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)