Source code for lenstronomy.LensModel.Profiles.multipole

__author__ = 'lynevdv'

import numpy as np

import lenstronomy.Util.param_util as param_util
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase

__all__ = ['Multipole']


[docs]class Multipole(LensProfileBase): """ This class contains a multipole contribution (for 1 component with m>=2) This uses the same definitions as Xu et al.(2013) in Appendix B3 https://arxiv.org/pdf/1307.4220.pdf m : int, multipole order, m>=2 a_m : float, multipole strength phi_m : float, multipole orientation in radian """ param_names = ['m', 'a_m', 'phi_m', 'center_x', 'center_y'] lower_limit_default = {'m': 2,'a_m':0, 'phi_m':-np.pi, 'center_x': -100, 'center_y': -100} upper_limit_default = {'m': 100,'a_m':100, 'phi_m':np.pi, 'center_x': 100, 'center_y': 100}
[docs] def function(self, x, y, m, a_m, phi_m, center_x=0, center_y=0): """ Lensing potential of multipole contribution (for 1 component with m>=2) This uses the same definitions as Xu et al.(2013) in Appendix B3 https://arxiv.org/pdf/1307.4220.pdf :param m: int, multipole order, m>=2 :param a_m: float, multipole strength :param phi_m: float, multipole orientation in radian :param center_x: x-position :param center_y: x-position :return: lensing potential """ r, phi = param_util.cart2polar(x, y, center_x=center_x, center_y=center_y) f_ = r*a_m /(1-m**2) * np.cos(m*(phi-phi_m)) return f_
[docs] def derivatives(self,x,y, m, a_m, phi_m, center_x=0, center_y=0): """ Deflection of a multipole contribution (for 1 component with m>=2) This uses the same definitions as Xu et al.(2013) in Appendix B3 https://arxiv.org/pdf/1307.4220.pdf :param m: int, multipole order, m>=2 :param a_m: float, multipole strength :param phi_m: float, multipole orientation in radian :param center_x: x-position :param center_y: x-position :return: deflection angles alpha_x, alpha_y """ r, phi = param_util.cart2polar(x, y, center_x=center_x, center_y=center_y) f_x = np.cos(phi)*a_m/(1-m**2) * np.cos(m*(phi-phi_m)) + np.sin(phi)*m*a_m/(1-m**2)*np.sin(m*(phi-phi_m)) f_y = np.sin(phi)*a_m/(1-m**2) * np.cos(m*(phi-phi_m)) - np.cos(phi)*m*a_m/(1-m**2)*np.sin(m*(phi-phi_m)) return f_x, f_y
[docs] def hessian(self, x, y, m, a_m, phi_m, center_x=0, center_y=0): """ Hessian of a multipole contribution (for 1 component with m>=2) This uses the same definitions as Xu et al.(2013) in Appendix B3 https://arxiv.org/pdf/1307.4220.pdf :param m: int, multipole order, m>=2 :param a_m: float, multipole strength :param phi_m: float, multipole orientation in radian :param center_x: x-position :param center_y: x-position :return: f_xx, f_xy, f_yx, f_yy """ r, phi = param_util.cart2polar(x, y, center_x=center_x, center_y=center_y) r = np.maximum(r, 0.000001) f_xx = 1./r * np.sin(phi)**2 * a_m *np.cos(m*(phi-phi_m)) f_yy = 1./r * np.cos(phi)**2 * a_m *np.cos(m*(phi-phi_m)) f_xy = -1./r * a_m * np.cos(phi) * np.sin(phi) * np.cos(m*(phi-phi_m)) return f_xx, f_xy, f_xy, f_yy