ddt_mean=ddt_mean,
ddt_sigma=ddt_sigma)
self._kinlikelihood = KinLikelihood(
z_lens,
z_source,
sigma_v_measurement,
j_model,
error_cov_measurement,
error_cov_j_sqrt,
sigma_sys_error_include=sigma_sys_error_include,
normalized=normalized)
self.num_data = self._ddt_gauss_likelihood.num_data + self._kinlikelihood.num_data
def __init__(self, z_lens, z_source, likelihood_type, name='name', **kwargs_likelihood):
"""
:param z_lens: lens redshift
:param z_source: source redshift
:param name: string (optional) to name the specific lens
:param likelihood_type: string to specify the likelihood type
:param kwargs_likelihood: keyword arguments specifying the likelihood function,
see individual classes for their use
"""
self._name = name
self._z_lens = z_lens
self._z_source = z_source
self.likelihood_type = likelihood_type
if likelihood_type in ['DdtGaussian']:
from hierarc.Likelihood.LensLikelihood.ddt_gauss_likelihood import DdtGaussianLikelihood
self._lens_type = DdtGaussianLikelihood(z_lens, z_source, **kwargs_likelihood)
elif likelihood_type in ['DdtDdKDE']:
from hierarc.Likelihood.LensLikelihood.ddt_dd_kde_likelihood import DdtDdKDELikelihood
self._lens_type = DdtDdKDELikelihood(z_lens, z_source, **kwargs_likelihood)
elif likelihood_type == 'DdtDdGaussian':
from hierarc.Likelihood.LensLikelihood.ddt_dd_gauss_likelihood import DdtDdGaussian
self._lens_type = DdtDdGaussian(z_lens, z_source, **kwargs_likelihood)
elif likelihood_type in ['DsDdsGaussian']:
from hierarc.Likelihood.LensLikelihood.ds_dds_gauss_likelihood import DsDdsGaussianLikelihood
self._lens_type = DsDdsGaussianLikelihood(z_lens, z_source, **kwargs_likelihood)
elif likelihood_type == 'DdtLogNorm':
from hierarc.Likelihood.LensLikelihood.ddt_lognorm_likelihood import DdtLogNormLikelihood
self._lens_type = DdtLogNormLikelihood(z_lens, z_source, **kwargs_likelihood)
elif likelihood_type == 'IFUKinCov':
from hierarc.Likelihood.LensLikelihood.kin_likelihood import KinLikelihood
self._lens_type = KinLikelihood(z_lens, z_source, **kwargs_likelihood)
elif likelihood_type == 'DdtHist':
from hierarc.Likelihood.LensLikelihood.ddt_hist_likelihood import DdtHistLikelihood
self._lens_type = DdtHistLikelihood(z_lens, z_source, **kwargs_likelihood)
elif likelihood_type == 'DdtHistKDE':
from hierarc.Likelihood.LensLikelihood.ddt_hist_likelihood import DdtHistKDELikelihood
self._lens_type = DdtHistKDELikelihood(z_lens, z_source, **kwargs_likelihood)
elif likelihood_type == 'DdtHistKin':
from hierarc.Likelihood.LensLikelihood.ddt_hist_kin_likelihood import DdtHistKinLikelihood
self._lens_type = DdtHistKinLikelihood(z_lens, z_source, **kwargs_likelihood)
elif likelihood_type == 'DdtGaussKin':
from hierarc.Likelihood.LensLikelihood.ddt_gauss_kin_likelihood import DdtGaussKinLikelihood
self._lens_type = DdtGaussKinLikelihood(z_lens, z_source, **kwargs_likelihood)
elif likelihood_type == 'Mag':
from hierarc.Likelihood.LensLikelihood.mag_likelihood import MagnificationLikelihood
self._lens_type = MagnificationLikelihood(**kwargs_likelihood)
elif likelihood_type == 'TDMag':
from hierarc.Likelihood.LensLikelihood.td_mag_likelihood import TDMagLikelihood
self._lens_type = TDMagLikelihood(**kwargs_likelihood)
else:
raise ValueError('likelihood_type %s not supported! Supported are %s.' % (likelihood_type, LIKELIHOOD_TYPES))
class TestDdtGaussKinLikelihood(object):
def setup(self):
self.z_lens = 0.8
self.z_source = 3.0
self.ddt_mean = 10
self.ddt_sigma = 0.1
self.dd_mean = 1.
kwargs_ddt_gauss = {
'z_lens': self.z_lens,
'z_source': self.z_source,
'ddt_mean': self.ddt_mean,
'ddt_sigma': self.ddt_sigma
}
ds_dds = self.ddt_mean / self.dd_mean / (1 + self.z_lens)
j_mean_list = np.ones(1)
scaling_ifu = 1
sigma_v_measurement = np.sqrt(
ds_dds * scaling_ifu * j_mean_list) * const.c / 1000
sigma_v_sigma = sigma_v_measurement / 10.
error_cov_measurement = np.diag(sigma_v_sigma**2)
error_cov_j_sqrt = np.diag(np.zeros_like(sigma_v_measurement))
self.kin_likelihood = KinLikelihood(self.z_lens,
self.z_source,
sigma_v_measurement,
j_mean_list,
error_cov_measurement,
error_cov_j_sqrt,
normalized=True)
self.ddt_gauss_likelihood = DdtGaussianLikelihood(**kwargs_ddt_gauss)
self.ddt_gauss_kin_likelihood = DdtGaussKinLikelihood(
self.z_lens,
self.z_source,
self.ddt_mean,
self.ddt_sigma,
sigma_v_measurement,
j_mean_list,
error_cov_measurement,
error_cov_j_sqrt,
sigma_sys_error_include=False)
self.sigma_v_measurement = sigma_v_measurement
self.error_cov_measurement = error_cov_measurement
def test_log_likelihood(self):
ddt, dd = 9, 0.9
lnlog_tot = self.ddt_gauss_kin_likelihood.log_likelihood(
ddt, dd, aniso_scaling=None, sigma_v_sys_error=None)
lnlog_ddt = self.ddt_gauss_likelihood.log_likelihood(ddt, dd)
lnlog_kin = self.kin_likelihood.log_likelihood(ddt,
dd,
aniso_scaling=None,
sigma_v_sys_error=None)
npt.assert_almost_equal(lnlog_tot, lnlog_ddt + lnlog_kin, decimal=5)
def test_ddt_measurement(self):
ddt_mean, ddt_sigma = self.ddt_gauss_kin_likelihood.ddt_measurement()
assert ddt_mean == self.ddt_mean
assert ddt_sigma == self.ddt_sigma
def test_sigma_v_measurement(self):
sigma_v_measurement_, error_cov_measurement_ = self.ddt_gauss_kin_likelihood.sigma_v_measurement(
)
assert sigma_v_measurement_[0] == self.sigma_v_measurement[0]
assert error_cov_measurement_[0, 0] == self.error_cov_measurement[0, 0]
sigma_v_predict, error_cov_predict = self.ddt_gauss_kin_likelihood.sigma_v_prediction(
self.ddt_mean, self.dd_mean, aniso_scaling=1)
assert sigma_v_predict[0] == self.sigma_v_measurement[0]
assert error_cov_predict[0, 0] == 0
class DdtGaussKinLikelihood(object):
"""
class for joint kinematics and time delay likelihood assuming that they are independent
Uses KinLikelihood and DdtHistLikelihood combined
"""
def __init__(self,
z_lens,
z_source,
ddt_mean,
ddt_sigma,
sigma_v_measurement,
j_model,
error_cov_measurement,
error_cov_j_sqrt,
sigma_sys_error_include=False,
normalized=True):
"""
:param z_lens: lens redshift
:param z_source: source redshift
:param ddt_mean: mean Ddt [Mpc] of time-delay and lens model likelihood
:param ddt_sigma: 1-sigma uncertainty in Ddt
:param sigma_v_measurement: numpy array, velocity dispersion measured
:param j_model: numpy array of the predicted dimensionless dispersion on the IFU's
:param error_cov_measurement: covariance matrix of the measured velocity dispersions in the IFU's
:param error_cov_j_sqrt: covariance matrix of sqrt(J) of the model predicted dimensionless dispersion on the IFU's
:param sigma_sys_error_include: bool, if True will include a systematic error in the velocity dispersion
measurement (if sampled from), otherwise this sampled value is ignored.
:param normalized: bool, if True, returns the normalized likelihood, if False, separates the constant prefactor
(in case of a Gaussian 1/(sigma sqrt(2 pi)) ) to compute the reduced chi2 statistics
"""
self._ddt_gauss_likelihood = DdtGaussianLikelihood(z_lens,
z_source,
ddt_mean=ddt_mean,
ddt_sigma=ddt_sigma)
self._kinlikelihood = KinLikelihood(
z_lens,
z_source,
sigma_v_measurement,
j_model,
error_cov_measurement,
error_cov_j_sqrt,
sigma_sys_error_include=sigma_sys_error_include,
normalized=normalized)
self.num_data = self._ddt_gauss_likelihood.num_data + self._kinlikelihood.num_data
def log_likelihood(self,
ddt,
dd,
aniso_scaling=None,
sigma_v_sys_error=None,
sigma_v_sys_offset=None):
"""
:param ddt: time-delay distance
:param dd: angular diameter distance to the deflector
:param aniso_scaling: array of size of the velocity dispersion measurement or None, scaling of the predicted
dimensionless quantity J (proportional to sigma_v^2) of the anisotropy model in the sampling relative to the
anisotropy model used to derive the prediction and covariance matrix in the init of this class.
:param sigma_v_sys_error: float (optional) added error on the velocity dispersion measurement in quadrature
:param sigma_v_sys_offset: float (optional) for a fractional systematic offset in the kinematic measurement
such that sigma_v = sigma_v_measured * (1 + sigma_v_sys_offset)
:return: log likelihood given the single lens analysis
"""
lnlikelihood = self._ddt_gauss_likelihood.log_likelihood(
ddt) + self._kinlikelihood.log_likelihood(
ddt,
dd,
aniso_scaling,
sigma_v_sys_error=sigma_v_sys_error,
sigma_v_sys_offset=sigma_v_sys_offset)
return lnlikelihood
def sigma_v_prediction(self, ddt, dd, aniso_scaling=1):
"""
model prediction mean velocity dispersion vector and model prediction covariance matrix
:param ddt: time-delay distance
:param dd: angular diameter distance to the deflector
:param aniso_scaling: array of size of the velocity dispersion measurement or None, scaling of the predicted
dimensionless quantity J (proportional to sigma_v^2) of the anisotropy model in the sampling relative to the
anisotropy model used to derive the prediction and covariance matrix in the init of this class.
:return: model prediction mean velocity dispersion vector and model prediction covariance matrix
"""
return self._kinlikelihood.sigma_v_prediction(ddt, dd, aniso_scaling)
def sigma_v_measurement(self,
sigma_v_sys_error=None,
sigma_v_sys_offset=None):
"""
:param sigma_v_sys_error: float (optional) added error on the velocity dispersion measurement in quadrature
:param sigma_v_sys_offset: float (optional) for a fractional systematic offset in the kinematic measurement
such that sigma_v = sigma_v_measured * (1 + sigma_v_sys_offset)
:return: measurement mean (vector), measurement covariance matrix
"""
return self._kinlikelihood.sigma_v_measurement(
sigma_v_sys_error=sigma_v_sys_error,
sigma_v_sys_offset=sigma_v_sys_offset)
def ddt_measurement(self):
"""
:return: mean, 1-sigma of the ddt inference/model measurement
"""
return self._ddt_gauss_likelihood.ddt_measurement()
def test_ddt_measurement(self):
likelihood = DdtGaussianLikelihood(**self.kwargs_lens)
ddt_mean, ddt_sigma = likelihood.ddt_measurement()
assert ddt_mean == self.ddt_mean
assert ddt_sigma == self.ddt_sigma