Source code for lenstronomy.LensModel.Profiles.flexionfg

from lenstronomy.LensModel.Profiles.flexion import Flexion
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase

__all__ = ['Flexionfg']


[docs]class Flexionfg(LensProfileBase): """ Flexion consist of basis F flexion and G flexion (F1,F2,G1,G2), see formulas 2.54, 2.55 in Massimo Meneghetti 2017 - "Introduction to Gravitational Lensing". """ param_names = ['F1', 'F2', 'G1', 'G2', 'ra_0', 'dec_0'] lower_limit_default = {'F1': -0.1, 'F2': -0.1, 'G1': -0.1, 'G2': -0.1, 'ra_0': -100, 'dec_0': -100} upper_limit_default = {'F1': 0.1, 'F2': 0.1, 'G1': 0.1, 'G2': 0.1, 'ra_0': 100, 'dec_0': 100} def __init__(self): self.flexion_cart = Flexion() super(Flexionfg, self).__init__()
[docs] def function(self, x, y, F1, F2, G1, G2, ra_0=0, dec_0=0): """ lensing potential :param x: x-coordinate :param y: y-coordinate :param F1: F1 flexion, derivative of kappa in x direction :param F2: F2 flexion, derivative of kappa in y direction :param G1: G1 flexion :param G2: G2 flexion :param ra_0: center x-coordinate :param dec_0: center y-coordinate :return: lensing potential """ _g1, _g2, _g3, _g4 = self.transform_fg(F1, F2, G1, G2) return self.flexion_cart.function(x, y, _g1, _g2, _g3, _g4, ra_0, dec_0)
[docs] def derivatives(self, x, y, F1, F2, G1, G2, ra_0=0, dec_0=0): """ deflection angle :param x: x-coordinate :param y: y-coordinate :param F1: F1 flexion, derivative of kappa in x direction :param F2: F2 flexion, derivative of kappa in y direction :param G1: G1 flexion :param G2: G2 flexion :param ra_0: center x-coordinate :param dec_0: center x-coordinate :return: deflection angle """ _g1, _g2, _g3, _g4 = self.transform_fg(F1, F2, G1, G2) return self.flexion_cart.derivatives(x, y, _g1, _g2, _g3, _g4, ra_0, dec_0)
[docs] def hessian(self, x, y, F1, F2, G1, G2, ra_0=0, dec_0=0): """ Hessian matrix :param x: x-coordinate :param y: y-coordinate :param F1: F1 flexion, derivative of kappa in x direction :param F2: F2 flexion, derivative of kappa in y direction :param G1: G1 flexion :param G2: G2 flexion :param ra_0: center x-coordinate :param dec_0: center y-coordinate :return: second order derivatives f_xx, f_yy, f_xy """ _g1, _g2, _g3, _g4 = self.transform_fg(F1, F2, G1, G2) return self.flexion_cart.hessian(x, y, _g1, _g2, _g3, _g4, ra_0, dec_0)
[docs] @staticmethod def transform_fg(F1, F2, G1, G2): """ basis transform from (F1,F2,G1,G2) to (g1,g2,g3,g4) :param F1: F1 flexion, derivative of kappa in x direction :param F2: F2 flexion, derivative of kappa in y direction :param G1: G1 flexion :param G2: G2 flexion :return: g1,g2,g3,g4 (phi_xxx, phi_xxy, phi_xyy, phi_yyy) """ g1 = (3*F1 + G1) * 0.5 g2 = (3*F2 + G2) * 0.5 g3 = (F1 - G1) * 0.5 g4 = (F2 - G2) * 0.5 return g1, g2, g3, g4