lenstronomy.ImSim package

Subpackages

• lenstronomy.ImSim.MultiBand package
  • Submodules
  • lenstronomy.ImSim.MultiBand.joint_linear module
  • lenstronomy.ImSim.MultiBand.multi_data_base module
  • lenstronomy.ImSim.MultiBand.multi_linear module
  • lenstronomy.ImSim.MultiBand.single_band_multi_model module
  • Module contents
• lenstronomy.ImSim.Numerics package
  • Submodules
  • lenstronomy.ImSim.Numerics.adaptive_numerics module
  • lenstronomy.ImSim.Numerics.convolution module
  • lenstronomy.ImSim.Numerics.grid module
  • lenstronomy.ImSim.Numerics.numba_convolution module
  • lenstronomy.ImSim.Numerics.numerics module
  • lenstronomy.ImSim.Numerics.partial_image module
  • lenstronomy.ImSim.Numerics.point_source_rendering module
  • Module contents

Submodules

lenstronomy.ImSim.de_lens module

get_param_WLS(A, C_D_inv, d, inv_bool=True)

Returns the parameter values given.

Parameters:

• A – response matrix Nd x Ns (Nd = # data points, Ns = # parameters)
• C_D_inv – inverse covariance matrix of the data, Nd x Nd, diagonal form
• d – data array, 1-d Nd
• inv_bool – boolean, whether returning also the inverse matrix or just solve the linear system

Returns:

1-d array of parameter values

marginalisation_const(M_inv)

Get marginalisation constant 1/2 log(M_beta) for flat priors.

Parameters:M_inv – 2D covariance matrix Returns:float

marginalization_new(M_inv, d_prior=None)

Parameters:

• M_inv – 2D covariance matrix
• d_prior – maximum prior length of linear parameters

Returns:

log determinant with eigenvalues to be smaller or equal d_prior

lenstronomy.ImSim.image2source_mapping module

class Image2SourceMapping(lensModel, sourceModel)

Bases: object

This class handles multiple source planes and performs the computation of predicted surface brightness at given image positions. The class is enable to deal with an arbitrary number of different source planes. There are two different settings:

Single lens plane modelling: In case of a single deflector, lenstronomy models the reduced deflection angles (matched to the source plane in single source plane mode). Each source light model can be added a number (scale_factor) that rescales the reduced deflection angle to the specific source plane.

Multiple lens plane modelling: The multi-plane lens modelling requires the assumption of a cosmology and the redshifts of the multiple lens and source planes. The backwards ray-tracing is performed and stopped at the different source plane redshift to compute the mapping between source to image plane.

__init__(lensModel, sourceModel)

Parameters:

• lensModel – LensModel() class instance
• sourceModel –

  LightModel() class instance. The lightModel includes:

  • source_scale_factor_list: list of floats corresponding to the rescaled deflection angles to the specific source components. None indicates that the list will be set to 1, meaning a single source plane model (in single lens plane mode).
  • source_redshift_list: list of redshifts of the light components (in multi lens plane mode)

image2source(x, y, kwargs_lens, index_source)

mapping of image plane to source plane coordinates WARNING: for multi lens plane computations and multi source planes, this computation can be slow and should be used as rarely as possible.

Parameters:

• x – image plane coordinate (angle)
• y – image plane coordinate (angle)
• kwargs_lens – lens model kwargs list
• index_source – int, index of source model

Returns:

source plane coordinate corresponding to the source model of index idex_source

image_flux_joint(x, y, kwargs_lens, kwargs_source, k=None)

Parameters:

• x – coordinate in image plane
• y – coordinate in image plane
• kwargs_lens – lens model kwargs list
• kwargs_source – source model kwargs list
• k – None or int or list of int for partial evaluation of light models

Returns:

surface brightness of all joint light components at image position (x, y)

image_flux_split(x, y, kwargs_lens, kwargs_source)

Parameters:

• x – coordinate in image plane
• y – coordinate in image plane
• kwargs_lens – lens model kwargs list
• kwargs_source – source model kwargs list

Returns:

list of responses of every single basis component with default amplitude amp=1, in the same order as the light_model_list

lenstronomy.ImSim.image_linear_solve module

class ImageLinearFit(data_class, psf_class=None, lens_model_class=None, source_model_class=None, lens_light_model_class=None, point_source_class=None, extinction_class=None, kwargs_numerics=None, likelihood_mask=None, psf_error_map_bool_list=None, kwargs_pixelbased=None, linear_solver=True)

Bases: lenstronomy.ImSim.image_model.ImageModel

Linear version class, inherits ImageModel.

When light models use pixel-based profile types, such as ‘SLIT_STARLETS’, the WLS linear inversion is replaced by the regularized inversion performed by an external solver. The current pixel-based solver is provided by the SLITronomy plug-in.

__init__(data_class, psf_class=None, lens_model_class=None, source_model_class=None, lens_light_model_class=None, point_source_class=None, extinction_class=None, kwargs_numerics=None, likelihood_mask=None, psf_error_map_bool_list=None, kwargs_pixelbased=None, linear_solver=True)

Parameters:

• data_class – ImageData() instance
• psf_class – PSF() instance
• lens_model_class – LensModel() instance
• source_model_class – LightModel() instance
• lens_light_model_class – LightModel() instance
• point_source_class – PointSource() instance
• kwargs_numerics – keyword arguments passed to the Numerics module
• likelihood_mask – 2d boolean array of pixels to be counted in the likelihood calculation/linear optimization
• psf_error_map_bool_list – list of boolean of length of point source models. Indicates whether PSF error map is used for the point source model stated as the index.
• kwargs_pixelbased – keyword arguments with various settings related to the pixel-based solver (see SLITronomy documentation) being applied to the point sources.
• linear_solver – bool, if True (default) fixes the linear amplitude parameters ‘amp’ (avoid sampling) such that they get overwritten by the linear solver solution.

array_masked2image(array)

Parameters:array – 1d array of values not masked out (part of linear fitting) Returns:2d array of full image

check_positive_flux(kwargs_source, kwargs_lens_light, kwargs_ps)

Checks whether the surface brightness profiles contain positive fluxes and returns bool if True.

Parameters:

• kwargs_source – source surface brightness keyword argument list
• kwargs_lens_light – lens surface brightness keyword argument list
• kwargs_ps – point source keyword argument list

Returns:

boolean

data_response

Returns the 1d array of the data element that is fitted for (including masking)

Returns:1d numpy array

error_map_source(kwargs_source, x_grid, y_grid, cov_param)

Variance of the linear source reconstruction in the source plane coordinates, computed by the diagonal elements of the covariance matrix of the source reconstruction as a sum of the errors of the basis set.

Parameters:

• kwargs_source – keyword arguments of source model
• x_grid – x-axis of positions to compute error map
• y_grid – y-axis of positions to compute error map
• cov_param – covariance matrix of liner inversion parameters

Returns:

diagonal covariance errors at the positions (x_grid, y_grid)

error_response(kwargs_lens, kwargs_ps, kwargs_special)

Returns the 1d array of the error estimate corresponding to the data response.

Returns:1d numpy array of response, 2d array of additional errors (e.g. point source uncertainties)

image2array_masked(image)

Returns 1d array of values in image that are not masked out for the likelihood computation/linear minimization :param image: 2d numpy array of full image :return: 1d array.

image_linear_solve(kwargs_lens=None, kwargs_source=None, kwargs_lens_light=None, kwargs_ps=None, kwargs_extinction=None, kwargs_special=None, inv_bool=False)

Computes the image (lens and source surface brightness with a given lens model). The linear parameters are computed with a weighted linear least square optimization (i.e. flux normalization of the brightness profiles) However in case of pixel-based modelling, pixel values are constrained by an external solver (e.g. SLITronomy).

Parameters:

• kwargs_lens – list of keyword arguments corresponding to the superposition of different lens profiles
• kwargs_source – list of keyword arguments corresponding to the superposition of different source light profiles
• kwargs_lens_light – list of keyword arguments corresponding to different lens light surface brightness profiles
• kwargs_ps – keyword arguments corresponding to “other” parameters, such as external shear and point source image positions
• inv_bool – if True, invert the full linear solver Matrix Ax = y for the purpose of the covariance matrix.

Returns:

2d array of surface brightness pixels of the optimal solution of the linear parameters to match the data

image_pixelbased_solve(kwargs_lens=None, kwargs_source=None, kwargs_lens_light=None, kwargs_ps=None, kwargs_extinction=None, kwargs_special=None, init_lens_light_model=None)

Computes the image (lens and source surface brightness with a given lens model) using the pixel-based solver.

Parameters:

• kwargs_lens – list of keyword arguments corresponding to the superposition of different lens profiles
• kwargs_source – list of keyword arguments corresponding to the superposition of different source light profiles
• kwargs_lens_light – list of keyword arguments corresponding to different lens light surface brightness profiles
• kwargs_ps – keyword arguments corresponding to point sources
• kwargs_extinction – keyword arguments corresponding to dust extinction
• kwargs_special – keyword arguments corresponding to “special” parameters
• init_lens_light_model – optional initial guess for the lens surface brightness

Returns:

2d array of surface brightness pixels of the optimal solution of the linear parameters to match the data

likelihood_data_given_model(kwargs_lens=None, kwargs_source=None, kwargs_lens_light=None, kwargs_ps=None, kwargs_extinction=None, kwargs_special=None, source_marg=False, linear_prior=None, check_positive_flux=False, linear_solver=True)

Computes the likelihood of the data given a model This is specified with the non-linear parameters and a linear inversion and prior marginalisation.

Parameters:

• kwargs_lens – list of keyword arguments corresponding to the superposition of different lens profiles
• kwargs_source – list of keyword arguments corresponding to the superposition of different source light profiles
• kwargs_lens_light – list of keyword arguments corresponding to different lens light surface brightness profiles
• kwargs_ps – keyword arguments corresponding to “other” parameters, such as external shear and point source image positions
• kwargs_extinction –
• kwargs_special –
• source_marg – bool, performs a marginalization over the linear parameters
• linear_prior – linear prior width in eigenvalues
• check_positive_flux – bool, if True, checks whether the linear inversion resulted in non-negative flux components and applies a punishment in the likelihood if so.
• linear_solver – bool, if True (default) fixes the linear amplitude parameters ‘amp’ (avoid sampling) such that they get overwritten by the linear solver solution.

Returns:

log likelihood (natural logarithm)

linear_param_from_kwargs(kwargs_source, kwargs_lens_light, kwargs_ps)

Inverse function of update_linear() returning the linear amplitude list for the keyword argument list.

Parameters:

• kwargs_source –
• kwargs_lens_light –
• kwargs_ps –

Returns:

list of linear coefficients

linear_response_matrix(kwargs_lens=None, kwargs_source=None, kwargs_lens_light=None, kwargs_ps=None, kwargs_extinction=None, kwargs_special=None)

Computes the linear response matrix (m x n), with n being the data size and m being the coefficients.

Parameters:

• kwargs_lens – lens model keyword argument list
• kwargs_source – extended source model keyword argument list
• kwargs_lens_light – lens light model keyword argument list
• kwargs_ps – point source model keyword argument list
• kwargs_extinction – extinction model keyword argument list
• kwargs_special – special keyword argument list

Returns:

linear response matrix

num_data_evaluate

Number of data points to be used in the linear solver :return: number of evaluated data points :rtype: int.

num_param_linear(kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps)

Returns:number of linear coefficients to be solved for in the linear inversion

point_source_linear_response_set(kwargs_ps, kwargs_lens, kwargs_special, with_amp=True)

Parameters:

• kwargs_ps – point source keyword argument list
• kwargs_lens – lens model keyword argument list
• kwargs_special – special keyword argument list, may include ‘delta_x_image’ and ‘delta_y_image’
• with_amp – bool, if True, relative magnification between multiply imaged point sources are held fixed.

Returns:

list of positions and amplitudes split in different basis components with applied astrometric corrections

reduced_chi2(model, error_map=0)

Returns reduced chi2 :param model: 2d numpy array of a model predicted image :param error_map: same format as model, additional error component (such as PSF errors) :return: reduced chi2.

reduced_residuals(model, error_map=0)

Parameters:

• model – 2d numpy array of the modeled image
• error_map – 2d numpy array of additional noise/error terms from model components (such as PSF model uncertainties)

Returns:

2d numpy array of reduced residuals per pixel

update_data(data_class)

Parameters:data_class – instance of Data() class Returns:no return. Class is updated.

update_linear_kwargs(param, kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps)

Links linear parameters to kwargs arguments.

Parameters:param – linear parameter vector corresponding to the response matrix Returns:updated list of kwargs with linear parameter values

update_pixel_kwargs(kwargs_source, kwargs_lens_light)

Update kwargs arguments for pixel-based profiles with fixed properties such as their number of pixels, scale, and center coordinates (fixed to the origin).

Parameters:

• kwargs_source – list of keyword arguments corresponding to the superposition of different source light profiles
• kwargs_lens_light – list of keyword arguments corresponding to the superposition of different lens light profiles

Returns:

updated kwargs_source and kwargs_lens_light

lenstronomy.ImSim.image_model module

class ImageModel(data_class, psf_class, lens_model_class=None, source_model_class=None, lens_light_model_class=None, point_source_class=None, extinction_class=None, kwargs_numerics=None, kwargs_pixelbased=None)

Bases: object

This class uses functions of lens_model and source_model to make a lensed image.

__init__(data_class, psf_class, lens_model_class=None, source_model_class=None, lens_light_model_class=None, point_source_class=None, extinction_class=None, kwargs_numerics=None, kwargs_pixelbased=None)

Parameters:

• data_class – instance of ImageData() or PixelGrid() class
• psf_class – instance of PSF() class
• lens_model_class – instance of LensModel() class
• source_model_class – instance of LightModel() class describing the source parameters
• lens_light_model_class – instance of LightModel() class describing the lens light parameters
• point_source_class – instance of PointSource() class describing the point sources
• kwargs_numerics – keyword arguments with various numeric description (see ImageNumerics class for options)
• kwargs_pixelbased – keyword arguments with various settings related to the pixel-based solver (see SLITronomy documentation)

extinction_map(kwargs_extinction=None, kwargs_special=None)

Differential extinction per pixel.

Parameters:

• kwargs_extinction – list of keyword arguments corresponding to the optical depth models tau, such that extinction is exp(-tau)
• kwargs_special – keyword arguments, additional parameter to the extinction

Returns:

2d array of size of the image

image(kwargs_lens=None, kwargs_source=None, kwargs_lens_light=None, kwargs_ps=None, kwargs_extinction=None, kwargs_special=None, unconvolved=False, source_add=True, lens_light_add=True, point_source_add=True)

Make an image with a realisation of linear parameter values “param”.

Parameters:

• kwargs_lens – list of keyword arguments corresponding to the superposition of different lens profiles
• kwargs_source – list of keyword arguments corresponding to the superposition of different source light profiles
• kwargs_lens_light – list of keyword arguments corresponding to different lens light surface brightness profiles
• kwargs_ps – keyword arguments corresponding to “other” parameters, such as external shear and point source image positions
• unconvolved – if True: returns the unconvolved light distribution (prefect seeing)
• source_add – if True, compute source, otherwise without
• lens_light_add – if True, compute lens light, otherwise without
• point_source_add – if True, add point sources, otherwise without

Returns:

2d array of surface brightness pixels of the simulation

lens_surface_brightness(kwargs_lens_light, unconvolved=False, k=None)

Computes the lens surface brightness distribution.

Parameters:

• kwargs_lens_light – list of keyword arguments corresponding to different lens light surface brightness profiles
• unconvolved – if True, returns unconvolved surface brightness (perfect seeing), otherwise convolved with PSF kernel

Returns:

2d array of surface brightness pixels

point_source(kwargs_ps, kwargs_lens=None, kwargs_special=None, unconvolved=False, k=None)

Computes the point source positions and paints PSF convolutions on them.

Parameters:

• kwargs_ps –
• kwargs_lens –
• kwargs_special –
• unconvolved –
• k –

Returns:

reset_point_source_cache(cache=True)

Deletes all the cache in the point source class and saves it from then on.

Parameters:cache – boolean, if True, saves the next occuring point source positions in the cache Returns:None

source_surface_brightness(kwargs_source, kwargs_lens=None, kwargs_extinction=None, kwargs_special=None, unconvolved=False, de_lensed=False, k=None, update_pixelbased_mapping=True)

Computes the source surface brightness distribution.

Parameters:

• kwargs_source – list of keyword arguments corresponding to the superposition of different source light profiles
• kwargs_lens – list of keyword arguments corresponding to the superposition of different lens profiles
• kwargs_extinction – list of keyword arguments of extinction model
• unconvolved – if True: returns the unconvolved light distribution (prefect seeing)
• de_lensed – if True: returns the un-lensed source surface brightness profile, otherwise the lensed.
• k – integer, if set, will only return the model of the specific index

Returns:

2d array of surface brightness pixels

update_psf(psf_class)

Update the instance of the class with a new instance of PSF() with a potentially different point spread function.

Parameters:psf_class – Returns:no return. Class is updated.

Module contents