Source code for lenstronomy.LensModel.Profiles.p_jaffe_ellipse

from lenstronomy.LensModel.Profiles.p_jaffe import PJaffe
import lenstronomy.Util.param_util as param_util
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
import numpy as np

__all__ = ['PJaffe_Ellipse']


[docs]class PJaffe_Ellipse(LensProfileBase): """ class to compute the DUAL PSEUDO ISOTHERMAL ELLIPTICAL MASS DISTRIBUTION based on Eliasdottir (2007) https://arxiv.org/pdf/0710.5636.pdf Appendix A with the ellipticity implemented in the potential Module name: 'PJAFFE_ELLIPSE'; An alternative name is dPIED. The 3D density distribution is .. math:: \\rho(r) = \\frac{\\rho_0}{(1+r^2/Ra^2)(1+r^2/Rs^2)} with :math:`Rs > Ra`. The projected density is .. math:: \\Sigma(R) = \\Sigma_0 \\frac{Ra Rs}{Rs-Ra}\\left(\\frac{1}{\\sqrt{Ra^2+R^2}} - \\frac{1}{\\sqrt{Rs^2+R^2}} \\right) with .. math:: \\Sigma_0 = \\pi \\rho_0 \\frac{Ra Rs}{Rs + Ra} In the lensing parameterization, .. math:: \\sigma_0 = \\frac{\\Sigma_0}{\\Sigma_{\\rm crit}} """ param_names = ['sigma0', 'Ra', 'Rs', 'e1', 'e2', 'center_x', 'center_y'] lower_limit_default = {'sigma0': 0, 'Ra': 0, 'Rs': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100} upper_limit_default = {'sigma0': 10, 'Ra': 100, 'Rs': 100, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100} def __init__(self): self.spherical = PJaffe() self._diff = 0.000001 super(PJaffe_Ellipse, self).__init__()
[docs] def function(self, x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0): """ returns double integral of NFW profile """ x_, y_ = param_util.transform_e1e2_square_average(x, y, e1, e2, center_x, center_y) f_ = self.spherical.function(x_, y_, sigma0, Ra, Rs) return f_
[docs] def derivatives(self, x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0): """ returns df/dx and df/dy of the function (integral of NFW) """ phi_G, q = param_util.ellipticity2phi_q(e1, e2) x_, y_ = param_util.transform_e1e2_square_average(x, y, e1, e2, center_x, center_y) e = param_util.q2e(q) cos_phi = np.cos(phi_G) sin_phi = np.sin(phi_G) f_x_prim, f_y_prim = self.spherical.derivatives(x_, y_, sigma0, Ra, Rs, center_x=0, center_y=0) 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, sigma0, Ra, Rs, 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, sigma0, Ra, Rs, e1, e2, center_x, center_y) diff = self._diff alpha_ra_dx, alpha_dec_dx = self.derivatives(x + diff, y, sigma0, Ra, Rs, e1, e2, center_x, center_y) alpha_ra_dy, alpha_dec_dy = self.derivatives(x, y + diff, sigma0, Ra, Rs, 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
[docs] def mass_3d_lens(self, r, sigma0, Ra, Rs, e1=0, e2=0): """ :param r: :param sigma0: :param Ra: :param Rs: :param e1: :param e2: :return: """ return self.spherical.mass_3d_lens(r, sigma0, Ra, Rs)