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
__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]
#kappa = util.array2image(kappa)
r_array = np.linspace(0, grid_num*grid_spacing/2., grid_num*2)
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 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_ext, 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_ext = (f_xx + f_yy)/2.
shear1 = 1./2 * (f_xx - f_yy)
shear2 = f_xy
return f_x, f_y, kappa_ext, 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
:param kwargs_lens: lens model keyword argument list
:param radius: radius from the center where to compute the logarithmic slope (angular units
: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 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 spherically 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