jaxtronomy.ImSim package

Subpackages

• jaxtronomy.ImSim.MultiBand package
  • Submodules
  • jaxtronomy.ImSim.MultiBand.single_band_multi_model module
    • SingleBandMultiModel
      • SingleBandMultiModel.__init__()
      • SingleBandMultiModel.image()
      • SingleBandMultiModel.source_surface_brightness()
      • SingleBandMultiModel.lens_surface_brightness()
      • SingleBandMultiModel.point_source()
      • SingleBandMultiModel.image_linear_solve()
      • SingleBandMultiModel.likelihood_data_given_model()
      • SingleBandMultiModel.update_linear_kwargs()
      • SingleBandMultiModel.num_param_linear()
      • SingleBandMultiModel.linear_response_matrix()
      • SingleBandMultiModel.error_map_source()
      • SingleBandMultiModel.error_response()
      • SingleBandMultiModel.linear_param_from_kwargs()
      • SingleBandMultiModel.select_kwargs()
  • Module contents
• jaxtronomy.ImSim.Numerics package
  • Submodules
  • jaxtronomy.ImSim.Numerics.convolution module
    • PixelKernelConvolution
      • PixelKernelConvolution.__init__()
      • PixelKernelConvolution.pixel_kernel()
      • PixelKernelConvolution.copy_transpose()
      • PixelKernelConvolution.convolution2d()
      • PixelKernelConvolution.re_size_convolve()
    • SubgridKernelConvolution
      • SubgridKernelConvolution.__init__()
      • SubgridKernelConvolution.convolution2d()
      • SubgridKernelConvolution.re_size_convolve()
    • PartialSubgridKernelConvolution
      • PartialSubgridKernelConvolution.__init__()
      • PartialSubgridKernelConvolution.re_size_convolve()
      • PartialSubgridKernelConvolution.convolution2d()
    • GaussianConvolution
      • GaussianConvolution.__init__()
      • GaussianConvolution.convolution2d()
      • GaussianConvolution.re_size_convolve()
      • GaussianConvolution.pixel_kernel()
  • jaxtronomy.ImSim.Numerics.grid module
    • AdaptiveGrid
      • AdaptiveGrid.__init__()
      • AdaptiveGrid.coordinates_evaluate
      • AdaptiveGrid.supersampling_factor
      • AdaptiveGrid.flux_array2image_low_high()
    • RegularGrid
      • RegularGrid.__init__()
      • RegularGrid.coordinates_evaluate
      • RegularGrid.grid_points_spacing
      • RegularGrid.num_grid_points_axes
      • RegularGrid.supersampling_factor
      • RegularGrid.flux_array2image_low_high()
  • jaxtronomy.ImSim.Numerics.numerics module
    • Numerics
      • Numerics.__init__()
      • Numerics.re_size_convolve()
      • Numerics.grid_supersampling_factor
      • Numerics.coordinates_evaluate
      • Numerics.convolution_class
      • Numerics.grid_class
  • jaxtronomy.ImSim.Numerics.numerics_subframe module
    • NumericsSubFrame
      • NumericsSubFrame.__init__()
      • NumericsSubFrame.re_size_convolve()
      • NumericsSubFrame.grid_supersampling_factor
      • NumericsSubFrame.coordinates_evaluate
      • NumericsSubFrame.convolution_class
      • NumericsSubFrame.grid_class
  • jaxtronomy.ImSim.Numerics.point_source_rendering module
    • PointSourceRendering
      • PointSourceRendering.__init__()
      • PointSourceRendering.point_source_rendering()
      • PointSourceRendering.psf_variance_map()
  • Module contents

Submodules

jaxtronomy.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

jaxtronomy.ImSim.image_linear_solve module

class ImageLinearFit(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, likelihood_mask=None, psf_error_map_bool_list=None, kwargs_pixelbased=None)

Bases: 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, 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)

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

• extinction_class – DifferentialExtinction() 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.

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). By default, 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

• kwargs_extinction – list of keyword arguments for extinction model

• kwargs_special – list of special keyword arguments

• inv_bool – if True, invert the full linear solver Matrix Ax = y for the purpose of the covariance matrix. This has no impact in case of pixel-based modelling.

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)

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 – list of keyword arguments for extinction model

• kwargs_special – list of special keyword arguments

• 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.

Returns:

log likelihood (natural logarithm), linear parameter list

likelihood_data_given_model_solution(model, model_error, cov_matrix, param, kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps, source_marg=False, linear_prior=None, check_positive_flux=False)

Parameters:

• model – 2d array, image model

• model_error – 2d array, uncertainties in each pixel

• cov_matrix – 2d array, covariance matrix

• param – linear parameter vector corresponding to the response matrix

• kwargs_lens – list of dicts containing lens model keyword arguments

• kwargs_source – list of dicts containing source model keyword arguments

• kwargs_lens_light – list of dicts containing lens light model keyword arguments

• kwargs_ps – list of dicts containing point source keyword arguments

• kwargs_extinction – list of keyword arguments for extinction model

• kwargs_special – list of special keyword arguments

• 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.

Returns:

float, likelihood data given model

num_param_linear(kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps)

Parameters:

• kwargs_lens – list of dicts containing lens model keyword arguments

• kwargs_source – list of dicts containing source model keyword arguments

• kwargs_lens_light – list of dicts containing lens light model keyword arguments

• kwargs_ps – list of dicts containing point source keyword arguments

Returns:

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

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

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

The calculation is done by - first (optional) computing differential extinctions - adding linear components of the lensed source(s) - adding linear components of the unlensed components (i.e. deflector) - adding point sources (can be multiple lensed or stars in the field)

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 – list of keyword arguments for extinction model

• kwargs_special – list of special keyword arguments

• unconvolved – bool, if True, computes components without convolution kernel (will not work for point sources)

Returns:

response matrix (m x n)

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

• kwargs_lens – list of dicts containing lens model keyword arguments

• kwargs_source – list of dicts containing source model keyword arguments

• kwargs_lens_light – list of dicts containing lens light model keyword arguments

• kwargs_ps – list of dicts containing point source keyword arguments

Returns:

updated list of kwargs with linear parameter values

linear_param_from_kwargs(kwargs_source, kwargs_lens_light, kwargs_ps)

Returns list of the linear amplitudes from the keyword arguments.

Parameters:

• kwargs_source – list of dicts containing source model keyword arguments

• kwargs_lens_light – list of dicts containing lens light model keyword arguments

• kwargs_ps – list of dicts containing point source keyword arguments

Returns:

list of linear coefficients

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 linear inversion parameters

Returns:

diagonal covariance errors at the positions (x_grid, y_grid)

point_source_linear_response_set(kwargs_ps, kwargs_lens, kwargs_special=None, 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

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

jaxtronomy.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, likelihood_mask=None, psf_error_map_bool_list=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, likelihood_mask=None, psf_error_map_bool_list=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)

• likelihood_mask – 2d boolean array of pixels to be counted in the likelihood calculation. Must be a np array; cannot be a jnp array.

• 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 – kwargs for pixelbased solver; not supported in jaxtronomy. Must be None

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)

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 dicts, keyword arguments corresponding to the superposition of different lens profiles in the same order of the lens_model_list

• kwargs_source – list of dicts, keyword arguments corresponding to the superposition of different source light profiles in the same order of light_model_list

• kwargs_lens_light – list of dicts, keyword arguments corresponding to different lens light surface brightness profiles in the same order of lens_light_model_list

• kwargs_ps – list of dicts, keyword arguments for the points source models in the same order of point_source_type_list

• kwargs_extinction – list of dicts, keyword arguments corresponding to different light profiles in the optical_depth_model

• kwargs_special – optional dict including keys “delta_x_image” and “delta_y_image” and array/list values indicating how much to shift each point source image in units of arcseconds

• 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. Should always be false in jaxtronomy

Returns:

log likelihood (natural logarithm), linear parameter list

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 dicts, keyword arguments corresponding to the superposition of different source light profiles in the same order of light_model_list

• kwargs_lens – list of dicts, keyword arguments corresponding to the superposition of different lens profiles in the same order of the lens_model_list

• kwargs_extinction – list of dicts, keyword arguments corresponding to different light profiles in the optical_depth_model

• kwargs_special – optional dict including keys “delta_x_image” and “delta_y_image” and array/list values indicating how much to shift each point source image in units of arcseconds

• 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

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 – list of dicts, keyword arguments for each point source model in the same order of the point_source_type_list

• kwargs_lens – list of dicts, keyword arguments for the full set of lens models in the same order of the lens_model_list

• kwargs_special – optional dict including keys “delta_x_image” and “delta_y_image” and array/list values indicating how much to shift each point source image in units of arcseconds

• unconvolved – bool, includes point source images if False, excludes ps if True

• k – optional int, include only the k-th point source model. If None, includes all

Returns:

rendered point source images

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 dicts, keyword arguments corresponding to the superposition of different lens profiles in the same order of the lens_model_list

• kwargs_source – list of dicts, keyword arguments corresponding to the superposition of different source light profiles in the same order of light_model_list

• kwargs_lens_light – list of dicts, keyword arguments corresponding to different lens light surface brightness profiles in the same order of lens_light_model_list

• kwargs_ps – list of dicts, keyword arguments for the points source models in the same order of point_source_type_list

• kwargs_extinction – list of dicts, keyword arguments corresponding to different light profiles in the optical_depth_model

• kwargs_special – optional dict including keys “delta_x_image” and “delta_y_image” and array/list values indicating how much to shift each point source image in units of arcseconds

• 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

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

reduced_chi2(model, error_map=0)

Returns reduced chi2.

Parameters:

• model – 2d numpy array of a model predicted image

• error_map – same format as model, additional error component (such as PSF errors)

Returns:

reduced chi2.

image2array_masked(image)

Returns 1d array of values in image that are not masked out for the likelihood computation/linear minimization.

Parameters:

image – 2d numpy array of full image

Returns:

1d array.

array_masked2image(array)

Converts the 1d masked array into a 2d image.

Parameters:

array – 1d array of values not masked out

Returns:

2d array of full image

property data_response

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

Returns:

1d numpy array.

error_response(kwargs_lens, kwargs_ps, kwargs_special)

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

Parameters:

• kwargs_lens – list of dicts, keyword arguments corresponding to the superposition of different lens profiles in the same order of the lens_model_list

• kwargs_ps – list of dicts, keyword arguments for the points source models in the same order of point_source_type_list

• kwargs_special – optional dict including keys “delta_x_image” and “delta_y_image” and array/list values indicating how much to shift each point source image in units of arcseconds

Returns:

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

update_psf(psf_class)

Update the psf class.

Not supported in jaxtronomy.

update_data(data_class)

Update the data class.

Not supported in jaxtronomy.

Module contents