lenstronomy.LensModel.Solver package

Submodules

lenstronomy.LensModel.Solver.lens_equation_solver module

class LensEquationSolver(lensModel)[source]

Bases: object

Class to solve for image positions given lens model and source position.

__init__(lensModel)[source]

This class must contain the following definitions (with same syntax as the standard LensModel() class: def ray_shooting() def hessian() def magnification()

Parameters:

lensModel – instance of a class according to lenstronomy.LensModel.lens_model

image_position_stochastic(source_x, source_y, kwargs_lens, search_window=10, precision_limit=1e-10, arrival_time_sort=True, x_center=0, y_center=0, num_random=1000)[source]

Solves the lens equation stochastic with the scipy minimization routine on the quadratic distance between the backwards ray-shooted proposed image position and the source position. Credits to Giulia Pagano.

Parameters:
  • source_x – source position

  • source_y – source position

  • kwargs_lens – lens model list of keyword arguments

  • search_window – angular size of search window

  • precision_limit – limit required on the precision in the source plane

  • arrival_time_sort – bool, if True sorts according to arrival time

  • x_center – center of search window

  • y_center – center of search window

  • num_random – number of random starting points of the non-linear solver in the search window

Returns:

x_image, y_image

candidate_solutions(sourcePos_x, sourcePos_y, kwargs_lens, min_distance=0.1, search_window=10, verbose=False, x_center=0, y_center=0)[source]

Finds pixels in the image plane possibly hosting a solution of the lens equation, for the given source position and lens model.

Parameters:
  • sourcePos_x – source position in units of angle

  • sourcePos_y – source position in units of angle

  • kwargs_lens – lens model parameters as keyword arguments

  • min_distance – minimum separation to consider for two images in units of angle

  • search_window – window size to be considered by the solver. Will not find image position outside this window

  • verbose – bool, if True, prints some useful information for the user

  • x_center – float, center of the window to search for point sources

  • y_center – float, center of the window to search for point sources

Returns:

(approximate) angular position of (multiple) images ra_pos, dec_pos in units of angles, related ray-traced source displacements and pixel width

Raises:

AttributeError, KeyError

image_position_analytical(x, y, kwargs_lens, arrival_time_sort=True, magnification_limit=None, **kwargs_solver)[source]

Solves the lens equation. Only supports EPL-like (plus shear) models. Uses a specialized recipe that solves a one-dimensional lens equation that is easier and more reliable to solve than the usual two-dimensional lens equation.

Parameters:
  • x – source position in units of angle, an array of positions is also supported.

  • y – source position in units of angle, an array of positions is also supported.

  • kwargs_lens – lens model parameters as keyword arguments

  • arrival_time_sort – bool, if True, sorts image position in arrival time (first arrival photon first listed)

  • magnification_limit – None or float, if set will only return image positions that have an abs(magnification) larger than this number

  • kwargs_solver – additional kwargs to be supplied to the solver. Particularly relevant are Nmeas and Nmeas_extra

Returns:

(exact) angular position of (multiple) images ra_pos, dec_pos in units of angle Note: in contrast to the other solvers, generally the (heavily demagnified) central image will also be included, so setting a a proper magnification_limit is more important. To get similar behaviour, a limit of 1e-1 is acceptable

image_position_from_source(sourcePos_x, sourcePos_y, kwargs_lens, solver='lenstronomy', **kwargs)[source]

Solves the lens equation, i.e. finds the image positions in the lens plane that are mapped to a given source position.

Parameters:
  • sourcePos_x – source position in units of angle

  • sourcePos_y – source position in units of angle

  • kwargs_lens – lens model parameters as keyword arguments

  • solver – which solver to use, can be ‘lenstronomy’ (default), ‘analytical’ or ‘stochastic’.

  • kwargs – Any additional kwargs are passed to the chosen solver, see the documentation of image_position_lenstronomy, image_position_analytical and image_position_stochastic

Returns:

(exact) angular position of (multiple) images ra_pos, dec_pos in units of angle

image_position_lenstronomy(sourcePos_x, sourcePos_y, kwargs_lens, min_distance=0.1, search_window=10, precision_limit=1e-10, num_iter_max=100, arrival_time_sort=True, initial_guess_cut=True, verbose=False, x_center=0, y_center=0, num_random=0, non_linear=False, magnification_limit=None)[source]

Finds image position given source position and lens model. The solver first samples does a grid search in the lens plane, and the grid points that are closest to the supplied source position are fed to a specialized gradient-based root finder that finds the exact solutions. Works with all lens models.

Parameters:
  • sourcePos_x – source position in units of angle

  • sourcePos_y – source position in units of angle

  • kwargs_lens – lens model parameters as keyword arguments

  • min_distance – minimum separation to consider for two images in units of angle

  • search_window – window size to be considered by the solver. Will not find image position outside this window

  • precision_limit – required precision in the lens equation solver (in units of angle in the source plane).

  • num_iter_max – maximum iteration of lens-source mapping conducted by solver to match the required precision

  • arrival_time_sort – bool, if True, sorts image position in arrival time (first arrival photon first listed)

  • initial_guess_cut – bool, if True, cuts initial local minima selected by the grid search based on distance criteria from the source position

  • verbose – bool, if True, prints some useful information for the user

  • x_center – float, center of the window to search for point sources

  • y_center – float, center of the window to search for point sources

  • num_random – int, number of random positions within the search window to be added to be starting positions for the gradient decent solver

  • non_linear – bool, if True applies a non-linear solver not dependent on Hessian computation

  • magnification_limit – None or float, if set will only return image positions that have an abs(magnification) larger than this number

Returns:

(exact) angular position of (multiple) images ra_pos, dec_pos in units of angle

Raises:

AttributeError, KeyError

findBrightImage(sourcePos_x, sourcePos_y, kwargs_lens, numImages=4, min_distance=0.01, search_window=5, precision_limit=1e-10, num_iter_max=10, arrival_time_sort=True, x_center=0, y_center=0, num_random=0, non_linear=False, magnification_limit=None, initial_guess_cut=True, verbose=False)[source]
Parameters:
  • sourcePos_x – source position in units of angle

  • sourcePos_y – source position in units of angle

  • kwargs_lens – lens model parameters as keyword arguments

  • min_distance – minimum separation to consider for two images in units of angle

  • search_window – window size to be considered by the solver. Will not find image position outside this window

  • precision_limit – required precision in the lens equation solver (in units of angle in the source plane).

  • num_iter_max – maximum iteration of lens-source mapping conducted by solver to match the required precision

  • arrival_time_sort – bool, if True, sorts image position in arrival time (first arrival photon first listed)

  • initial_guess_cut – bool, if True, cuts initial local minima selected by the grid search based on distance criteria from the source position

  • verbose – bool, if True, prints some useful information for the user

  • x_center – float, center of the window to search for point sources

  • y_center – float, center of the window to search for point sources

  • num_random – int, number of random positions within the search window to be added to be starting positions for the gradient decent solver

  • non_linear – bool, if True applies a non-linear solver not dependent on Hessian computation

  • magnification_limit – None or float, if set will only return image positions that have an abs(magnification) larger than this number

Returns:

(exact) angular position of (multiple) images ra_pos, dec_pos in units of angle

sort_arrival_times(x_mins, y_mins, kwargs_lens)[source]

Sort arrival times (fermat potential) of image positions in increasing order of light travel time.

Parameters:
  • x_mins – ra position of images

  • y_mins – dec position of images

  • kwargs_lens – keyword arguments of lens model

Returns:

sorted lists of x_mins and y_mins

lenstronomy.LensModel.Solver.solver module

class Solver(solver_type, lensModel, num_images)[source]

Bases: object

Joint solve class to manage with type of solver to be executed and checks whether the requirements are fulfilled.

__init__(solver_type, lensModel, num_images)[source]
Parameters:
  • solver_type – string, option for specific solver type see detailed instruction of the Solver4Point and Solver2Point classes

  • lensModel – instance of a LensModel() class

  • num_images – int, number of images to be solved for

constraint_lensmodel(x_pos, y_pos, kwargs_list, xtol=1.49012e-12)[source]
Parameters:
  • x_pos – x-position constraints on images

  • y_pos – y-position constraints on images

  • kwargs_list – lens model keyword argument list

  • xtol – tolerance level of solution when to stop the non-linear solver

Returns:

updated lens model that satisfies the lens equation for the point sources, accuracy

update_solver(kwargs_lens, x_pos, y_pos)[source]
Parameters:
  • kwargs_lens – lens model keyword argument list

  • x_pos – x-position constraints on images

  • y_pos – y-position constraints on images

Returns:

updated lens model that satisfies the lens equation for the point sources

check_solver(image_x, image_y, kwargs_lens)[source]

Returns the precision of the solver to match the image position.

Parameters:
  • kwargs_lens – full lens model (including solved parameters)

  • image_x – point source in image

  • image_y – point source in image

Returns:

precision of Euclidean distances between the different rays arriving at the image positions

add_fixed_lens(kwargs_fixed_lens, kwargs_lens_init)[source]

Returns kwargs that are kept fixed during run, depending on options.

Parameters:
  • kwargs_fixed_lens – keyword argument list of fixed parameters (indicated by fitting argument of the user)

  • kwargs_lens_init – Initial values of the full lens model keyword arguments

Returns:

updated kwargs_fixed_lens, added fixed parameters being added (and replaced later on) by the non-linear solver.

lenstronomy.LensModel.Solver.solver2point module

class Solver2Point(lensModel, solver_type='CENTER', decoupling=True)[source]

Bases: object

Class to solve a constraint lens model with two point source positions.

options are: ‘CENTER’: solves for ‘center_x’, ‘center_y’ parameters of the first lens model ‘ELLIPSE’: solves for ‘e1’, ‘e2’ of the first lens (can also be shear) ‘SHAPELETS’: solves for shapelet coefficients c01, c10 ‘THETA_E_PHI: solves for Einstein radius of first lens model and shear angle of second model

__init__(lensModel, solver_type='CENTER', decoupling=True)[source]
Parameters:
  • lensModel – instance of LensModel class

  • solver_type – string

  • decoupling – bool

constraint_lensmodel(x_pos, y_pos, kwargs_list, xtol=1.49012e-12)[source]

Constrains lens model parameters by demanding the solution to match the image positions to a single source position.

Parameters:
  • x_pos – list of image positions (x-axis)

  • y_pos – list of image position (y-axis)

  • kwargs_list – list of lens model kwargs

  • xtol – tolerance level of solution when to stop the non-linear solver

Returns:

updated lens model that satisfies the lens equation for the point sources

solve(x_pos, y_pos, init, kwargs_list, a, xtol=1.49012e-12)[source]
add_fixed_lens(kwargs_fixed_lens_list, kwargs_lens_init)[source]
Parameters:
  • kwargs_fixed_lens_list

  • kwargs_lens_init

Returns:

lenstronomy.LensModel.Solver.solver4point module

class Solver4Point(lensModel, solver_type='PROFILE')[source]

Bases: object

Class to make the constraints for the solver.

__init__(lensModel, solver_type='PROFILE')[source]
constraint_lensmodel(x_pos, y_pos, kwargs_list, xtol=1.49012e-12)[source]
Parameters:
  • x_pos – list of image positions (x-axis)

  • y_pos – list of image position (y-axis)

  • xtol – numerical tolerance level

  • kwargs_list – list of lens model kwargs

Returns:

updated lens model that satisfies the lens equation for the point sources, accuracy

solve(x_pos, y_pos, init, kwargs_list, a, xtol=1.49012e-10)[source]
add_fixed_lens(kwargs_fixed_lens_list, kwargs_lens_init)[source]
Parameters:
  • kwargs_fixed_lens_list

  • kwargs_lens_init

Returns:

Module contents