def test_multi_gaussian_decomposition(self):
Rs = 1.
kwargs_light = [{'Rs': Rs, 'amp': 1., 'center_x': 0, 'center_y': 0}]
kwargs_options = {'light_model_list': ['HERNQUIST']}
lightModel = LightModel(**kwargs_options)
profile = LightProfileAnalysis(light_model=lightModel)
amplitudes, sigmas, center_x, center_y = profile.multi_gaussian_decomposition(kwargs_light, grid_spacing=0.01, grid_num=100, model_bool_list=None, n_comp=20,
center_x=None, center_y=None)
mge = MultiGaussian()
r_array = np.logspace(start=-2, stop=0.5, num=10)
print(r_array, 'test r_array')
flux = mge.function(r_array, 0, amp=amplitudes, sigma=sigmas, center_x=center_x, center_y=center_y)
flux_true = lightModel.surface_brightness(r_array, 0, kwargs_light)
npt.assert_almost_equal(flux / flux_true, 1, decimal=2)
# test off-center
Rs = 1.
offset = 1.
kwargs_light = [{'Rs': Rs, 'amp': 1., 'center_x': offset, 'center_y': 0}]
kwargs_options = {'light_model_list': ['HERNQUIST']}
lightModel = LightModel(**kwargs_options)
profile = LightProfileAnalysis(light_model=lightModel)
amplitudes, sigmas, center_x, center_y = profile.multi_gaussian_decomposition(kwargs_light, grid_spacing=0.01,
grid_num=100, model_bool_list=None,
n_comp=20,
center_x=None, center_y=None)
assert center_x == offset
assert center_y == 0
mge = MultiGaussian()
r_array = np.logspace(start=-2, stop=0.5, num=10)
print(r_array, 'test r_array')
flux = mge.function(r_array, 0, amp=amplitudes, sigma=sigmas, center_x=center_x, center_y=center_y)
flux_true = lightModel.surface_brightness(r_array, 0, kwargs_light)
npt.assert_almost_equal(flux / flux_true, 1, decimal=2)
"""
class KinematicsAPI(object):
"""
this class contains routines to compute time delays, magnification ratios, line of sight velocity dispersions etc
for a given lens model
"""
def __init__(self,
z_lens,
z_source,
kwargs_model,
kwargs_aperture,
kwargs_seeing,
anisotropy_model,
cosmo=None,
lens_model_kinematics_bool=None,
light_model_kinematics_bool=None,
multi_observations=False,
kwargs_numerics_galkin=None,
analytic_kinematics=False,
Hernquist_approx=False,
MGE_light=False,
MGE_mass=False,
kwargs_mge_light=None,
kwargs_mge_mass=None,
sampling_number=1000,
num_kin_sampling=1000,
num_psf_sampling=100):
"""
:param z_lens: redshift of lens
:param z_source: redshift of source
:param kwargs_model: model keyword arguments, needs 'lens_model_list', 'lens_light_model_list'
:param kwargs_aperture: spectroscopic aperture keyword arguments, see lenstronomy.Galkin.aperture for options
:param kwargs_seeing: seeing condition of spectroscopic observation, corresponds to kwargs_psf in the GalKin module specified in lenstronomy.GalKin.psf
:param cosmo: astropy.cosmology instance, if None then will be set to the default cosmology
:param lens_model_kinematics_bool: bool list of length of the lens model. Only takes a subset of all the models
as part of the kinematics computation (can be used to ignore substructure, shear etc that do not describe the
main deflector potential
:param light_model_kinematics_bool: bool list of length of the light model. Only takes a subset of all the models
as part of the kinematics computation (can be used to ignore light components that do not describe the main
deflector
:param multi_observations: bool, if True uses multi-observation to predict a set of different observations with
the GalkinMultiObservation() class. kwargs_aperture and kwargs_seeing require to be lists of the individual
observations.
:param anisotropy_model: type of stellar anisotropy model. See details in MamonLokasAnisotropy() class of lenstronomy.GalKin.anisotropy
:param analytic_kinematics: boolean, if True, used the analytic JAM modeling for a power-law profile on top of a Hernquist light profile
ATTENTION: This may not be accurate for your specific problem!
:param Hernquist_approx: bool, if True, uses a Hernquist light profile matched to the half light radius of the deflector light profile to compute the kinematics
:param MGE_light: bool, if true performs the MGE for the light distribution
:param MGE_mass: bool, if true performs the MGE for the mass distribution
:param kwargs_numerics_galkin: numerical settings for the integrated line-of-sight velocity dispersion
:param kwargs_mge_mass: keyword arguments that go into the MGE decomposition routine
:param kwargs_mge_light: keyword arguments that go into the MGE decomposition routine
:param sampling_number: int, number of spectral rendering to compute the light weighted integrated LOS
dispersion within the aperture. This keyword should be chosen high enough to result in converged results within the tolerance.
:param num_kin_sampling: number of kinematic renderings on a total IFU
:param num_psf_sampling: number of PSF displacements for each kinematic rendering on the IFU
"""
self.z_d = z_lens
self.z_s = z_source
self._kwargs_aperture_kin = kwargs_aperture
self._kwargs_psf_kin = kwargs_seeing
self.lensCosmo = LensCosmo(z_lens, z_source, cosmo=cosmo)
self.LensModel, self.SourceModel, self.LensLightModel, self.PointSource, extinction_class = class_creator.create_class_instances(
all_models=True, **kwargs_model)
self._lensLightProfile = LightProfileAnalysis(
light_model=self.LensLightModel)
self._lensMassProfile = LensProfileAnalysis(lens_model=self.LensModel)
self._lens_light_model_list = self.LensLightModel.profile_type_list
self._lens_model_list = self.LensModel.lens_model_list
self._kwargs_cosmo = {
'd_d': self.lensCosmo.dd,
'd_s': self.lensCosmo.ds,
'd_ds': self.lensCosmo.dds
}
self._lens_model_kinematics_bool = lens_model_kinematics_bool
self._light_model_kinematics_bool = light_model_kinematics_bool
self._sampling_number = sampling_number
self._num_kin_sampling = num_kin_sampling
self._num_psf_sampling = num_psf_sampling
if kwargs_mge_mass is None:
self._kwargs_mge_mass = {'n_comp': 20}
else:
self._kwargs_mge_mass = kwargs_mge_mass
if kwargs_mge_light is None:
self._kwargs_mge_light = {
'grid_spacing': 0.01,
'grid_num': 100,
'n_comp': 20,
'center_x': None,
'center_y': None
}
else:
self._kwargs_mge_light = kwargs_mge_light
if kwargs_numerics_galkin is None:
kwargs_numerics_galkin = {
'interpol_grid_num':
1000, # numerical interpolation, should converge -> infinity
'log_integration':
True, # log or linear interpolation of surface brightness and mass models
'max_integrate': 100,
'min_integrate': 0.001
} # lower/upper bound of numerical integrals
self._kwargs_numerics_kin = kwargs_numerics_galkin
self._anisotropy_model = anisotropy_model
self._analytic_kinematics = analytic_kinematics
self._Hernquist_approx = Hernquist_approx
self._MGE_light = MGE_light
self._MGE_mass = MGE_mass
self._multi_observations = multi_observations
def velocity_dispersion(self,
kwargs_lens,
kwargs_lens_light,
kwargs_anisotropy,
r_eff=None,
theta_E=None,
gamma=None,
kappa_ext=0):
"""
API for both, analytic and numerical JAM to compute the velocity dispersion [km/s]
This routine uses the galkin_setting() routine for the Galkin configurations (see there what options and input
is relevant.
:param kwargs_lens: lens model keyword arguments
:param kwargs_lens_light: lens light model keyword arguments
:param kwargs_anisotropy: stellar anisotropy keyword arguments
:param r_eff: projected half-light radius of the stellar light associated with the deflector galaxy, optional,
if set to None will be computed in this function with default settings that may not be accurate.
:param theta_E: Einstein radius (optional)
:param gamma: power-law slope (optional)
:param kappa_ext: external convergence (optional)
:return: velocity dispersion [km/s]
"""
galkin, kwargs_profile, kwargs_light = self.galkin_settings(
kwargs_lens,
kwargs_lens_light,
r_eff=r_eff,
theta_E=theta_E,
gamma=gamma)
sigma_v = galkin.dispersion(kwargs_profile,
kwargs_light,
kwargs_anisotropy,
sampling_number=self._sampling_number)
sigma_v = self.transform_kappa_ext(sigma_v, kappa_ext=kappa_ext)
return sigma_v
def velocity_dispersion_map(self,
kwargs_lens,
kwargs_lens_light,
kwargs_anisotropy,
r_eff=None,
theta_E=None,
gamma=None,
kappa_ext=0):
"""
API for both, analytic and numerical JAM to compute the velocity dispersion map with IFU data [km/s]
:param kwargs_lens: lens model keyword arguments
:param kwargs_lens_light: lens light model keyword arguments
:param kwargs_anisotropy: stellar anisotropy keyword arguments
:param r_eff: projected half-light radius of the stellar light associated with the deflector galaxy, optional,
if set to None will be computed in this function with default settings that may not be accurate.
:param theta_E: circularized Einstein radius, optional, if not provided will either be computed in this
function with default settings or not required
:param gamma: power-law slope at the Einstein radius, optional
:param kappa_ext: external convergence
:return: velocity dispersion [km/s]
"""
galkin, kwargs_profile, kwargs_light = self.galkin_settings(
kwargs_lens,
kwargs_lens_light,
r_eff=r_eff,
theta_E=theta_E,
gamma=gamma)
sigma_v_map = galkin.dispersion_map(
kwargs_profile,
kwargs_light,
kwargs_anisotropy,
num_kin_sampling=self._num_kin_sampling,
num_psf_sampling=self._num_psf_sampling)
sigma_v_map = self.transform_kappa_ext(sigma_v_map,
kappa_ext=kappa_ext)
return sigma_v_map
def velocity_dispersion_analytical(self,
theta_E,
gamma,
r_eff,
r_ani,
kappa_ext=0):
"""
computes the LOS velocity dispersion of the lens within a slit of size R_slit x dR_slit and seeing psf_fwhm.
The assumptions are a Hernquist light profile and the spherical power-law lens model at the first position and
an Osipkov and Merritt ('OM') stellar anisotropy distribution.
Further information can be found in the AnalyticKinematics() class.
:param theta_E: Einstein radius
:param gamma: power-low slope of the mass profile (=2 corresponds to isothermal)
:param r_ani: anisotropy radius in units of angles
:param r_eff: projected half-light radius
:param kappa_ext: external convergence not accounted in the lens models
:return: velocity dispersion in units [km/s]
"""
galkin = Galkin(kwargs_model={'anisotropy_model': 'OM'},
kwargs_aperture=self._kwargs_aperture_kin,
kwargs_psf=self._kwargs_psf_kin,
kwargs_cosmo=self._kwargs_cosmo,
kwargs_numerics={},
analytic_kinematics=True)
kwargs_profile = {'theta_E': theta_E, 'gamma': gamma}
kwargs_light = {'r_eff': r_eff}
kwargs_anisotropy = {'r_ani': r_ani}
sigma_v = galkin.dispersion(kwargs_profile,
kwargs_light,
kwargs_anisotropy,
sampling_number=self._sampling_number)
sigma_v = self.transform_kappa_ext(sigma_v, kappa_ext=kappa_ext)
return sigma_v
def galkin_settings(self,
kwargs_lens,
kwargs_lens_light,
r_eff=None,
theta_E=None,
gamma=None):
"""
:param kwargs_lens: lens model keyword argument list
:param kwargs_lens_light: deflector light keyword argument list
:param r_eff: half-light radius (optional)
:param theta_E: Einstein radius (optional)
:param gamma: local power-law slope at the Einstein radius (optional)
:return: Galkin() instance and mass and light profiles configured for the Galkin module
"""
if r_eff is None:
r_eff = self._lensLightProfile.half_light_radius(
kwargs_lens_light,
grid_spacing=0.05,
grid_num=200,
center_x=None,
center_y=None,
model_bool_list=self._light_model_kinematics_bool)
if theta_E is None:
theta_E = self._lensMassProfile.effective_einstein_radius(
kwargs_lens,
center_x=None,
center_y=None,
model_bool_list=self._lens_model_kinematics_bool,
grid_num=200,
grid_spacing=0.05,
get_precision=False,
verbose=True)
if gamma is None and self._analytic_kinematics is True:
gamma = self._lensMassProfile.profile_slope(
kwargs_lens,
theta_E,
center_x=None,
center_y=None,
model_list_bool=self._lens_model_kinematics_bool,
num_points=10)
mass_profile_list, kwargs_profile = self.kinematic_lens_profiles(
kwargs_lens,
MGE_fit=self._MGE_mass,
theta_E=theta_E,
model_kinematics_bool=self._lens_model_kinematics_bool,
kwargs_mge=self._kwargs_mge_mass,
gamma=gamma,
analytic_kinematics=self._analytic_kinematics)
light_profile_list, kwargs_light = self.kinematic_light_profile(
kwargs_lens_light,
r_eff=r_eff,
MGE_fit=self._MGE_light,
kwargs_mge=self._kwargs_mge_light,
model_kinematics_bool=self._light_model_kinematics_bool,
Hernquist_approx=self._Hernquist_approx,
analytic_kinematics=self._analytic_kinematics)
kwargs_model = {
'mass_profile_list': mass_profile_list,
'light_profile_list': light_profile_list,
'anisotropy_model': self._anisotropy_model
}
if self._multi_observations is True:
galkin = GalkinMultiObservation(
kwargs_model=kwargs_model,
kwargs_aperture_list=self._kwargs_aperture_kin,
kwargs_psf_list=self._kwargs_psf_kin,
kwargs_cosmo=self._kwargs_cosmo,
kwargs_numerics=self._kwargs_numerics_kin,
analytic_kinematics=self._analytic_kinematics)
else:
galkin = Galkin(kwargs_model=kwargs_model,
kwargs_aperture=self._kwargs_aperture_kin,
kwargs_psf=self._kwargs_psf_kin,
kwargs_cosmo=self._kwargs_cosmo,
kwargs_numerics=self._kwargs_numerics_kin,
analytic_kinematics=self._analytic_kinematics)
return galkin, kwargs_profile, kwargs_light
def kinematic_lens_profiles(self,
kwargs_lens,
MGE_fit=False,
model_kinematics_bool=None,
theta_E=None,
gamma=None,
kwargs_mge=None,
analytic_kinematics=False):
"""
translates the lenstronomy lens and mass profiles into a (sub) set of profiles that are compatible with the
GalKin module to compute the kinematics thereof.
The requirement is that the
profiles are centered at (0, 0) and that for all profile types there exists a 3d de-projected analytical
representation.
:param kwargs_lens: lens model parameters
:param MGE_fit: bool, if true performs the MGE for the mass distribution
:param model_kinematics_bool: bool list of length of the lens model. Only takes a subset of all the models
as part of the kinematics computation (can be used to ignore substructure, shear etc that do not describe the
main deflector potential
:param theta_E: (optional float) estimate of the Einstein radius. If present, does not numerically compute this
quantity in this routine numerically
:param gamma: local power-law slope at the Einstein radius (optional)
:param kwargs_mge: keyword arguments that go into the MGE decomposition routine
:param analytic_kinematics: bool, if True, solves the Jeans equation analytically for the
power-law mass profile with Hernquist light profile
:return: mass_profile_list, keyword argument list
"""
if analytic_kinematics is True:
if gamma is None or theta_E is None:
raise ValueError(
'power-law slope and Einstein radius must be set to allow for analytic kinematics to '
'be computed!')
return None, {'theta_E': theta_E, 'gamma': gamma}
mass_profile_list = []
kwargs_profile = []
if model_kinematics_bool is None:
model_kinematics_bool = [True] * len(kwargs_lens)
for i, lens_model in enumerate(self._lens_model_list):
if model_kinematics_bool[i] is True:
mass_profile_list.append(lens_model)
if lens_model in ['INTERPOL', 'INTERPOL_SCLAED']:
center_x_i, center_y_i = self._lensMassProfile.convergence_peak(
kwargs_lens,
model_bool_list=i,
grid_num=200,
grid_spacing=0.01,
center_x_init=0,
center_y_init=0)
kwargs_lens_i = copy.deepcopy(kwargs_lens[i])
kwargs_lens_i['grid_interp_x'] -= center_x_i
kwargs_lens_i['grid_interp_y'] -= center_y_i
else:
kwargs_lens_i = {
k: v
for k, v in kwargs_lens[i].items()
if not k in ['center_x', 'center_y']
}
kwargs_profile.append(kwargs_lens_i)
if MGE_fit is True:
if kwargs_mge is None:
raise ValueError('kwargs_mge needs to be specified!')
if theta_E is None:
raise ValueError(
'rough estimate of the Einstein radius needs to be provided to compute the MGE!'
)
r_array = np.logspace(-4, 2, 200) * theta_E
if self._lens_model_list[0] in ['INTERPOL', 'INTERPOL_SCLAED']:
center_x, center_y = self._lensMassProfile.convergence_peak(
kwargs_lens,
model_bool_list=model_kinematics_bool,
grid_num=200,
grid_spacing=0.01,
center_x_init=0,
center_y_init=0)
else:
center_x, center_y = None, None
mass_r = self._lensMassProfile.radial_lens_profile(
r_array,
kwargs_lens,
center_x=center_x,
center_y=center_y,
model_bool_list=model_kinematics_bool)
amps, sigmas, norm = mge.mge_1d(r_array,
mass_r,
N=kwargs_mge.get('n_comp', 20))
mass_profile_list = ['MULTI_GAUSSIAN_KAPPA']
kwargs_profile = [{'amp': amps, 'sigma': sigmas}]
return mass_profile_list, kwargs_profile
def kinematic_light_profile(self,
kwargs_lens_light,
r_eff=None,
MGE_fit=False,
model_kinematics_bool=None,
Hernquist_approx=False,
kwargs_mge=None,
analytic_kinematics=False):
"""
setting up of the light profile to compute the kinematics in the GalKin module. The requirement is that the
profiles are centered at (0, 0) and that for all profile types there exists a 3d de-projected analytical
representation.
:param kwargs_lens_light: deflector light model keyword argument list
:param r_eff: (optional float, else=None) Pre-calculated projected half-light radius of the deflector profile.
If not provided, numerical calculation is done in this routine if required.
:param MGE_fit: boolean, if True performs a Multi-Gaussian expansion of the radial light profile and returns
this solution.
:param model_kinematics_bool: list of booleans to indicate a subset of light profiles to be part of the physical
deflector light.
:param Hernquist_approx: boolean, if True replaces the actual light profile(s) with a Hernquist model with
matched half-light radius.
:param kwargs_mge: keyword arguments that go into the MGE decomposition routine
:param analytic_kinematics: bool, if True, solves the Jeans equation analytically for the
power-law mass profile with Hernquist light profile and adjust the settings accordingly
:return: deflector type list, keyword arguments list
"""
if analytic_kinematics is True:
if r_eff is None:
raise ValueError(
'half light radius "r_eff" needs to be set to allow for analytic kinematics to be '
'computed!')
return None, {'r_eff': r_eff}
light_profile_list = []
kwargs_light = []
if model_kinematics_bool is None:
model_kinematics_bool = [True] * len(kwargs_lens_light)
for i, light_model in enumerate(self._lens_light_model_list):
if model_kinematics_bool[i] is True:
light_profile_list.append(light_model)
kwargs_lens_light_i = {
k: v
for k, v in kwargs_lens_light[i].items()
if not k in ['center_x', 'center_y']
}
if 'e1' in kwargs_lens_light_i:
kwargs_lens_light_i['e1'] = 0
kwargs_lens_light_i['e2'] = 0
kwargs_light.append(kwargs_lens_light_i)
if Hernquist_approx is True:
if r_eff is None:
raise ValueError(
'r_eff needs to be pre-computed and specified when using the Hernquist approximation'
)
light_profile_list = ['HERNQUIST']
kwargs_light = [{'Rs': r_eff * 0.551, 'amp': 1.}]
else:
if MGE_fit is True:
if kwargs_mge is None:
raise ValueError(
'kwargs_mge must be provided to compute the MGE')
amps, sigmas, center_x, center_y = self._lensLightProfile.multi_gaussian_decomposition(
kwargs_lens_light,
model_bool_list=model_kinematics_bool,
r_h=r_eff,
**kwargs_mge)
light_profile_list = ['MULTI_GAUSSIAN']
kwargs_light = [{'amp': amps, 'sigma': sigmas}]
return light_profile_list, kwargs_light
def kinematics_modeling_settings(self,
anisotropy_model,
kwargs_numerics_galkin,
analytic_kinematics=False,
Hernquist_approx=False,
MGE_light=False,
MGE_mass=False,
kwargs_mge_light=None,
kwargs_mge_mass=None,
sampling_number=1000,
num_kin_sampling=1000,
num_psf_sampling=100):
"""
:param anisotropy_model: type of stellar anisotropy model. See details in MamonLokasAnisotropy() class of lenstronomy.GalKin.anisotropy
:param analytic_kinematics: boolean, if True, used the analytic JAM modeling for a power-law profile on top of a Hernquist light profile
ATTENTION: This may not be accurate for your specific problem!
:param Hernquist_approx: bool, if True, uses a Hernquist light profile matched to the half light radius of the deflector light profile to compute the kinematics
:param MGE_light: bool, if true performs the MGE for the light distribution
:param MGE_mass: bool, if true performs the MGE for the mass distribution
:param kwargs_numerics_galkin: numerical settings for the integrated line-of-sight velocity dispersion
:param kwargs_mge_mass: keyword arguments that go into the MGE decomposition routine
:param kwargs_mge_light: keyword arguments that go into the MGE decomposition routine
:param sampling_number: number of spectral rendering on a single slit
:param num_kin_sampling: number of kinematic renderings on a total IFU
:param num_psf_sampling: number of PSF displacements for each kinematic rendering on the IFU
:return:
"""
if kwargs_mge_mass is None:
self._kwargs_mge_mass = {'n_comp': 20}
else:
self._kwargs_mge_mass = kwargs_mge_mass
if kwargs_mge_light is None:
self._kwargs_mge_light = {
'grid_spacing': 0.01,
'grid_num': 100,
'n_comp': 20,
'center_x': None,
'center_y': None
}
else:
self._kwargs_mge_light = kwargs_mge_light
self._kwargs_numerics_kin = kwargs_numerics_galkin
self._anisotropy_model = anisotropy_model
self._analytic_kinematics = analytic_kinematics
self._Hernquist_approx = Hernquist_approx
self._MGE_light = MGE_light
self._MGE_mass = MGE_mass
self._sampling_number = sampling_number
self._num_kin_sampling = num_kin_sampling
self._num_psf_sampling = num_psf_sampling
@staticmethod
def transform_kappa_ext(sigma_v, kappa_ext=0):
"""
:param sigma_v: velocity dispersion estimate of the lensing deflector without considering external convergence
:param kappa_ext: external convergence to be used in the mass-sheet degeneracy
:return: transformed velocity dispersion
"""
sigma_v_mst = sigma_v * np.sqrt(1 - kappa_ext)
return sigma_v_mst
class KinematicAPI(object):
"""
this class contains routines to compute time delays, magnification ratios, line of sight velocity dispersions etc
for a given lens model
"""
def __init__(self,
z_lens,
z_source,
kwargs_model,
cosmo=None,
lens_model_kinematics_bool=None,
light_model_kinematics_bool=None):
"""
:param z_lens: redshift of lens
:param z_source: redshift of source
:param kwargs_model: model keyword arguments
:param cosmo: astropy.cosmology instance, if None then will be set to the default cosmology
:param lens_model_kinematics_bool: bool list of length of the lens model. Only takes a subset of all the models
as part of the kinematics computation (can be used to ignore substructure, shear etc that do not describe the
main deflector potential
:param light_model_kinematics_bool: bool list of length of the light model. Only takes a subset of all the models
as part of the kinematics computation (can be used to ignore light components that do not describe the main
deflector
"""
self.z_d = z_lens
self.z_s = z_source
self.lensCosmo = LensCosmo(z_lens, z_source, cosmo=cosmo)
self.LensModel, self.SourceModel, self.LensLightModel, self.PointSource, extinction_class = class_creator.create_class_instances(
all_models=True, **kwargs_model)
self._lensLightProfile = LightProfileAnalysis(
light_model=self.LensLightModel)
self._lensMassProfile = LensProfileAnalysis(lens_model=self.LensModel)
self.kwargs_model = kwargs_model
self._kwargs_cosmo = {
'D_d': self.lensCosmo.D_d,
'D_s': self.lensCosmo.D_s,
'D_ds': self.lensCosmo.D_ds
}
self._lens_model_kinematics_bool = lens_model_kinematics_bool
self._light_model_kinematics_bool = light_model_kinematics_bool
def velocity_dispersion_analytical(self,
theta_E,
gamma,
r_eff,
kwargs_aperture,
kwargs_psf,
r_ani,
num_evaluate=1000,
kappa_ext=0):
"""
computes the LOS velocity dispersion of the lens within a slit of size R_slit x dR_slit and seeing psf_fwhm.
The assumptions are a Hernquist light profile and the spherical power-law lens model at the first position and
an 'OsipkovMerritt' stellar anisotropy distribution.
Further information can be found in the AnalyticKinematics() class.
:param theta_E: Einstein radius
:param gamma: power-low slope of the mass profile (=2 corresponds to isothermal)
:param r_ani: anisotropy radius in units of angles
:param r_eff: projected half-light radius
:param kwargs_aperture: aperture parameters (see Galkin module)
:param num_evaluate: number of spectral rendering of the light distribution that end up on the slit
:param kappa_ext: external convergence not accounted in the lens models
:return: velocity dispersion in units [km/s]
"""
analytic_kinematics = AnalyticKinematics(
kwargs_psf=kwargs_psf,
kwargs_aperture=kwargs_aperture,
**self._kwargs_cosmo)
sigma = analytic_kinematics.vel_disp(gamma,
theta_E,
r_eff,
r_ani,
rendering_number=num_evaluate)
sigma *= np.sqrt(1 - kappa_ext)
return sigma
def velocity_dispersion_numerical(self,
kwargs_lens,
kwargs_lens_light,
kwargs_anisotropy,
kwargs_aperture,
kwargs_psf,
anisotropy_model,
r_eff=None,
theta_E=None,
kwargs_numerics={},
MGE_light=False,
kwargs_mge_light=None,
MGE_mass=False,
kwargs_mge_mass=None,
Hernquist_approx=False,
kappa_ext=0):
"""
Computes the LOS velocity dispersion of the deflector galaxy with arbitrary combinations of light and mass models.
For a detailed description, visit the description of the Galkin() class.
Additionally to executing the GalKin routine, it has an optional Multi-Gaussian-Expansion decomposition of lens
and light models that do not have a three-dimensional distribution built in, such as Sersic profiles etc.
The center of all the lens and lens light models that are part of the kinematic estimate must be centered on the
same point.
:param kwargs_lens: lens model parameters
:param kwargs_lens_light: lens light parameters
:param kwargs_anisotropy: anisotropy parameters (see Galkin module)
:param kwargs_aperture: aperture parameters (see Galkin module)
:param kwargs_psf: seeing conditions and model (see GalKin module)
:param anisotropy_model: stellar anisotropy model (see Galkin module)
:param r_eff: a rough estimate of the half light radius of the lens light in case of computing the MGE of the
light profile
:param theta_E: a rough estimate of the Einstein radius when performing the MGE of the deflector
:param kwargs_numerics: keyword arguments that contain numerical options (see Galkin module)
:param MGE_light: bool, if true performs the MGE for the light distribution
:param MGE_mass: bool, if true performs the MGE for the mass distribution
:param Hernquist_approx: bool, if True, uses a Hernquist light profile matched to the half light radius of the deflector light profile to compute the kinematics
:param kappa_ext: external convergence not accounted in the lens models
:param kwargs_mge_light: keyword arguments that go into the MGE decomposition routine
:param kwargs_mge_mass: keyword arguments that go into the MGE decomposition routine
:return: LOS velocity dispersion [km/s]
"""
mass_profile_list, kwargs_profile = self.kinematic_lens_profiles(
kwargs_lens,
MGE_fit=MGE_mass,
theta_E=theta_E,
model_kinematics_bool=self._lens_model_kinematics_bool,
kwargs_mge=kwargs_mge_mass)
light_profile_list, kwargs_light = self.kinematic_light_profile(
kwargs_lens_light,
r_eff=r_eff,
MGE_fit=MGE_light,
kwargs_mge=kwargs_mge_light,
model_kinematics_bool=self._light_model_kinematics_bool,
Hernquist_approx=Hernquist_approx)
galkin = Galkin(mass_profile_list,
light_profile_list,
kwargs_aperture=kwargs_aperture,
kwargs_psf=kwargs_psf,
anisotropy_model=anisotropy_model,
kwargs_cosmo=self._kwargs_cosmo,
**kwargs_numerics)
sigma = galkin.vel_disp(kwargs_profile, kwargs_light,
kwargs_anisotropy)
sigma *= np.sqrt(1 - kappa_ext)
return sigma
def kinematic_lens_profiles(self,
kwargs_lens,
MGE_fit=False,
model_kinematics_bool=None,
theta_E=None,
kwargs_mge=None):
"""
translates the lenstronomy lens and mass profiles into a (sub) set of profiles that are compatible with the
GalKin module to compute the kinematics thereof.
The requirement is that the
profiles are centered at (0, 0) and that for all profile types there exists a 3d de-projected analytical
representation.
:param kwargs_lens: lens model parameters
:param MGE_fit: bool, if true performs the MGE for the mass distribution
:param model_kinematics_bool: bool list of length of the lens model. Only takes a subset of all the models
as part of the kinematics computation (can be used to ignore substructure, shear etc that do not describe the
main deflector potential
:param theta_E: (optional float) estimate of the Einstein radius. If present, does not numerically compute this
quantity in this routine numerically
:param kwargs_mge: keyword arguments that go into the MGE decomposition routine
:return: mass_profile_list, keyword argument list
"""
mass_profile_list = []
kwargs_profile = []
if model_kinematics_bool is None:
model_kinematics_bool = [True] * len(kwargs_lens)
for i, lens_model in enumerate(self.kwargs_model['lens_model_list']):
if model_kinematics_bool[i] is True:
mass_profile_list.append(lens_model)
if lens_model in ['INTERPOL', 'INTERPOL_SCLAED']:
center_x_i, center_y_i = self._lensMassProfile.convergence_peak(
kwargs_lens,
model_bool_list=i,
grid_num=200,
grid_spacing=0.01,
center_x_init=0,
center_y_init=0)
kwargs_lens_i = copy.deepcopy(kwargs_lens[i])
kwargs_lens_i['grid_interp_x'] -= center_x_i
kwargs_lens_i['grid_interp_y'] -= center_y_i
else:
kwargs_lens_i = {
k: v
for k, v in kwargs_lens[i].items()
if not k in ['center_x', 'center_y']
}
kwargs_profile.append(kwargs_lens_i)
if MGE_fit is True:
if kwargs_mge is None:
raise ValueError('kwargs_mge needs to be specified!')
if theta_E is None:
raise ValueError(
'rough estimate of the Einstein radius needs to be provided to compute the MGE!'
)
r_array = np.logspace(-4, 2, 200) * theta_E
if self.kwargs_model['lens_model_list'][0] in [
'INTERPOL', 'INTERPOL_SCLAED'
]:
center_x, center_y = self._lensMassProfile.convergence_peak(
kwargs_lens,
model_bool_list=model_kinematics_bool,
grid_num=200,
grid_spacing=0.01,
center_x_init=0,
center_y_init=0)
else:
center_x, center_y = None, None
mass_r = self._lensMassProfile.radial_lens_profile(
r_array,
kwargs_lens,
center_x=center_x,
center_y=center_y,
model_bool_list=model_kinematics_bool)
amps, sigmas, norm = mge.mge_1d(r_array,
mass_r,
N=kwargs_mge.get('n_comp', 20))
mass_profile_list = ['MULTI_GAUSSIAN_KAPPA']
kwargs_profile = [{'amp': amps, 'sigma': sigmas}]
return mass_profile_list, kwargs_profile
def kinematic_light_profile(self,
kwargs_lens_light,
r_eff=None,
MGE_fit=False,
model_kinematics_bool=None,
Hernquist_approx=False,
kwargs_mge=None):
"""
setting up of the light profile to compute the kinematics in the GalKin module. The requirement is that the
profiles are centered at (0, 0) and that for all profile types there exists a 3d de-projected analytical
representation.
:param kwargs_lens_light: deflector light model keyword argument list
:param r_eff: (optional float, else=None) Pre-calculated projected half-light radius of the deflector profile.
If not provided, numerical calculation is done in this routine if required.
:param MGE_fit: boolean, if True performs a Multi-Gaussian expansion of the radial light profile and returns
this solution.
:param model_kinematics_bool: list of booleans to indicate a subset of light profiles to be part of the physical
deflector light.
:param Hernquist_approx: boolean, if True replaces the actual light profile(s) with a Hernquist model with
matched half-light radius.
:param kwargs_mge: keyword arguments that go into the MGE decomposition routine
:return: deflector type list, keyword arguments list
"""
light_profile_list = []
kwargs_light = []
if model_kinematics_bool is None:
model_kinematics_bool = [True] * len(kwargs_lens_light)
for i, light_model in enumerate(
self.kwargs_model['lens_light_model_list']):
if model_kinematics_bool[i] is True:
light_profile_list.append(light_model)
kwargs_lens_light_i = {
k: v
for k, v in kwargs_lens_light[i].items()
if not k in ['center_x', 'center_y']
}
if 'e1' in kwargs_lens_light_i:
kwargs_lens_light_i['e1'] = 0
kwargs_lens_light_i['e2'] = 0
kwargs_light.append(kwargs_lens_light_i)
if Hernquist_approx is True:
if r_eff is None:
raise ValueError(
'r_eff needs to be pre-computed and specified when using the Hernquist approximation'
)
light_profile_list = ['HERNQUIST']
kwargs_light = [{'Rs': r_eff * 0.551, 'amp': 1.}]
else:
if MGE_fit is True:
if kwargs_mge is None:
raise ValueError(
'kwargs_mge must be provided to compute the MGE')
amps, sigmas, center_x, center_y = self._lensLightProfile.multi_gaussian_decomposition(
kwargs_lens_light,
model_bool_list=model_kinematics_bool,
**kwargs_mge)
light_profile_list = ['MULTI_GAUSSIAN']
kwargs_light = [{'amp': amps, 'sigma': sigmas}]
return light_profile_list, kwargs_light
def model_velocity_dispersion(self,
kwargs_lens,
kwargs_lens_light,
kwargs_anisotropy,
r_eff=None,
theta_E=None,
gamma=None):
"""
API for both, analytic and numerical JAM to compute the velocity dispersion [km/s]
:param kwargs_lens: lens model keyword arguments
:param kwargs_lens_light: lens light model keyword arguments
:param kwargs_anisotropy: stellar anisotropy keyword arguments
:param r_eff: projected half-light radius of the stellar light associated with the deflector galaxy, optional,
if set to None will be computed in this function with default settings that may not be accurate.
:return: velocity dispersion [km/s]
"""
if r_eff is None:
r_eff = self._lensLightProfile.half_light_radius(
kwargs_lens_light,
grid_spacing=0.05,
grid_num=200,
center_x=None,
center_y=None,
model_bool_list=self._light_model_kinematics_bool)
if theta_E is None:
theta_E = self._lensMassProfile.effective_einstein_radius(
kwargs_lens,
center_x=None,
center_y=None,
model_bool_list=self._lens_model_kinematics_bool,
grid_num=200,
grid_spacing=0.05,
get_precision=False,
verbose=True)
if gamma is None:
gamma = self._lensMassProfile.profile_slope(
kwargs_lens,
theta_E,
center_x=None,
center_y=None,
model_list_bool=self._lens_model_kinematics_bool,
num_points=10)
if self._analytic_kinematics is True:
r_ani = kwargs_anisotropy.get('r_ani')
num_evaluate = self._kwargs_numerics_kin.get(
'sampling_number', 1000)
sigma_v = self.velocity_dispersion_analytical(
theta_E,
gamma,
r_eff,
self._kwargs_aperture_kin,
self._kwargs_psf_kin,
r_ani=r_ani,
num_evaluate=num_evaluate,
kappa_ext=0)
else:
sigma_v = self.velocity_dispersion_numerical(
kwargs_lens,
kwargs_lens_light,
kwargs_anisotropy=kwargs_anisotropy,
kwargs_aperture=self._kwargs_aperture_kin,
kwargs_psf=self._kwargs_psf_kin,
anisotropy_model=self._anisotropy_model,
r_eff=r_eff,
theta_E=theta_E,
kwargs_numerics=self._kwargs_numerics_kin,
MGE_light=self._MGE_light,
MGE_mass=self._MGE_mass,
Hernquist_approx=self._Hernquist_approx,
kappa_ext=0,
kwargs_mge_mass=self._kwargs_mge_mass,
kwargs_mge_light=self._kwargs_mge_light)
return sigma_v
def kinematic_observation_settings(self, kwargs_aperture, kwargs_seeing):
"""
:param kwargs_aperture: spectroscopic aperture keyword arguments, see lenstronomy.Galkin.aperture for options
:param kwargs_seeing: seeing condition of spectroscopic observation, corresponds to kwargs_psf in the GalKin module specified in lenstronomy.GalKin.psf
:return: None
"""
self._kwargs_aperture_kin = kwargs_aperture
self._kwargs_psf_kin = kwargs_seeing
def kinematics_modeling_settings(self,
anisotropy_model,
kwargs_numerics_galkin,
analytic_kinematics=False,
Hernquist_approx=False,
MGE_light=False,
MGE_mass=False,
kwargs_mge_light=None,
kwargs_mge_mass=None):
"""
:param anisotropy_model: type of stellar anisotropy model. See details in MamonLokasAnisotropy() class of lenstronomy.GalKin.anisotropy
:param analytic_kinematics: boolean, if True, used the analytic JAM modeling for a power-law profile on top of a Hernquist light profile
ATTENTION: This may not be accurate for your specific problem!
:param Hernquist_approx: bool, if True, uses a Hernquist light profile matched to the half light radius of the deflector light profile to compute the kinematics
:param MGE_light: bool, if true performs the MGE for the light distribution
:param MGE_mass: bool, if true performs the MGE for the mass distribution
:param kwargs_numerics_galkin: numerical settings for the integrated line-of-sight velocity dispersion
:param kwargs_mge_mass: keyword arguments that go into the MGE decomposition routine
:param kwargs_mge_light: keyword arguments that go into the MGE decomposition routine
:return:
"""
if kwargs_mge_mass is None:
self._kwargs_mge_mass = {'n_comp': 20}
else:
self._kwargs_mge_mass = kwargs_mge_mass
if kwargs_mge_light is None:
self._kwargs_mge_light = {
'grid_spacing': 0.01,
'grid_num': 100,
'n_comp': 20,
'center_x': None,
'center_y': None
}
else:
self._kwargs_mge_light = kwargs_mge_light
self._kwargs_numerics_kin = kwargs_numerics_galkin
self._anisotropy_model = anisotropy_model
self._analytic_kinematics = analytic_kinematics
self._Hernquist_approx = Hernquist_approx
self._MGE_light = MGE_light
self._MGE_mass = MGE_mass
