class LikelihoodModule(object):
"""
this class contains the routines to run a MCMC process
the key components are:
- imSim_class: an instance of a class that simulates one (or more) images and returns the likelihood, such as
ImageModel(), Multiband(), MultiExposure()
- param_class: instance of a Param() class that can cast the sorted list of parameters that are sampled into the conventions of the imSim_class
Additional arguments are supported for adding a time-delay likelihood etc (see __init__ definition)
"""
def __init__(self,
kwargs_data_joint,
kwargs_model,
param_class,
image_likelihood=True,
check_bounds=True,
check_matched_source_position=False,
astrometric_likelihood=False,
image_position_likelihood=False,
source_position_likelihood=False,
image_position_uncertainty=0.004,
check_positive_flux=False,
source_position_tolerance=0.001,
source_position_sigma=0.001,
force_no_add_image=False,
source_marg=False,
linear_prior=None,
restrict_image_number=False,
max_num_images=None,
bands_compute=None,
time_delay_likelihood=False,
force_minimum_source_surface_brightness=False,
flux_min=0,
image_likelihood_mask_list=None,
flux_ratio_likelihood=False,
kwargs_flux_compute={},
prior_lens=[],
prior_source=[],
prior_extinction=[],
prior_lens_light=[],
prior_ps=[],
prior_special=[],
prior_lens_kde=[],
prior_source_kde=[],
prior_lens_light_kde=[],
prior_ps_kde=[],
prior_special_kde=[],
prior_extinction_kde=[],
prior_lens_lognormal=[],
prior_source_lognormal=[],
prior_extinction_lognormal=[],
prior_lens_light_lognormal=[],
prior_ps_lognormal=[],
prior_special_lognormal=[],
custom_logL_addition=None):
"""
initializing class
:param param_class: instance of a Param() class that can cast the sorted list of parameters that are sampled into the
conventions of the imSim_class
:param image_likelihood: bool, option to compute the imaging likelihood
:param source_position_likelihood: bool, if True, ray-traces image positions back to source plane and evaluates
relative errors in respect ot the position_uncertainties in the image plane
:param check_bounds: bool, option to punish the hard bounds in parameter space
:param check_matched_source_position: bool, option to check whether point source position solver finds a solution to match all
the image positions in the same source plane coordinate
:param astrometric_likelihood: bool, additional likelihood term of the predicted vs modelled point source position
:param flaot, image_position_uncertainty: 1-sigma Gaussian uncertainty on the point source position
(only used if point_source_likelihood=True)
:param check_positive_flux: bool, option to punish models that do not have all positive linear amplitude parameters
:param source_position_tolerance: float, punishment of check_solver occurs when image positions are predicted further
away than this number
:param image_likelihood_mask_list: list of boolean 2d arrays of size of images marking the pixels to be evaluated in the likelihood
:param force_no_add_image: bool, if True: computes ALL image positions of the point source. If there are more
images predicted than modelled, a punishment occures
:param source_marg: marginalization addition on the imaging likelihood based on the covariance of the infered
linear coefficients
:param linear_prior: float or list of floats (when multi-linear setting is chosen) indicating the range of
linear amplitude priors when computing the marginalization term.
:param restrict_image_number: bool, if True: computes ALL image positions of the point source. If there are more
images predicted than indicated in max_num_images, a punishment occurs
:param max_num_images: int, see restrict_image_number
:param bands_compute: list of bools with same length as data objects, indicates which "band" to include in the fitting
:param time_delay_likelihood: bool, if True computes the time-delay likelihood of the FIRST point source
:param force_minimum_source_surface_brightness: bool, if True, evaluates the source surface brightness on a grid
and evaluates if all positions have positive flux
:param kwargs_flux_compute: keyword arguments of how to compute the image position fluxes (see FluxRatioLikeliood)
:param custom_logL_addition: a definition taking as arguments (kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps, kwargs_special, kwargs_extinction)
and returns a logL (punishing) value.
"""
multi_band_list, image_type, time_delays_measured, time_delays_uncertainties, flux_ratios, flux_ratio_errors, ra_image_list, dec_image_list = self._unpack_data(
**kwargs_data_joint)
if len(multi_band_list) == 0:
image_likelihood = False
self.param = param_class
self._lower_limit, self._upper_limit = self.param.param_limits()
lens_model_class, source_model_class, lens_light_model_class, point_source_class, extinction_class = class_creator.create_class_instances(
**kwargs_model)
self.PointSource = point_source_class
self._prior_likelihood = PriorLikelihood(
prior_lens,
prior_source,
prior_lens_light,
prior_ps,
prior_special,
prior_extinction,
prior_lens_kde,
prior_source_kde,
prior_lens_light_kde,
prior_ps_kde,
prior_special_kde,
prior_extinction_kde,
prior_lens_lognormal,
prior_source_lognormal,
prior_lens_light_lognormal,
prior_ps_lognormal,
prior_special_lognormal,
prior_extinction_lognormal,
)
self._time_delay_likelihood = time_delay_likelihood
if self._time_delay_likelihood is True:
self.time_delay_likelihood = TimeDelayLikelihood(
time_delays_measured, time_delays_uncertainties,
lens_model_class, point_source_class)
self._image_likelihood = image_likelihood
if self._image_likelihood is True:
self.image_likelihood = ImageLikelihood(
multi_band_list,
image_type,
kwargs_model,
bands_compute=bands_compute,
likelihood_mask_list=image_likelihood_mask_list,
source_marg=source_marg,
linear_prior=linear_prior,
force_minimum_source_surface_brightness=
force_minimum_source_surface_brightness,
flux_min=flux_min)
self._position_likelihood = PositionLikelihood(
point_source_class,
astrometric_likelihood=astrometric_likelihood,
image_position_likelihood=image_position_likelihood,
source_position_likelihood=source_position_likelihood,
ra_image_list=ra_image_list,
dec_image_list=dec_image_list,
image_position_uncertainty=image_position_uncertainty,
check_matched_source_position=check_matched_source_position,
source_position_tolerance=source_position_tolerance,
source_position_sigma=source_position_sigma,
force_no_add_image=force_no_add_image,
restrict_image_number=restrict_image_number,
max_num_images=max_num_images)
self._flux_ratio_likelihood = flux_ratio_likelihood
self._kwargs_flux_compute = kwargs_flux_compute
if self._flux_ratio_likelihood is True:
self.flux_ratio_likelihood = FluxRatioLikelihood(
lens_model_class, flux_ratios, flux_ratio_errors,
**self._kwargs_flux_compute)
self._check_positive_flux = check_positive_flux
self._check_bounds = check_bounds
self._custom_logL_addition = custom_logL_addition
def _unpack_data(self,
multi_band_list=[],
multi_band_type='multi-linear',
time_delays_measured=None,
time_delays_uncertainties=None,
flux_ratios=None,
flux_ratio_errors=None,
ra_image_list=[],
dec_image_list=[]):
"""
:param multi_band_list: list of [[kwargs_data, kwargs_psf, kwargs_numerics], [], ...]
:param multi_band_type: string, type of multi-plane settings (multi-linear or joint-linear)
:param time_delays_measured: measured time delays (units of days)
:param time_delays_uncertainties: uncertainties in time-delay measurement
:param flux_ratios: flux ratios of point sources
:param flux_ratio_errors: error in flux ratio measurement
:return:
"""
return multi_band_list, multi_band_type, time_delays_measured, time_delays_uncertainties, flux_ratios, flux_ratio_errors, ra_image_list, dec_image_list
def _reset_point_source_cache(self, bool=True):
self.PointSource.delete_lens_model_cache()
self.PointSource.set_save_cache(bool)
if self._image_likelihood is True:
self.image_likelihood.reset_point_source_cache(bool)
def logL(self, args, verbose=False):
"""
routine to compute X2 given variable parameters for a MCMC/PSO chain
"""
#extract parameters
kwargs_return = self.param.args2kwargs(args)
if self._check_bounds is True:
penalty, bound_hit = self.check_bounds(args,
self._lower_limit,
self._upper_limit,
verbose=verbose)
if bound_hit is True:
#print(-penalty, 'test penalty')
return -np.inf
return self.log_likelihood(kwargs_return, verbose=verbose)
def log_likelihood(self, kwargs_return, verbose=False):
kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps, kwargs_special = kwargs_return['kwargs_lens'], \
kwargs_return['kwargs_source'], \
kwargs_return['kwargs_lens_light'], \
kwargs_return['kwargs_ps'], \
kwargs_return['kwargs_special']
#generate image and computes likelihood
self._reset_point_source_cache(bool=True)
logL = 0
if self._image_likelihood is True:
logL_image = self.image_likelihood.logL(**kwargs_return)
logL += logL_image
if verbose is True:
print('image logL = %s' % logL_image)
if self._time_delay_likelihood is True:
logL_time_delay = self.time_delay_likelihood.logL(
kwargs_lens, kwargs_ps, kwargs_special)
logL += logL_time_delay
if verbose is True:
print('time-delay logL = %s' % logL_time_delay)
if self._check_positive_flux is True:
bool = self.param.check_positive_flux(kwargs_source,
kwargs_lens_light, kwargs_ps)
if bool is False:
logL -= 10**5
if verbose is True:
print(
'non-positive surface brightness parameters detected!')
if self._flux_ratio_likelihood is True:
ra_image_list, dec_image_list = self.PointSource.image_position(
kwargs_ps=kwargs_ps, kwargs_lens=kwargs_lens)
#x_pos, y_pos = self.param.real_image_positions(ra_image_list[0], dec_image_list[0], kwargs_special)
x_pos, y_pos = ra_image_list[0], dec_image_list[0]
logL_flux_ratios = self.flux_ratio_likelihood.logL(
x_pos, y_pos, kwargs_lens, kwargs_special)
logL += logL_flux_ratios
if verbose is True:
print('flux ratio logL = %s' % logL_flux_ratios)
logL += self._position_likelihood.logL(kwargs_lens,
kwargs_ps,
kwargs_special,
verbose=verbose)
logL_prior = self._prior_likelihood.logL(**kwargs_return)
logL += logL_prior
if verbose is True:
print('Prior likelihood = %s' % logL_prior)
if self._custom_logL_addition is not None:
logL_cond = self._custom_logL_addition(**kwargs_return)
logL += logL_cond
if verbose is True:
print('custom added logL = %s' % logL_cond)
self._reset_point_source_cache(bool=False)
return logL #, None
@staticmethod
def check_bounds(args, lowerLimit, upperLimit, verbose=False):
"""
checks whether the parameter vector has left its bound, if so, adds a big number
"""
penalty = 0.
bound_hit = False
for i in range(0, len(args)):
if args[i] < lowerLimit[i] or args[i] > upperLimit[i]:
penalty = 10.**5
bound_hit = True
if verbose is True:
print(
'parameter %s with value %s hit the bounds [%s, %s] ' %
(i, args[i], lowerLimit[i], upperLimit[i]))
return penalty, bound_hit
return penalty, bound_hit
@property
def num_data(self):
"""
:return: number of independent data points in the combined fitting
"""
num_data = 0
if self._image_likelihood is True:
num_data += self.image_likelihood.num_data
if self._time_delay_likelihood is True:
num_data += self.time_delay_likelihood.num_data
if self._flux_ratio_likelihood is True:
num_data += self.flux_ratio_likelihood.num_data
num_data += self._position_likelihood.num_data
return num_data
@property
def param_limits(self):
return self._lower_limit, self._upper_limit
def effectiv_num_data_points(self, **kwargs):
"""
returns the effective number of data points considered in the X2 estimation to compute the reduced X2 value
"""
num_linear = 0
if self._image_likelihood is True:
num_linear = self.image_likelihood.num_param_linear(**kwargs)
num_param, param_names = self.param.num_param()
return self.num_data - num_param - num_linear
def __call__(self, a):
return self.logL(a)
def likelihood(self, a):
return self.logL(a)
def likelihood_derivative(self, a):
"""
:param a: array
:return: logL, derivative estimatoe (None)
"""
return self.logL(a), None
class LikelihoodModule(object):
"""
this class contains the routines to run a MCMC process
the key components are:
- imSim_class: an instance of a class that simulates one (or more) images and returns the likelihood, such as
ImageModel(), Multiband(), MultiExposure()
- param_class: instance of a Param() class that can cast the sorted list of parameters that are sampled into the conventions of the imSim_class
Additional arguments are supported for adding a time-delay likelihood etc (see __init__ definition)
"""
def __init__(self,
kwargs_data_joint,
kwargs_model,
param_class,
image_likelihood=True,
check_bounds=True,
check_solver=False,
point_source_likelihood=False,
position_uncertainty=0.004,
check_positive_flux=False,
solver_tolerance=0.001,
force_no_add_image=False,
source_marg=False,
restrict_image_number=False,
max_num_images=None,
bands_compute=None,
time_delay_likelihood=False,
force_minimum_source_surface_brightness=False,
flux_min=0,
image_likelihood_mask_list=None,
flux_ratio_likelihood=False,
kwargs_flux_compute={},
prior_lens=[],
prior_source=[],
prior_lens_light=[],
prior_ps=[],
prior_cosmo=[]):
"""
initializing class
:param param_class: instance of a Param() class that can cast the sorted list of parameters that are sampled into the
conventions of the imSim_class
:param image_likelihood: bool, option to compute the imaging likelihood
:param check_bounds: bool, option to punish the hard bounds in parameter space
:param check_solver: bool, option to check whether point source position solver finds a solution to match all
the image positions in the same source plane coordinate
:param point_source_likelihood: bool, additional likelihood term of the predicted vs modelled point source position
:param flaot, position_uncertainty: 1-sigma Gaussian uncertainty on the point source position
(only used if point_source_likelihood=True)
:param check_positive_flux: bool, option to punish models that do not have all positive linear amplitude parameters
:param solver_tolerance: float, punishment of check_solver occures when image positions are predicted further
away than this number
:param image_likelihood_mask_list: list of boolean 2d arrays of size of images marking the pixels to be evaluated in the likelihood
:param force_no_add_image: bool, if True: computes ALL image positions of the point source. If there are more
images predicted than modelled, a punishment occures
:param source_marg: marginalization addition on the imaging likelihood based on the covariance of the infered
linear coefficients
:param restrict_image_number: bool, if True: computes ALL image positions of the point source. If there are more
images predicted than indicated in max_num_images, a punishment occures
:param max_num_images: int, see restrict_image_number
:param bands_compute: list of bools with same length as data objects, indicates which "band" to include in the fitting
:param time_delay_likelihood: bool, if True computes the time-delay likelihood of the FIRST point source
:param force_minimum_source_surface_brightness: bool, if True, evaluates the source surface brightness on a grid
and evaluates if all positions have positive flux
:param kwargs_flux_compute: keyword arguments of how to compute the image position fluxes (see FluxRatioLikeliood)
"""
multi_band_list = kwargs_data_joint.get('multi_band_list', [])
multi_band_type = kwargs_data_joint.get('image_type', 'single-band')
time_delays_measured = kwargs_data_joint.get('time_delays_measured',
None)
time_delays_uncertainties = kwargs_data_joint.get(
'time_delays_uncertainties', None)
flux_ratios = kwargs_data_joint.get('flux_ratios', None)
flux_ratio_errors = kwargs_data_joint.get('flux_ratio_errors', None)
self.param = param_class
self._lower_limit, self._upper_limit = self.param.param_limits()
lens_model_class, source_model_class, lens_light_model_class, point_source_class = class_reator.create_class_instances(
**kwargs_model)
self.PointSource = point_source_class
self._prior_likelihood = PriorLikelihood(prior_lens, prior_source,
prior_lens_light, prior_ps,
prior_cosmo)
self._time_delay_likelihood = time_delay_likelihood
if self._time_delay_likelihood is True:
self.time_delay_likelihood = TimeDelayLikelihood(
time_delays_measured, time_delays_uncertainties,
lens_model_class, point_source_class, param_class)
self._image_likelihood = image_likelihood
if self._image_likelihood is True:
self.image_likelihood = ImageLikelihood(
multi_band_list,
multi_band_type,
kwargs_model,
bands_compute=bands_compute,
likelihood_mask_list=image_likelihood_mask_list,
source_marg=source_marg,
force_minimum_source_surface_brightness=
force_minimum_source_surface_brightness,
flux_min=flux_min)
self._position_likelihood = PositionLikelihood(
point_source_class, param_class, point_source_likelihood,
position_uncertainty, check_solver, solver_tolerance,
force_no_add_image, restrict_image_number, max_num_images)
self._flux_ratio_likelihood = flux_ratio_likelihood
self._kwargs_flux_compute = kwargs_flux_compute
if self._flux_ratio_likelihood is True:
self.flux_ratio_likelihood = FluxRatioLikelihood(
point_source_class, lens_model_class, param_class, flux_ratios,
flux_ratio_errors, **self._kwargs_flux_compute)
self._check_positive_flux = check_positive_flux
self._check_bounds = check_bounds
def _reset_point_source_cache(self, bool=True):
self.PointSource.delete_lens_model_cach()
self.PointSource.set_save_cache(bool)
if self._image_likelihood is True:
self.image_likelihood.reset_point_source_cache(bool)
def logL(self, args):
"""
routine to compute X2 given variable parameters for a MCMC/PSO chain
"""
#extract parameters
kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps, kwargs_cosmo = self.param.args2kwargs(
args)
#generate image and computes likelihood
self._reset_point_source_cache(bool=True)
logL = 0
if self._check_bounds is True:
penalty, bound_hit = self.check_bounds(args, self._lower_limit,
self._upper_limit)
logL -= penalty
if bound_hit:
return logL, None
if self._image_likelihood is True:
logL += self.image_likelihood.logL(kwargs_lens, kwargs_source,
kwargs_lens_light, kwargs_ps)
if self._time_delay_likelihood is True:
logL += self.time_delay_likelihood.logL(kwargs_lens, kwargs_ps,
kwargs_cosmo)
if self._check_positive_flux is True:
bool = self.param.check_positive_flux(kwargs_source,
kwargs_lens_light, kwargs_ps)
if bool is False:
logL -= 10**10
if self._flux_ratio_likelihood is True:
logL += self.flux_ratio_likelihood.logL(kwargs_lens, kwargs_ps,
kwargs_cosmo)
logL += self._position_likelihood.logL(kwargs_lens, kwargs_ps,
kwargs_cosmo)
logL += self._prior_likelihood.logL(kwargs_lens, kwargs_source,
kwargs_lens_light, kwargs_ps,
kwargs_cosmo)
self._reset_point_source_cache(bool=False)
return logL, None
@staticmethod
def check_bounds(args, lowerLimit, upperLimit):
"""
checks whether the parameter vector has left its bound, if so, adds a big number
"""
penalty = 0
bound_hit = False
for i in range(0, len(args)):
if args[i] < lowerLimit[i] or args[i] > upperLimit[i]:
penalty = 10**15
bound_hit = True
return penalty, bound_hit
@property
def num_data(self):
"""
:return: number of independent data points in the combined fitting
"""
num_data = 0
if self._image_likelihood is True:
num_data += self.image_likelihood.num_data
if self._time_delay_likelihood is True:
num_data += self.time_delay_likelihood.num_data
return num_data
@property
def param_limits(self):
return self._lower_limit, self._upper_limit
def effectiv_num_data_points(self, kwargs_lens, kwargs_source,
kwargs_lens_light, kwargs_ps):
"""
returns the effective number of data points considered in the X2 estimation to compute the reduced X2 value
"""
num_linear = 0
if self._image_likelihood is True:
num_linear = self.image_likelihood.num_param_linear(
kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps)
num_param, _ = self.param.num_param()
return self.num_data - num_param - num_linear
def __call__(self, a):
return self.logL(a)
def likelihood(self, a):
return self.logL(a)
def computeLikelihood(self, ctx):
logL, _ = self.logL(ctx.getParams())
return logL
def setup(self):
pass
class TestPositionLikelihood(object):
def setup(self):
# compute image positions
lensModel = LensModel(lens_model_list=['SIE'])
solver = LensEquationSolver(lensModel=lensModel)
self._kwargs_lens = [{
'theta_E': 1,
'e1': 0.1,
'e2': -0.03,
'center_x': 0,
'center_y': 0
}]
x_pos, y_pos = solver.image_position_from_source(
sourcePos_x=0.01, sourcePos_y=-0.01, kwargs_lens=self._kwargs_lens)
point_source_class = PointSource(
point_source_type_list=['LENSED_POSITION'], lensModel=lensModel)
self.likelihood = PositionLikelihood(point_source_class,
position_uncertainty=0.005,
astrometric_likelihood=True,
image_position_likelihood=True,
ra_image_list=[x_pos],
dec_image_list=[y_pos],
source_position_likelihood=True,
check_solver=False,
solver_tolerance=0.001,
force_no_add_image=False,
restrict_image_number=False,
max_num_images=None)
self._x_pos, self._y_pos = x_pos, y_pos
def test_image_position_likelihood(self):
kwargs_ps = [{'ra_image': self._x_pos, 'dec_image': self._y_pos}]
logL = self.likelihood.image_position_likelihood(kwargs_ps,
self._kwargs_lens,
sigma=0.01)
npt.assert_almost_equal(logL, 0, decimal=8)
kwargs_ps = [{
'ra_image': self._x_pos + 0.01,
'dec_image': self._y_pos
}]
logL = self.likelihood.image_position_likelihood(kwargs_ps,
self._kwargs_lens,
sigma=0.01)
npt.assert_almost_equal(logL, -2, decimal=8)
def test_astrometric_likelihood(self):
kwargs_ps = [{'ra_image': self._x_pos, 'dec_image': self._y_pos}]
kwargs_special = {
'delta_x_image': [0, 0, 0, 0.],
'delta_y_image': [0, 0, 0, 0.]
}
logL = self.likelihood.astrometric_likelihood(kwargs_ps,
kwargs_special,
sigma=0.01)
npt.assert_almost_equal(logL, 0, decimal=8)
kwargs_special = {
'delta_x_image': [0, 0, 0, 0.01],
'delta_y_image': [0, 0, 0, 0.01]
}
logL = self.likelihood.astrometric_likelihood(kwargs_ps,
kwargs_special,
sigma=0.01)
npt.assert_almost_equal(logL, -1, decimal=8)
logL = self.likelihood.astrometric_likelihood([],
kwargs_special,
sigma=0.01)
npt.assert_almost_equal(logL, 0, decimal=8)
logL = self.likelihood.astrometric_likelihood(kwargs_ps, {},
sigma=0.01)
npt.assert_almost_equal(logL, 0, decimal=8)
def test_check_additional_images(self):
point_source_class = PointSource(
point_source_type_list=['LENSED_POSITION'],
additional_images_list=[True],
lensModel=LensModel(lens_model_list=['SIE']))
likelihood = PositionLikelihood(point_source_class)
kwargs_ps = [{'ra_image': self._x_pos, 'dec_image': self._y_pos}]
bool = likelihood.check_additional_images(kwargs_ps, self._kwargs_lens)
assert bool is False
kwargs_ps = [{
'ra_image': self._x_pos[1:],
'dec_image': self._y_pos[1:]
}]
bool = likelihood.check_additional_images(kwargs_ps, self._kwargs_lens)
assert bool is True
def test_solver_penalty(self):
kwargs_ps = [{'ra_image': self._x_pos, 'dec_image': self._y_pos}]
logL = self.likelihood.solver_penalty(self._kwargs_lens,
kwargs_ps,
tolerance=0.0001,
verbose=False)
assert logL == 0
kwargs_ps = [{
'ra_image': self._x_pos + 0.01,
'dec_image': self._y_pos
}]
logL = self.likelihood.solver_penalty(self._kwargs_lens,
kwargs_ps,
tolerance=0.001,
verbose=False)
npt.assert_almost_equal(logL, 123518245.5117848, decimal=0)
def test_logL(self):
kwargs_ps = [{'ra_image': self._x_pos, 'dec_image': self._y_pos}]
kwargs_special = {
'delta_x_image': [0, 0, 0, 0.],
'delta_y_image': [0, 0, 0, 0.]
}
logL = self.likelihood.logL(self._kwargs_lens,
kwargs_ps,
kwargs_special,
verbose=True)
npt.assert_almost_equal(logL, 0, decimal=9)
def test_source_position_likelihood(self):
kwargs_ps = [{'ra_image': self._x_pos, 'dec_image': self._y_pos}]
logL = self.likelihood.source_position_likelihood(self._kwargs_lens,
kwargs_ps,
sigma=0.01)
npt.assert_almost_equal(logL, 0, decimal=9)
x_pos = copy.deepcopy(self._x_pos)
x_pos[0] += 0.01
kwargs_ps = [{'ra_image': x_pos, 'dec_image': self._y_pos}]
logL = self.likelihood.source_position_likelihood(self._kwargs_lens,
kwargs_ps,
sigma=0.01)
npt.assert_almost_equal(logL, -0.33011713058631054, decimal=4)
class LikelihoodModule(object):
"""
this class contains the routines to run a MCMC process
the key components are:
- imSim_class: an instance of a class that simulates one (or more) images and returns the likelihood, such as
ImageModel(), Multiband(), MultiExposure()
- param_class: instance of a Param() class that can cast the sorted list of parameters that are sampled into the
conventions of the imSim_class
Additional arguments are supported for adding a time-delay likelihood etc (see __init__ definition)
"""
def __init__(self,
kwargs_data_joint,
kwargs_model,
param_class,
image_likelihood=True,
check_bounds=True,
check_matched_source_position=False,
astrometric_likelihood=False,
image_position_likelihood=False,
source_position_likelihood=False,
image_position_uncertainty=0.004,
check_positive_flux=False,
source_position_tolerance=0.001,
source_position_sigma=0.001,
force_no_add_image=False,
source_marg=False,
linear_prior=None,
restrict_image_number=False,
max_num_images=None,
bands_compute=None,
time_delay_likelihood=False,
image_likelihood_mask_list=None,
flux_ratio_likelihood=False,
kwargs_flux_compute=None,
prior_lens=None,
prior_source=None,
prior_extinction=None,
prior_lens_light=None,
prior_ps=None,
prior_special=None,
prior_lens_kde=None,
prior_source_kde=None,
prior_lens_light_kde=None,
prior_ps_kde=None,
prior_special_kde=None,
prior_extinction_kde=None,
prior_lens_lognormal=None,
prior_source_lognormal=None,
prior_extinction_lognormal=None,
prior_lens_light_lognormal=None,
prior_ps_lognormal=None,
prior_special_lognormal=None,
custom_logL_addition=None,
kwargs_pixelbased=None):
"""
initializing class
:param param_class: instance of a Param() class that can cast the sorted list of parameters that are sampled
into the conventions of the imSim_class
:param image_likelihood: bool, option to compute the imaging likelihood
:param source_position_likelihood: bool, if True, ray-traces image positions back to source plane and evaluates
relative errors in respect ot the position_uncertainties in the image plane
:param check_bounds: bool, option to punish the hard bounds in parameter space
:param check_matched_source_position: bool, option to check whether point source position of solver finds a
solution to match all the image positions in the same source plane coordinate
:param astrometric_likelihood: bool, additional likelihood term of the predicted vs modelled point source
position
:param image_position_uncertainty: float, 1-sigma Gaussian uncertainty on the point source position
(only used if point_source_likelihood=True)
:param check_positive_flux: bool, option to punish models that do not have all positive linear amplitude
parameters
:param source_position_tolerance: float, punishment of check_solver occurs when image positions are predicted
further away than this number
:param image_likelihood_mask_list: list of boolean 2d arrays of size of images marking the pixels to be
evaluated in the likelihood
:param force_no_add_image: bool, if True: computes ALL image positions of the point source. If there are more
images predicted than modelled, a punishment occures
:param source_marg: marginalization addition on the imaging likelihood based on the covariance of the inferred
linear coefficients
:param linear_prior: float or list of floats (when multi-linear setting is chosen) indicating the range of
linear amplitude priors when computing the marginalization term.
:param restrict_image_number: bool, if True: computes ALL image positions of the point source. If there are more
images predicted than indicated in max_num_images, a punishment occurs
:param max_num_images: int, see restrict_image_number
:param bands_compute: list of bools with same length as data objects, indicates which "band" to include in the
fitting
:param time_delay_likelihood: bool, if True computes the time-delay likelihood of the FIRST point source
:param kwargs_flux_compute: keyword arguments of how to compute the image position fluxes
(see FluxRatioLikeliood)
:param custom_logL_addition: a definition taking as arguments (kwargs_lens, kwargs_source, kwargs_lens_light,
kwargs_ps, kwargs_special, kwargs_extinction) and returns a logL (punishing) value.
:param kwargs_pixelbased: keyword arguments with various settings related to the pixel-based solver
(see SLITronomy documentation)
"""
multi_band_list, multi_band_type, time_delays_measured, time_delays_uncertainties, flux_ratios, flux_ratio_errors, ra_image_list, dec_image_list = self._unpack_data(
**kwargs_data_joint)
if len(multi_band_list) == 0:
image_likelihood = False
self.param = param_class
self._lower_limit, self._upper_limit = self.param.param_limits()
self._prior_likelihood = PriorLikelihood(
prior_lens,
prior_source,
prior_lens_light,
prior_ps,
prior_special,
prior_extinction,
prior_lens_kde,
prior_source_kde,
prior_lens_light_kde,
prior_ps_kde,
prior_special_kde,
prior_extinction_kde,
prior_lens_lognormal,
prior_source_lognormal,
prior_lens_light_lognormal,
prior_ps_lognormal,
prior_special_lognormal,
prior_extinction_lognormal,
)
self._time_delay_likelihood = time_delay_likelihood
self._image_likelihood = image_likelihood
self._flux_ratio_likelihood = flux_ratio_likelihood
if kwargs_flux_compute is None:
kwargs_flux_compute = {}
self._kwargs_flux_compute = kwargs_flux_compute
self._check_bounds = check_bounds
self._custom_logL_addition = custom_logL_addition
self._kwargs_time_delay = {
'time_delays_measured': time_delays_measured,
'time_delays_uncertainties': time_delays_uncertainties
}
self._kwargs_imaging = {
'multi_band_list': multi_band_list,
'multi_band_type': multi_band_type,
'bands_compute': bands_compute,
'image_likelihood_mask_list': image_likelihood_mask_list,
'source_marg': source_marg,
'linear_prior': linear_prior,
'check_positive_flux': check_positive_flux,
'kwargs_pixelbased': kwargs_pixelbased
}
self._kwargs_position = {
'astrometric_likelihood': astrometric_likelihood,
'image_position_likelihood': image_position_likelihood,
'source_position_likelihood': source_position_likelihood,
'ra_image_list': ra_image_list,
'dec_image_list': dec_image_list,
'image_position_uncertainty': image_position_uncertainty,
'check_matched_source_position': check_matched_source_position,
'source_position_tolerance': source_position_tolerance,
'source_position_sigma': source_position_sigma,
'force_no_add_image': force_no_add_image,
'restrict_image_number': restrict_image_number,
'max_num_images': max_num_images
}
self._kwargs_flux = {
'flux_ratios': flux_ratios,
'flux_ratio_errors': flux_ratio_errors
}
self._kwargs_flux.update(self._kwargs_flux_compute)
self._class_instances(kwargs_model=kwargs_model,
kwargs_imaging=self._kwargs_imaging,
kwargs_position=self._kwargs_position,
kwargs_flux=self._kwargs_flux,
kwargs_time_delay=self._kwargs_time_delay)
def _class_instances(self, kwargs_model, kwargs_imaging, kwargs_position,
kwargs_flux, kwargs_time_delay):
"""
:param kwargs_model: lenstronomy model keyword arguments
:param kwargs_imaging: keyword arguments for imaging likelihood
:param kwargs_position: keyword arguments for positional likelihood
:param kwargs_flux: keyword arguments for flux ratio likelihood
:param kwargs_time_delay: keyword arguments for time delay likelihood
:return: updated model instances of this class
"""
lens_model_class, source_model_class, lens_light_model_class, point_source_class, extinction_class = class_creator.create_class_instances(
**kwargs_model)
self.PointSource = point_source_class
if self._time_delay_likelihood is True:
self.time_delay_likelihood = TimeDelayLikelihood(
lens_model_class=lens_model_class,
point_source_class=point_source_class,
**kwargs_time_delay)
if self._image_likelihood is True:
self.image_likelihood = ImageLikelihood(kwargs_model=kwargs_model,
**kwargs_imaging)
self._position_likelihood = PositionLikelihood(point_source_class,
**kwargs_position)
if self._flux_ratio_likelihood is True:
self.flux_ratio_likelihood = FluxRatioLikelihood(
lens_model_class, **kwargs_flux)
def __call__(self, a):
return self.logL(a)
def logL(self, args, verbose=False):
"""
routine to compute X2 given variable parameters for a MCMC/PSO chain
"""
# extract parameters
kwargs_return = self.param.args2kwargs(args)
if self._check_bounds is True:
penalty, bound_hit = self.check_bounds(args,
self._lower_limit,
self._upper_limit,
verbose=verbose)
if bound_hit is True:
return -10**15
return self.log_likelihood(kwargs_return, verbose=verbose)
def log_likelihood(self, kwargs_return, verbose=False):
kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps, kwargs_special = kwargs_return['kwargs_lens'], \
kwargs_return['kwargs_source'], \
kwargs_return['kwargs_lens_light'], \
kwargs_return['kwargs_ps'], \
kwargs_return['kwargs_special']
# update model instance in case of changes affecting it (i.e. redshift sampling in multi-plane)
self._update_model(kwargs_special)
# generate image and computes likelihood
self._reset_point_source_cache(bool_input=True)
logL = 0
if self._image_likelihood is True:
logL_image = self.image_likelihood.logL(**kwargs_return)
logL += logL_image
if verbose is True:
print('image logL = %s' % logL_image)
if self._time_delay_likelihood is True:
logL_time_delay = self.time_delay_likelihood.logL(
kwargs_lens, kwargs_ps, kwargs_special)
logL += logL_time_delay
if verbose is True:
print('time-delay logL = %s' % logL_time_delay)
if self._flux_ratio_likelihood is True:
ra_image_list, dec_image_list = self.PointSource.image_position(
kwargs_ps=kwargs_ps, kwargs_lens=kwargs_lens)
x_pos, y_pos = ra_image_list[0], dec_image_list[0]
logL_flux_ratios = self.flux_ratio_likelihood.logL(
x_pos, y_pos, kwargs_lens, kwargs_special)
logL += logL_flux_ratios
if verbose is True:
print('flux ratio logL = %s' % logL_flux_ratios)
logL += self._position_likelihood.logL(kwargs_lens,
kwargs_ps,
kwargs_special,
verbose=verbose)
logL_prior = self._prior_likelihood.logL(**kwargs_return)
logL += logL_prior
if verbose is True:
print('Prior likelihood = %s' % logL_prior)
if self._custom_logL_addition is not None:
logL_cond = self._custom_logL_addition(**kwargs_return)
logL += logL_cond
if verbose is True:
print('custom added logL = %s' % logL_cond)
self._reset_point_source_cache(bool_input=False)
return logL # , None
@staticmethod
def check_bounds(args, lowerLimit, upperLimit, verbose=False):
"""
checks whether the parameter vector has left its bound, if so, adds a big number
"""
penalty = 0.
bound_hit = False
args = np.atleast_1d(args)
for i in range(0, len(args)):
if args[i] < lowerLimit[i] or args[i] > upperLimit[i]:
penalty = 10.**5
bound_hit = True
if verbose is True:
print(
'parameter %s with value %s hit the bounds [%s, %s] ' %
(i, args[i], lowerLimit[i], upperLimit[i]))
return penalty, bound_hit
return penalty, bound_hit
@property
def num_data(self):
"""
:return: number of independent data points in the combined fitting
"""
num_data = 0
if self._image_likelihood is True:
num_data += self.image_likelihood.num_data
if self._time_delay_likelihood is True:
num_data += self.time_delay_likelihood.num_data
if self._flux_ratio_likelihood is True:
num_data += self.flux_ratio_likelihood.num_data
num_data += self._position_likelihood.num_data
return num_data
@property
def param_limits(self):
return self._lower_limit, self._upper_limit
def effective_num_data_points(self, **kwargs):
"""
returns the effective number of data points considered in the X2 estimation to compute the reduced X2 value
"""
num_linear = 0
if self._image_likelihood is True:
num_linear = self.image_likelihood.num_param_linear(**kwargs)
num_param, param_names = self.param.num_param()
return self.num_data - num_param - num_linear
def likelihood(self, a):
return self.logL(a)
def negativelogL(self, a):
"""
for minimizer function, the negative value of the logl value is requested
:param a: array of parameters
:return: -logL
"""
return -self.logL(a)
@staticmethod
def _unpack_data(multi_band_list=None,
multi_band_type='multi-linear',
time_delays_measured=None,
time_delays_uncertainties=None,
flux_ratios=None,
flux_ratio_errors=None,
ra_image_list=None,
dec_image_list=None):
"""
:param multi_band_list: list of [[kwargs_data, kwargs_psf, kwargs_numerics], [], ...]
:param multi_band_type: string, type of multi-plane settings (multi-linear or joint-linear)
:param time_delays_measured: measured time delays (units of days)
:param time_delays_uncertainties: uncertainties in time-delay measurement
:param flux_ratios: flux ratios of point sources
:param flux_ratio_errors: error in flux ratio measurement
:return:
"""
if multi_band_list is None:
multi_band_list = []
if ra_image_list is None:
ra_image_list = []
if dec_image_list is None:
dec_image_list = []
return multi_band_list, multi_band_type, time_delays_measured, time_delays_uncertainties, flux_ratios, \
flux_ratio_errors, ra_image_list, dec_image_list
def _reset_point_source_cache(self, bool_input=True):
self.PointSource.delete_lens_model_cache()
self.PointSource.set_save_cache(bool_input)
if self._image_likelihood is True:
self.image_likelihood.reset_point_source_cache(bool_input)
def _update_model(self, kwargs_special):
"""
updates lens model instance of this class (and all class instances related to it) when an update to the
modeled redshifts of the deflector and/or source planes are made
:param kwargs_special: keyword arguments from SpecialParam() class return of sampling arguments
:return: None, all class instances updated to recent modek
"""
kwargs_model, update_bool = self.param.update_kwargs_model(
kwargs_special)
if update_bool is True:
self._class_instances(kwargs_model=kwargs_model,
kwargs_imaging=self._kwargs_imaging,
kwargs_position=self._kwargs_position,
kwargs_flux=self._kwargs_flux,
kwargs_time_delay=self._kwargs_time_delay)