lenstronomy.Analysis package

Submodules

lenstronomy.Analysis.image_reconstruction module

class MultiBandImageReconstruction(multi_band_list, kwargs_model, kwargs_params, multi_band_type='multi-linear', kwargs_likelihood=None, verbose=True)

Bases: object

This class manages the output/results of a fitting process and can conveniently access image reconstruction properties in multi-band fitting. In particular, the fitting result does not come with linear inversion parameters (which may or may not be joint or different for multiple bands) and this class performs the linear inversion for the surface brightness amplitudes and stores them for each individual band to be accessible by the user.

This class is the backbone of the ModelPlot routine that provides the interface of this class with plotting and illustration routines.

__init__(multi_band_list, kwargs_model, kwargs_params, multi_band_type='multi-linear', kwargs_likelihood=None, verbose=True)

Parameters:

• multi_band_list – list of imaging data configuration [[kwargs_data, kwargs_psf, kwargs_numerics], […]]

• kwargs_model – model keyword argument list

• kwargs_params – keyword arguments of the model parameters, same as output of FittingSequence() ‘kwargs_result’

• multi_band_type – string, option when having multiple imaging data sets modelled simultaneously. Options are: - ‘multi-linear’: linear amplitudes are inferred on single data set - ‘linear-joint’: linear amplitudes ae jointly inferred - ‘single-band’: single band

• kwargs_likelihood – likelihood keyword arguments as supported by the Likelihood() class

• verbose – if True (default), computes and prints the total log-likelihood. This option can be deactivated for speedup purposes (does not run linear inversion again), and reduces the number of prints.

band_setup(band_index=0)

ImageModel() instance and keyword arguments of the model components to execute all the options of the ImSim core modules.

Parameters:

band_index – integer (>=0) of imaging band in order of multi_band_list input to this class

Returns:

ImageModel() instance and keyword arguments of the model

class ModelBand(multi_band_list, kwargs_model, model, error_map, cov_param, param, kwargs_params, image_likelihood_mask_list=None, band_index=0, verbose=True, linear_solver=True)

Bases: object

Class to plot a single band given the full modeling results This class has its specific role when the linear inference is performed on the joint band level and/or when only a subset of model components get used for this specific band in the modeling.

__init__(multi_band_list, kwargs_model, model, error_map, cov_param, param, kwargs_params, image_likelihood_mask_list=None, band_index=0, verbose=True, linear_solver=True)

Parameters:

• multi_band_list – list of imaging data configuration [[kwargs_data, kwargs_psf, kwargs_numerics], […]]

• kwargs_model – model keyword argument list for the full multi-band modeling

• model – 2d numpy array of modeled image for the specified band

• error_map – 2d numpy array of size of the image, additional error in the pixels coming from PSF uncertainties

• cov_param – covariance matrix of the linear inversion

• param – 1d numpy array of the linear coefficients of this imaging band

• kwargs_params – keyword argument of keyword argument lists of the different model components selected for the imaging band, NOT including linear amplitudes (not required as being overwritten by the param list)

• image_likelihood_mask_list – list of 2d numpy arrays of likelihood masks (for all bands)

• band_index – integer of the band to be considered in this class

• verbose – if True (default), prints the reduced chi2 value for the current band.

• linear_solver – bool, if True (default) fixes the linear amplitude parameters ‘amp’ (avoid sampling) such that they get overwritten by the linear solver solution.

property model

Returns:

model, 2d numpy array

property norm_residuals

Returns:

normalized residuals, 2d numpy array

property image_model_class

ImageModel() class instance of the single band with only the model components applied to this band.

Returns:

SingleBandMultiModel() instance, which inherits the ImageModel instance

property kwargs_model

Returns:

keyword argument of keyword argument lists of the different model components selected for the imaging band, including linear amplitudes. These format matches the image_model_class() return

point_source_residuals(aperture_radius)

Computes integrated residuals within circular apertures around point sources. This routine can assess the accuracy of point source flux measurements.

Parameters:

aperture_radius – radius of the aperture considering the residuals around the point sources

Returns:

list of integrated flux residuals (data - model) within the apertures around the point sources

check_solver_error(image)

Parameters:

image – numpy array of modelled image from linear inversion

Returns:

bool, True if solver could not find a unique solution, False if solver works

lenstronomy.Analysis.kinematics_api module

lenstronomy.Analysis.lens_profile module

class LensProfileAnalysis(lens_model)

Bases: object

Class with analysis routines to compute derived properties of the lens model.

__init__(lens_model)

Parameters:

lens_model – LensModel instance

effective_einstein_radius_grid(kwargs_lens, center_x=None, center_y=None, model_bool_list=None, grid_num=200, grid_spacing=0.05, get_precision=False, verbose=True)

Computes the radius with mean convergence=1 on a grid.

Parameters:

• kwargs_lens – list of lens model keyword arguments

• center_x – position of the center (if not set, is attempting to find it from the parameters kwargs_lens)

• center_y – position of the center (if not set, is attempting to find it from the parameters kwargs_lens)

• model_bool_list – list of booleans indicating the addition (=True) of a model component in computing the Einstein radius

• grid_num – integer, number of grid points to numerically evaluate the convergence and estimate the Einstein radius

• grid_spacing – spacing in angular units of the grid

• get_precision – If True, return the precision of estimated Einstein radius

• verbose (bool) – if True, indicates warning when Einstein radius can not be computed

Returns:

estimate of the Einstein radius

effective_einstein_radius(kwargs_lens, r_min=0.001, r_max=10.0, num_points=30, spherical_model=False)

Numerical estimate of the Einstein radius with integral approximation of radial convergence profile.

Parameters:

• kwargs_lens – list of lens model keyword arguments

• r_min – minimum radius of the convergence integrand

• r_max – maximum radius of the convergence integrand (should be larger than Einstein radius)

• num_points – number of radial points in log spacing

• spherical_model – if True, assumes the model is spherical and only calculates the convergence along one axis (for speed improvements)

Returns:

estimate of the Einstein radius

static effective_einstein_radius_from_radial_profile(r_array, kappa_r)

Numerical estimate of the Einstein radius with integral approximation of radial convergence profile.

Parameters:

• r_array – radius at which convergence is measured

• kappa_r – convergence array measured at r_array

Returns:

estimate of the Einstein radius

local_lensing_effect(kwargs_lens, ra_pos=0, dec_pos=0, model_list_bool=None)

Computes deflection, shear and convergence at (ra_pos,dec_pos) for those part of the lens model not included in the main deflector.

Parameters:

• kwargs_lens – lens model keyword argument list

• ra_pos – RA position where to compute the external effect

• dec_pos – DEC position where to compute the external effect

• model_list_bool – boolean list indicating which models effect to be added to the estimate

Returns:

alpha_x, alpha_y, kappa, shear1, shear2

profile_slope(kwargs_lens, radius, center_x=None, center_y=None, model_list_bool=None, num_points=10, alpha_differentials=True)

Computes the logarithmic power-law slope of a profile. ATTENTION: this is not an observable!

Parameters:

• kwargs_lens – lens model keyword argument list

• radius – radius from the center where to compute the logarithmic slope (angular units

• center_x – center of profile from where to compute the slope

• center_y – center of profile from where to compute the slope

• model_list_bool – bool list, indicate which part of the model to consider

• num_points – number of estimates around the Einstein radius

• alpha_differentials (bool) – if True, uses the deflection angle differentials, else the convergence differentials

Returns:

logarithmic power-law slope

mst_invariant_differential(kwargs_lens, radius, center_x=None, center_y=None, model_list_bool=None, num_points=10)

Average of the radial stretch differential in radial direction, divided by the radial stretch factor.

\[\xi = \frac{\partial \lambda_{\rm rad}}{\partial r} \frac{1}{\lambda_{\rm rad}}\]

This quantity is invariant under the MST. The specific definition is provided by Birrer 2021. Equivalent (proportional) definitions are provided by e.g. Kochanek 2020, Sonnenfeld 2018.

Parameters:

• kwargs_lens – lens model keyword argument list

• radius – radius from the center where to compute the MST invariant differential

• center_x – center position

• center_y – center position

• model_list_bool – indicate which part of the model to consider

• num_points – number of estimates around the radius

Returns:

xi

radial_lens_profile(r_list, kwargs_lens, center_x=None, center_y=None, model_bool_list=None, num_azimuthal_points=20)

Parameters:

• r_list – list of radii to compute the spherically averaged lens light profile

• center_x – center of the profile

• center_y – center of the profile

• kwargs_lens – lens parameter keyword argument list

• model_bool_list – bool list or None, indicating which profiles to sum over

• num_azimuthal_points (int) – number of points equally spaced azimuthally to create an average

Returns:

flux amplitudes at r_list radii azimuthally averaged

multi_gaussian_lens(kwargs_lens, center_x=None, center_y=None, model_bool_list=None, n_comp=20)

Multi-gaussian lens model in convergence space.

Parameters:

• kwargs_lens

• n_comp

Returns:

mass_fraction_within_radius(kwargs_lens, center_x, center_y, theta_E, num_pix=100)

Computes the mean convergence of all the different lens model components within a spherical aperture.

Parameters:

• kwargs_lens – lens model keyword argument list

• center_x – center of the aperture

• center_y – center of the aperture

• theta_E – radius of aperture

Returns:

list of average convergences for all the model components

convergence_peak(kwargs_lens, model_bool_list=None, grid_num=200, grid_spacing=0.01, center_x_init=0, center_y_init=0)

Computes the maximal convergence position on a grid and returns its coordinate.

Parameters:

• kwargs_lens – lens model keyword argument list

• model_bool_list – bool list (optional) to include certain models or not

Returns:

center_x, center_y

m_delta_crit(kwargs_lens, z_lens, z_source, cosmo, delta_crit=200)

Calculates the mass enclosed an average of delta_crit above the critical background density.

Parameters:

• kwargs_lens – list of lens model dictionary

• z_lens – redshift of the deflector

• z_source – redshift of the source (for lens model conventions)

• cosmo – ~astropy.cosmology instance

• delta_crit – relative overdensity relative to the critical density of the universe

Returns:

m(<delta_crit) [M_sol], r(delta_crit) [arcsec]

lenstronomy.Analysis.light2mass module

light2mass_interpol(lens_light_model_list, kwargs_lens_light, lens_light_profile_kwargs_list=None, num_pix=100, delta_pix=0.05, subgrid_res=5, center_x=0, center_y=0)

Takes a lens light model and turns it numerically in a lens model (with all lensmodel quantities computed on a grid). Then provides an interpolated grid for the quantities.

Parameters:

• lens_light_model_list – list of strings indicating the type of lens light models

• kwargs_lens_light – lens light keyword argument list

• lens_light_profile_kwargs_list – list of dicts, keyword arguments used to initialize lens light profile classes in the same order of the lens_light_model_list. If any of the profile_kwargs are None, then that profile will be initialized using default settings.

• num_pix – number of pixels per axis for the return interpolation

• delta_pix – interpolation/pixel size

• center_x – center of the grid

• center_y – center of the grid

• subgrid_res – subgrid for the numerical integrals

Returns:

keyword arguments for ‘INTERPOL’ lens model

lenstronomy.Analysis.light_profile module

class LightProfileAnalysis(light_model)

Bases: object

Class with analysis routines to compute derived properties of the lens model.

__init__(light_model)

Parameters:

light_model – LightModel instance

ellipticity(kwargs_light, grid_spacing, grid_num, center_x=None, center_y=None, model_bool_list=None, num_iterative=10, iterative=False)

Make sure that the window covers all the light, otherwise the moments may give a too low answers.

Parameters:

• kwargs_light – keyword argument list of profiles

• center_x – center of profile, if None takes it from the first profile in kwargs_light

• center_y – center of profile, if None takes it from the first profile in kwargs_light

• model_bool_list – list of booleans to select subsets of the profile

• grid_spacing – grid spacing over which the moments are computed

• grid_num – grid size over which the moments are computed

• iterative (boolean) – if True iteratively adopts an eccentric mask to overcome edge effects

• num_iterative (int) – number of iterative changes in ellipticity

Returns:

eccentricities e1, e2

half_light_radius(kwargs_light, grid_spacing, grid_num, center_x=None, center_y=None, model_bool_list=None)

Computes numerically the half-light-radius of the deflector light and the total photon flux.

Parameters:

• kwargs_light – keyword argument list of profiles

• center_x – center of profile, if None takes it from the first profile in kwargs_light

• center_y – center of profile, if None takes it from the first profile in kwargs_light

• model_bool_list – list of booleans to select subsets of the profile

• grid_spacing – grid spacing over which the moments are computed

• grid_num – grid size over which the moments are computed

Returns:

half-light radius

radial_light_profile(r_list, kwargs_light, center_x=None, center_y=None, model_bool_list=None)

Parameters:

• r_list – list of radii to compute the spherically averaged lens light profile

• center_x – center of the profile

• center_y – center of the profile

• kwargs_light – lens light parameter keyword argument list

• model_bool_list – bool list or None, indicating which profiles to sum over

Returns:

flux amplitudes at r_list radii spherically averaged

multi_gaussian_decomposition(kwargs_light, model_bool_list=None, n_comp=20, center_x=None, center_y=None, r_h=None, grid_spacing=0.02, grid_num=200)

Multi-gaussian decomposition of the lens light profile (in 1-dimension)

Parameters:

• kwargs_light – keyword argument list of profiles

• center_x – center of profile, if None takes it from the first profile in kwargs_light

• center_y – center of profile, if None takes it from the first profile in kwargs_light

• model_bool_list – list of booleans to select subsets of the profile

• grid_spacing – grid spacing over which the moments are computed for the half-light radius

• grid_num – grid size over which the moments are computed

• n_comp – maximum number of Gaussian’s in the MGE

• r_h – float, half light radius to be used for MGE (optional, otherwise using a numerical grid)

Returns:

amplitudes, sigmas, center_x, center_y

multi_gaussian_decomposition_ellipse(kwargs_light, model_bool_list=None, center_x=None, center_y=None, grid_num=100, grid_spacing=0.05, n_comp=20)

MGE with ellipticity estimate. Attention: numerical grid settings for ellipticity estimate and radial MGE may not necessarily be the same!

Parameters:

• kwargs_light – keyword argument list of profiles

• center_x – center of profile, if None takes it from the first profile in kwargs_light

• center_y – center of profile, if None takes it from the first profile in kwargs_light

• model_bool_list – list of booleans to select subsets of the profile

• grid_spacing – grid spacing over which the moments are computed

• grid_num – grid size over which the moments are computed

• n_comp – maximum number of Gaussians in the MGE

Returns:

keyword arguments of the elliptical multi Gaussian profile in lenstronomy conventions

flux_components(kwargs_light, grid_num=400, grid_spacing=0.01)

Computes the total flux in each component of the model.

Parameters:

• kwargs_light

• grid_num

• grid_spacing

Returns:

lenstronomy.Analysis.multi_patch_reconstruction module

class MultiPatchReconstruction(multi_band_list, kwargs_model, kwargs_params, multi_band_type='joint-linear', kwargs_likelihood=None, kwargs_pixel_grid=None, verbose=True)

Bases: MultiBandImageReconstruction

This class illustrates the model of disconnected multi-patch modeling with ‘joint-linear’ option in one single array.

__init__(multi_band_list, kwargs_model, kwargs_params, multi_band_type='joint-linear', kwargs_likelihood=None, kwargs_pixel_grid=None, verbose=True)

Parameters:

• multi_band_list – list of imaging data configuration [[kwargs_data, kwargs_psf, kwargs_numerics], […]]

• kwargs_model – model keyword argument list

• kwargs_params – keyword arguments of the model parameters, same as output of FittingSequence() ‘kwargs_result’

• multi_band_type – string, option when having multiple imaging data sets modelled simultaneously. Options are: - ‘multi-linear’: linear amplitudes are inferred on single data set - ‘linear-joint’: linear amplitudes ae jointly inferred - ‘single-band’: single band

• kwargs_likelihood – likelihood keyword arguments as supported by the Likelihood() class

• kwargs_pixel_grid – keyword argument of PixelGrid() class. This is optional and overwrites a minimal grid Attention for consistent pixel grid definitions!

• verbose – if True (default), computes and prints the total log-likelihood. This can de-activated for speedup purposes (does not run linear inversion again), and reduces the number of prints.

property pixel_grid_joint

Returns:

PixelGrid() class instance covering the entire window of the sky including all individual patches

image_joint()

Patch together the individual patches of data and models.

Returns:

image_joint, model_joint, norm_residuals_joint

lens_model_joint()

Patch together the individual patches of the lens model (can be discontinues)

Returns:

2d numpy arrays of kappa_joint, magnification_joint, alpha_x_joint, alpha_y_joint

source(num_pix, delta_pix, center=None)

Source in the same coordinate system as the image.

Parameters:

• num_pix – number of pixels per axes

• delta_pix – pixel size

• center – list with two entries [center_x, center_y] (optional)

Returns:

2d surface brightness grid of the reconstructed source and PixelGrid() instance of source grid

lenstronomy.Analysis.td_cosmography module

Module contents