Source code for lenstronomy.Analysis.lens_profile

import numpy as np
from lenstronomy.Util import util
from lenstronomy.Util import mask_util as mask_util
import lenstronomy.Util.multi_gauss_expansion as mge
from lenstronomy.Util import analysis_util
from lenstronomy.LensModel.lens_model_extensions import LensModelExtensions

__all__ = ['LensProfileAnalysis']


[docs]class LensProfileAnalysis(object): """ class with analysis routines to compute derived properties of the lens model """ def __init__(self, lens_model): """ :param lens_model: LensModel instance """ self._lens_model = lens_model
[docs] def effective_einstein_radius(self, 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 :param kwargs_lens: list of lens model keyword arguments :param center_x: position of the center (if not set, is attempting to find it from the parameters kwargs_lens) :param center_y: position of the center (if not set, is attempting to find it from the parameters kwargs_lens) :param model_bool_list: list of booleans indicating the addition (=True) of a model component in computing the Einstein radius :param grid_num: integer, number of grid points to numerically evaluate the convergence and estimate the Einstein radius :param grid_spacing: spacing in angular units of the grid :param get_precision: If `True`, return the precision of estimated Einstein radius :param verbose: boolean, if True prints warning if indication of insufficient result :return: estimate of the Einstein radius """ center_x, center_y = analysis_util.profile_center(kwargs_lens, center_x, center_y) x_grid, y_grid = util.make_grid(numPix=grid_num, deltapix=grid_spacing) x_grid += center_x y_grid += center_y kappa = self._lens_model.kappa(x_grid, y_grid, kwargs_lens, k=model_bool_list) if self._lens_model.lens_model_list[0] in ['INTERPOL', 'INTERPOL_SCALED']: center_x = x_grid[kappa == np.max(kappa)][0] center_y = y_grid[kappa == np.max(kappa)][0] r_array = np.linspace(0, grid_num*grid_spacing/2., grid_num*2) inner_most_bin = True for r in r_array: mask = np.array(1 - mask_util.mask_center_2d(center_x, center_y, r, x_grid, y_grid)) sum_mask = np.sum(mask) if sum_mask > 0: kappa_mean = np.sum(kappa*mask)/np.sum(mask) if inner_most_bin: if kappa_mean < 1: Warning( "Central convergence value is subcritical <1 and hence an Einstein radius is ill defined.") if get_precision: return np.nan, 0 else: return np.nan inner_most_bin = False if kappa_mean < 1: if get_precision: return r, r_array[1] - r_array[0] else: return r if verbose: Warning("No Einstein radius computed for the following model!", kwargs_lens) return np.nan
[docs] def local_lensing_effect(self, 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. :param kwargs_lens: lens model keyword argument list :param ra_pos: RA position where to compute the external effect :param dec_pos: DEC position where to compute the external effect :param model_list_bool: boolean list indicating which models effect to be added to the estimate :return: alpha_x, alpha_y, kappa, shear1, shear2 """ f_x, f_y = self._lens_model.alpha(ra_pos, dec_pos, kwargs_lens, k=model_list_bool) f_xx, f_xy, f_yx, f_yy = self._lens_model.hessian(ra_pos, dec_pos, kwargs_lens, k=model_list_bool) kappa = (f_xx + f_yy)/2. shear1 = 1./2 * (f_xx - f_yy) shear2 = f_xy return f_x, f_y, kappa, shear1, shear2
[docs] def profile_slope(self, kwargs_lens, radius, center_x=None, center_y=None, model_list_bool=None, num_points=10): """ computes the logarithmic power-law slope of a profile. ATTENTION: this is not an observable! :param kwargs_lens: lens model keyword argument list :param radius: radius from the center where to compute the logarithmic slope (angular units :param center_x: center of profile from where to compute the slope :param center_y: center of profile from where to compute the slope :param model_list_bool: bool list, indicate which part of the model to consider :param num_points: number of estimates around the Einstein radius :return: logarithmic power-law slope """ center_x, center_y = analysis_util.profile_center(kwargs_lens, center_x, center_y) x, y = util.points_on_circle(radius, num_points) dr = 0.01 x_dr, y_dr = util.points_on_circle(radius + dr, num_points) alpha_E_x_i, alpha_E_y_i = self._lens_model.alpha(center_x + x, center_y + y, kwargs_lens, k=model_list_bool) alpha_E_r = np.sqrt(alpha_E_x_i**2 + alpha_E_y_i**2) alpha_E_dr_x_i, alpha_E_dr_y_i = self._lens_model.alpha(center_x + x_dr, center_y + y_dr, kwargs_lens, k=model_list_bool) alpha_E_dr = np.sqrt(alpha_E_dr_x_i ** 2 + alpha_E_dr_y_i ** 2) slope = np.mean(np.log(alpha_E_dr / alpha_E_r) / np.log((radius + dr) / radius)) gamma = -slope + 2 return gamma
[docs] def mst_invariant_differential(self, 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. .. math:: \\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. :param kwargs_lens: lens model keyword argument list :param radius: radius from the center where to compute the MST invariant differential :param center_x: center position :param center_y: center position :param model_list_bool: indicate which part of the model to consider :param num_points: number of estimates around the radius :return: xi """ center_x, center_y = analysis_util.profile_center(kwargs_lens, center_x, center_y) x, y = util.points_on_circle(radius, num_points) ext = LensModelExtensions(lensModel=self._lens_model) lambda_rad, lambda_tan, orientation_angle, dlambda_tan_dtan, dlambda_tan_drad, dlambda_rad_drad, dlambda_rad_dtan, dphi_tan_dtan, dphi_tan_drad, dphi_rad_drad, dphi_rad_dtan = ext.radial_tangential_differentials(x, y, kwargs_lens, center_x=center_x, center_y=center_y) xi = np.mean(dlambda_rad_drad/lambda_rad) return xi
[docs] def radial_lens_profile(self, r_list, kwargs_lens, center_x=None, center_y=None, model_bool_list=None): """ :param r_list: list of radii to compute the spherically averaged lens light profile :param center_x: center of the profile :param center_y: center of the profile :param kwargs_lens: lens parameter keyword argument list :param model_bool_list: bool list or None, indicating which profiles to sum over :return: flux amplitudes at r_list radii azimuthally averaged """ center_x, center_y = analysis_util.profile_center(kwargs_lens, center_x, center_y) kappa_list = [] for r in r_list: x, y = util.points_on_circle(r, num_points=20) f_r = self._lens_model.kappa(x + center_x, y + center_y, kwargs=kwargs_lens, k=model_bool_list) kappa_list.append(np.average(f_r)) return kappa_list
[docs] def multi_gaussian_lens(self, kwargs_lens, center_x=None, center_y=None, model_bool_list=None, n_comp=20): """ multi-gaussian lens model in convergence space :param kwargs_lens: :param n_comp: :return: """ center_x, center_y = analysis_util.profile_center(kwargs_lens, center_x, center_y) theta_E = self.effective_einstein_radius(kwargs_lens) r_array = np.logspace(-4, 2, 200) * theta_E kappa_s = self.radial_lens_profile(r_array, kwargs_lens, center_x=center_x, center_y=center_y, model_bool_list=model_bool_list) amplitudes, sigmas, norm = mge.mge_1d(r_array, kappa_s, N=n_comp) return amplitudes, sigmas, center_x, center_y
[docs] def mass_fraction_within_radius(self, kwargs_lens, center_x, center_y, theta_E, numPix=100): """ computes the mean convergence of all the different lens model components within a spherical aperture :param kwargs_lens: lens model keyword argument list :param center_x: center of the aperture :param center_y: center of the aperture :param theta_E: radius of aperture :return: list of average convergences for all the model components """ x_grid, y_grid = util.make_grid(numPix=numPix, deltapix=2.*theta_E / numPix) x_grid += center_x y_grid += center_y mask = mask_util.mask_azimuthal(x_grid, y_grid, center_x, center_y, theta_E) kappa_list = [] for i in range(len(kwargs_lens)): kappa = self._lens_model.kappa(x_grid, y_grid, kwargs_lens, k=i) kappa_mean = np.sum(kappa * mask) / np.sum(mask) kappa_list.append(kappa_mean) return kappa_list
[docs] def convergence_peak(self, 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 :param kwargs_lens: lens model keyword argument list :param model_bool_list: bool list (optional) to include certain models or not :return: center_x, center_y """ x_grid, y_grid = util.make_grid(numPix=grid_num, deltapix=grid_spacing) x_grid += center_x_init y_grid += center_y_init kappa = self._lens_model.kappa(x_grid, y_grid, kwargs_lens, k=model_bool_list) center_x = x_grid[kappa == np.max(kappa)] center_y = y_grid[kappa == np.max(kappa)] return center_x, center_y