import numpy as np
import scipy.stats as stats
import astropy.units as u
from addict import Dict
import lenstronomy.Util.param_util as param_util
from .base_bnn_prior import BaseBNNPrior
from .base_cosmo_bnn_prior import BaseCosmoBNNPrior
from . import kinematics_models, parameter_models
[docs]class EmpiricalBNNPrior(BaseBNNPrior, BaseCosmoBNNPrior):
"""BNN prior that encodes physical correlations between parameters
"""
def __init__(self, bnn_omega, components):
"""
Note
----
The dictionary attributes are copies of the config corresponding to each component.
The number of attributes depends on the number of components.
Attributes
----------
bnn_omega : dict
copy of `cfg.bnn_omega`
components : list
list of components, e.g. `lens_mass`
"""
BaseBNNPrior.__init__(self, bnn_omega, components)
BaseCosmoBNNPrior.__init__(self, bnn_omega)
self.params_to_exclude = [('lens_mass', 'theta_E'), ('lens_mass', 'gamma'), ('lens_mass', 'q'), ('lens_light', 'magnitude'), ('lens_light', 'R_sersic'), ('lens_light', 'q'),
('src_light', 'magnitude'), ('src_light', 'R_sersic'),
('agn_light', 'magnitude')
]
self.set_params_list(self.params_to_exclude)
self.set_comps_qphi_to_e1e2()
# TODO: AGN parameters are sampled even when it's not rendered on image (not in self.components)
self._define_kinematics_models(self.kinematics)
self._define_parameter_models(self.lens_mass, self.lens_light, self.src_light, self.agn_light)
def _define_kinematics_models(self, kinematics_cfg):
"""Set the empirical models related to the kinematics, based on the config
Parameters
----------
kinematics_cfg : dict
Copy of `cfg.bnn_omega.kinematics`
"""
self.vel_disp_function = getattr(kinematics_models, kinematics_cfg.vel_disp.model)
def _define_parameter_models(self, lens_mass_cfg, lens_light_cfg, src_light_cfg, agn_light_cfg):
"""Set the empirical models, with which to generate all the training samples,
based on each component key in `cfg.bnn_omega`
Parameters
----------
lens_mass_cfg : dict
Copy of `cfg.bnn_omega.lens_mass`
lens_light_cfg : dict
Copy of `cfg.bnn_omega.lens_light`
src_light_cfg : dict
Copy of `cfg.bnn_omega.src_light`
agn_light_cfg : dict
Copy of `cfg.bnn_omega.agn_light`
"""
# lens_mass
self.gamma_model = getattr(parameter_models, lens_mass_cfg.gamma.model)(**lens_mass_cfg.gamma.model_kwargs).get_gamma_from_vel_disp
self.theta_E_model = getattr(parameter_models, lens_mass_cfg.theta_E.model)
self.lens_axis_ratio_model = getattr(parameter_models, lens_light_cfg.q.model)(**lens_light_cfg.q.model_kwargs).get_axis_ratio
# lens_light
self.lens_luminosity_model = getattr(parameter_models, lens_light_cfg.magnitude.model)(**lens_light_cfg.magnitude.model_kwargs).get_luminosity
self.lens_light_size_model = getattr(parameter_models, lens_light_cfg.R_sersic.model)(**lens_light_cfg.R_sersic.model_kwargs).get_effective_radius
#self.lens_axis_ratio_model = getattr(parameter_models, lens_light_cfg.q.model)(**lens_light_cfg.q.model_kwargs).get_axis_ratio
# src_light
self.src_luminosity_model = getattr(parameter_models, src_light_cfg.magnitude.model)
self.src_light_size_model = getattr(parameter_models, src_light_cfg.R_sersic.model)
# agn_light
self.agn_luminosity_model = getattr(parameter_models, agn_light_cfg.magnitude.model)(**agn_light_cfg.magnitude.model_kwargs).sample_agn_luminosity
[docs] def sample_vel_disp(self, vel_disp_cfg):
"""Sample velocity dispersion from the config-specified model,
on a grid with the range and resolution specified in the config
Parameters
----------
vel_disp_cfg : dict
Copy of `cfg.bnn_omega.kinematics.vel_disp`
Returns
-------
float
a realization of velocity dispersion
"""
vel_disp_grid = np.arange(**vel_disp_cfg.grid)
dn = self.vel_disp_function(vel_disp_grid)
dn_normed = dn/np.sum(dn)
sampled_vel_disp = np.random.choice(vel_disp_grid, None, replace=True, p=dn_normed)
return sampled_vel_disp
[docs] def get_lens_absolute_magnitude(self, vel_disp):
"""Get the lens absolute magnitude from the Faber-Jackson relation
given the realized velocity dispersion, with some scatter
Parameters
----------
vel_disp : float
the velocity dispersion in km/s
Returns
-------
float
the V-band absolute magnitude
"""
log_L_V = self.lens_luminosity_model(vel_disp)
M_V_sol = 4.84
M_V = -2.5 * log_L_V + M_V_sol
return M_V
[docs] def get_lens_apparent_magnitude(self, M_lens, z_lens):
"""Get the lens apparent magnitude from the Faber-Jackson relation
given the realized velocity dispersion, with some scatter
Parameters
----------
M_lens : float
the V-band absolute magnitude of lens
z_lens : float
the lens redshift
Note
----
Does not account for peculiar velocity or dust. K-correction is approximate and implicit,
as the absolute magnitude is in the V-band (480nm ~ 650nm) and, for z ~ 2-3, this portion
of the SED roughly lands in the IR.
Returns
-------
float
the apparent magnitude in the IR
"""
# FIXME: I could grab some template SEDs and K-correct explicitly, accounting for band throughput
# for IR WF F140W. Should I do this?
dist_mod = self.cosmo.distmod(z_lens).value
# FIXME: Enter good model for dust?
A_V = 0.0 # V-band dust attenuation along LOS
apmag = M_lens + dist_mod - A_V
return apmag
[docs] def get_lens_size(self, vel_disp, z_lens, m_V):
"""Get the lens V-band efefctive radius from the Fundamental Plane relation
given the realized velocity dispersion and apparent magnitude, with some scatter
Parameters
----------
vel_disp : float
the velocity dispersion in km/s
z_lens : float
redshift
m_V : float
V-band apparent magnitude
Returns
-------
tuple
the effective radius in kpc and arcsec
"""
R_eff = self.lens_light_size_model(vel_disp, m_V) # in kpc
r_eff = R_eff * self.cosmo.arcsec_per_kpc_comoving(z_lens).value # in arcsec
return R_eff, r_eff
[docs] def get_src_absolute_magnitude(self, z_src):
"""Sample the UV absolute magnitude from the luminosity function for the given redshift
and convert into apparent magnitude
Parameters
----------
z_src : float
the source redshift
Returns
-------
float
the absolute magnitude at 1500A
"""
M_grid = np.arange(-23.0, -17.8, 0.2)
nM_dM1500 = self.src_luminosity_model(z_src, M_grid)
nM_dM1500_normed = nM_dM1500/np.sum(nM_dM1500)
M1500_src = np.random.choice(M_grid, None, replace=True, p=nM_dM1500_normed)
return M1500_src
[docs] def get_src_apparent_magnitude(self, M_src, z_src):
"""Convert the souce absolute magnitude into apparent magnitude
Parameters
----------
M_src : float
the source absolute magnitude
z_src : float
the source redshift
Note
----
Does not account for peculiar velocity or dust. K-correction is approximate and implicit,
as the absolute magnitude is at 150nm and, for z ~ 5-9, this portion
of the SED roughly lands in the IR.
Returns
-------
float
the apparent magnitude in the IR
"""
dust = 0.0
dist_mod = self.cosmo.distmod(z_src).value
m_src = M_src + dist_mod - dust
return m_src
[docs] def get_src_size(self, z_src, M_V_src):
"""Get the effective radius of the source from its empirical relation with V-band absolute
magnitude and redshift
Parameters
----------
M_V_src : float
V-band absolute magnitude of the source
z_src : float
source redshift
Returns
-------
tuple
tuple of the effective radius in kpc and arcsec
"""
R_eff = self.src_light_size_model(z_src, M_V_src)
r_eff = R_eff * self.cosmo.arcsec_per_kpc_comoving(z_src).value # in arcsec
return R_eff, r_eff
[docs] def get_agn_absolute_magnitude(self, z_src):
"""Get the AGN absolute magnitude at 1450A, sampled from the luminosity function for its redshift bin
Parameters
----------
z_src : float
the AGN redshift
Returns
-------
float
AGN absolute magnitude at 1450A
"""
M_agn = self.agn_luminosity_model(z_src)
return M_agn
[docs] def sample(self):
"""Gets kwargs of sampled parameters to be passed to lenstronomy
Returns
-------
dict
dictionary of config-specified components (e.g. lens mass), itself
a dictionary of sampled parameters corresponding to the config-specified
profile of that component
"""
kwargs = Dict()
# Sample redshifts
z_lens, z_src = self.sample_redshifts(redshifts_cfg=self.redshift)
# Sample velocity dispersion
vel_disp_iso = self.sample_vel_disp(vel_disp_cfg=self.kinematics.vel_disp)
# Sample lens_mass and lens_light parameters
abmag_lens = self.get_lens_absolute_magnitude(vel_disp_iso)
apmag_lens = self.get_lens_apparent_magnitude(abmag_lens, z_lens)
theta_E = self.theta_E_model(vel_disp_iso, z_lens, z_src, self.cosmo)
R_eff_lens, r_eff_lens = self.get_lens_size(vel_disp_iso, z_lens, apmag_lens)
gamma = self.gamma_model(R_eff_lens)
kwargs['lens_mass'] = dict(
theta_E=theta_E,
gamma=gamma,
q=self.lens_axis_ratio_model(vel_disp_iso),
)
kwargs['lens_light'] = dict(
magnitude=apmag_lens,
R_sersic=r_eff_lens,
q=self.lens_axis_ratio_model(vel_disp_iso),
)
kwargs['external_shear'] = {}
# Sample src_light parameters
abmag_src = self.get_src_absolute_magnitude(z_src)
apmag_src = self.get_src_apparent_magnitude(abmag_src, z_src)
R_eff_src, r_eff_src = self.get_src_size(z_src, abmag_src)
kwargs['src_light'] = dict(
magnitude=apmag_src,
R_sersic=r_eff_src,
)
# Sample AGN_light parameters
if 'agn_light' in self.components:
abmag_agn = self.get_agn_absolute_magnitude(z_src)
apmag_agn = self.get_src_apparent_magnitude(abmag_agn, z_src)
kwargs['agn_light'] = dict(
magnitude=apmag_agn,
)
# Miscellaneous other parameters to export
kwargs['misc'] = dict(
z_lens=z_lens,
z_src=z_src,
vel_disp_iso=vel_disp_iso,
lens_light_R_eff=R_eff_lens,
src_light_R_eff=R_eff_src,
lens_light_abmag=abmag_lens,
src_light_abmag=abmag_src,
)
# Sample remaining parameters, not constrained by the above empirical relations,
# independently from their (marginally) diagonal BNN prior
for comp, param_name in self.params_to_realize:
hyperparams = getattr(self, comp)[param_name].copy()
kwargs[comp][param_name] = self.sample_param(hyperparams)
# Convert any q, phi into e1, e2 as required by lenstronomy
for comp in self.comps_qphi_to_e1e2: # e.g. 'lens_mass'
q = kwargs[comp].pop('q')
phi = kwargs[comp].pop('phi')
e1, e2 = param_util.phi_q2_ellipticity(phi, q)
kwargs[comp]['e1'] = e1
kwargs[comp]['e2'] = e2
# Source pos is defined wrt the lens pos
kwargs['src_light']['center_x'] += kwargs['lens_mass']['center_x']
kwargs['src_light']['center_y'] += kwargs['lens_mass']['center_y']
# Ext shear is defined wrt the lens center
kwargs['external_shear']['ra_0'] = kwargs['lens_mass']['center_x']
kwargs['external_shear']['dec_0'] = kwargs['lens_mass']['center_y']
if 'lens_light' in self.components:
# Lens light shares center with lens mass
kwargs['lens_light']['center_x'] = kwargs['lens_mass']['center_x']
kwargs['lens_light']['center_y'] = kwargs['lens_mass']['center_y']
return kwargs