Source code for lenstronomy.LensModel.Profiles.sersic_ellipse_potential

__author__ = 'sibirrer'
#this file contains a class to make a gaussian

import numpy as np
from lenstronomy.LensModel.Profiles.sersic import Sersic
import lenstronomy.Util.param_util as param_util
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase

__all__ = ['SersicEllipse']


[docs]class SersicEllipse(LensProfileBase): """ this class contains functions to evaluate a Sersic mass profile: https://arxiv.org/pdf/astro-ph/0311559.pdf """ param_names = ['k_eff', 'R_sersic', 'n_sersic', 'e1', 'e2', 'center_x', 'center_y'] lower_limit_default = {'k_eff': 0, 'R_sersic': 0, 'n_sersic': 0.5, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100} upper_limit_default = {'k_eff': 10, 'R_sersic': 100, 'n_sersic': 8, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100} def __init__(self): self.sersic = Sersic() self._diff = 0.000001 super(SersicEllipse, self).__init__()
[docs] def function(self, x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0): """ returns Gaussian """ phi_G, q = param_util.ellipticity2phi_q(e1, e2) x_, y_ = self._coord_transf(x, y, q, phi_G, center_x, center_y) f_ = self.sersic.function(x_, y_, n_sersic, R_sersic, k_eff) return f_
[docs] def derivatives(self, x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0): """ returns df/dx and df/dy of the function """ phi_G, q = param_util.ellipticity2phi_q(e1, e2) e = abs(1. - q) cos_phi = np.cos(phi_G) sin_phi = np.sin(phi_G) x_, y_ = self._coord_transf(x, y, q, phi_G, center_x, center_y) f_x_prim, f_y_prim = self.sersic.derivatives(x_, y_, n_sersic, R_sersic, k_eff) f_x_prim *= np.sqrt(1 - e) f_y_prim *= np.sqrt(1 + e) f_x = cos_phi*f_x_prim-sin_phi*f_y_prim f_y = sin_phi*f_x_prim+cos_phi*f_y_prim return f_x, f_y
[docs] def hessian(self, x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0): """ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2 """ alpha_ra, alpha_dec = self.derivatives(x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x, center_y) diff = self._diff alpha_ra_dx, alpha_dec_dx = self.derivatives(x + diff, y, n_sersic, R_sersic, k_eff, e1, e2, center_x, center_y) alpha_ra_dy, alpha_dec_dy = self.derivatives(x, y + diff, n_sersic, R_sersic, k_eff, e1, e2, center_x, center_y) f_xx = (alpha_ra_dx - alpha_ra)/diff f_xy = (alpha_ra_dy - alpha_ra)/diff f_yx = (alpha_dec_dx - alpha_dec)/diff f_yy = (alpha_dec_dy - alpha_dec)/diff return f_xx, f_xy, f_yx, f_yy
@staticmethod def _coord_transf(x, y, q, phi_G, center_x, center_y): """ :param x: :param y: :param q: :param phi_G: :param center_x: :param center_y: :return: """ x_shift = x - center_x y_shift = y - center_y cos_phi = np.cos(phi_G) sin_phi = np.sin(phi_G) e = abs(1 - q) x_ = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e) y_ = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e) return x_, y_