Source code for lenstronomy.LensModel.Profiles.chameleon

from lenstronomy.LensModel.Profiles.nie import NIE
from lenstronomy.LensModel.Profiles.point_mass import PointMass
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
import lenstronomy.Util.param_util as param_util
import numpy as np

from lenstronomy.Util.package_util import exporter
export, __all__ = exporter()


[docs]@export class Chameleon(LensProfileBase): """ class of the Chameleon model (See Suyu+2014) an elliptical truncated double isothermal profile """ param_names = ['alpha_1', 'w_c', 'w_t', 'e1', 'e2', 'center_x', 'center_y'] lower_limit_default = {'alpha_1': 0, 'w_c': 0, 'w_t': 0, 'e1': -0.8, 'e2': -0.8, 'center_x': -100, 'center_y': -100} upper_limit_default = {'alpha_1': 100, 'w_c': 100, 'w_t': 100, 'e1': 0.8, 'e2': 0.8, 'center_x': 100, 'center_y': 100} def __init__(self, static=False): self._nie_1 = NIE() self._nie_2 = NIE() super(Chameleon, self).__init__() self._static = static
[docs] def function(self, x, y, alpha_1, w_c, w_t, e1, e2, center_x=0, center_y=0): """ :param x: ra-coordinate :param y: dec-coordinate :param alpha_1: deflection angle at 1 (arcseconds) from the center :param w_c: see Suyu+2014 :param w_t: see Suyu+2014 :param e1: ellipticity parameter :param e2: ellipticity parameter :param center_x: ra center :param center_y: dec center :return: lensing potential """ theta_E_conv, w_c, w_t, s_scale_1, s_scale_2 = self.param_convert(alpha_1, w_c, w_t, e1, e2) f_1 = self._nie_1.function(x, y, theta_E_conv, e1, e2, s_scale_1, center_x, center_y) f_2 = self._nie_2.function(x, y, theta_E_conv, e1, e2, s_scale_2, center_x, center_y) f_ = f_1 - f_2 return f_
[docs] def derivatives(self, x, y, alpha_1, w_c, w_t, e1, e2, center_x=0, center_y=0): """ :param x: ra-coordinate :param y: dec-coordinate :param alpha_1: deflection angle at 1 (arcseconds) from the center :param w_c: see Suyu+2014 :param w_t: see Suyu+2014 :param e1: ellipticity parameter :param e2: ellipticity parameter :param center_x: ra center :param center_y: dec center :return: deflection angles (RA, DEC) """ theta_E_conv, w_c, w_t, s_scale_1, s_scale_2 = self.param_convert(alpha_1, w_c, w_t, e1, e2) f_x_1, f_y_1 = self._nie_1.derivatives(x, y, theta_E_conv, e1, e2, s_scale_1, center_x, center_y) f_x_2, f_y_2 = self._nie_2.derivatives(x, y, theta_E_conv, e1, e2, s_scale_2, center_x, center_y) f_x = f_x_1 - f_x_2 f_y = f_y_1 - f_y_2 return f_x, f_y
[docs] def hessian(self, x, y, alpha_1, w_c, w_t, e1, e2, center_x=0, center_y=0): """ :param x: ra-coordinate :param y: dec-coordinate :param alpha_1: deflection angle at 1 (arcseconds) from the center :param w_c: see Suyu+2014 :param w_t: see Suyu+2014 :param e1: ellipticity parameter :param e2: ellipticity parameter :param center_x: ra center :param center_y: dec center :return: second derivatives of the lensing potential (Hessian: f_xx, f_xy, f_yx, f_yy) """ theta_E_conv, w_c, w_t, s_scale_1, s_scale_2 = self.param_convert(alpha_1, w_c, w_t, e1, e2) f_xx_1, f_xy_1, f_yx_1, f_yy_1 = self._nie_1.hessian(x, y, theta_E_conv, e1, e2, s_scale_1, center_x, center_y) f_xx_2, f_xy_2, f_yx_2, f_yy_2 = self._nie_2.hessian(x, y, theta_E_conv, e1, e2, s_scale_2, center_x, center_y) f_xx = f_xx_1 - f_xx_2 f_yy = f_yy_1 - f_yy_2 f_xy = f_xy_1 - f_xy_2 f_yx = f_yx_1 - f_yx_2 return f_xx, f_xy, f_yx, f_yy
[docs] def density_lens(self, r, alpha_1, w_c, w_t, e1=0, e2=0, center_x=0, center_y=0): """ spherical average density as a function of 3d radius :param r: 3d radius :param alpha_1: deflection angle at 1 (arcseconds) from the center :param w_c: see Suyu+2014 :param w_t: see Suyu+2014 :param e1: ellipticity parameter :param e2: ellipticity parameter :param center_x: ra center :param center_y: dec center :return: matter density at 3d radius r """ theta_E_conv, w_c, w_t, s_scale_1, s_scale_2 = self.param_convert(alpha_1, w_c, w_t, e1, e2) f_1 = self._nie_1.density_lens(r, theta_E_conv, e1, e2, s_scale_1, center_x, center_y) f_2 = self._nie_2.density_lens(r, theta_E_conv, e1, e2, s_scale_2, center_x, center_y) f_ = f_1 - f_2 return f_
[docs] def mass_3d_lens(self, r, alpha_1, w_c, w_t, e1=0, e2=0, center_x=0, center_y=0): """ mass enclosed 3d radius :param r: 3d radius :param alpha_1: deflection angle at 1 (arcseconds) from the center :param w_c: see Suyu+2014 :param w_t: see Suyu+2014 :param e1: ellipticity parameter :param e2: ellipticity parameter :param center_x: ra center :param center_y: dec center :return: mass enclosed 3d radius r """ theta_E_conv, w_c, w_t, s_scale_1, s_scale_2 = self.param_convert(alpha_1, w_c, w_t, e1, e2) m_1 = self._nie_1.mass_3d_lens(r, theta_E_conv, e1, e2, s_scale_1, center_x, center_y) m_2 = self._nie_2.mass_3d_lens(r, theta_E_conv, e1, e2, s_scale_2, center_x, center_y) m_ = m_1 - m_2 return m_
[docs] def param_convert(self, alpha_1, w_c, w_t, e1, e2): """ convert the parameter alpha_1 (deflection angle one arcsecond from the center) into the "Einstein radius" scale parameter of the two NIE profiles :param alpha_1: deflection angle at 1 (arcseconds) from the center :param w_c: see Suyu+2014 :param w_t: see Suyu+2014 :param e1: eccentricity modulus :param e2: eccentricity modulus :return: """ if self._static is True: return self._theta_convert_static, self._w_c_static, self._w_t_stactic, self._s_scale_1_static, self._s_scale_2_static return self._param_convert(alpha_1, w_c, w_t, e1, e2)
def _param_convert(self, alpha_1, w_c, w_t, e1, e2): if not w_t >= w_c: return 0, w_t, w_c, 1, 1 s_scale_1 = w_c s_scale_2 = w_t f_x_1, f_y_1 = self._nie_1.derivatives(1, 0, theta_E=1, e1=0, e2=0, s_scale=s_scale_1) f_x_2, f_y_2 = self._nie_2.derivatives(1, 0, theta_E=1, e1=0, e2=0, s_scale=s_scale_2) f_x = f_x_1 - f_x_2 theta_E_convert = alpha_1 / f_x phi_G, q = param_util.ellipticity2phi_q(e1, e2) s_scale_1 = np.sqrt(4 * w_c ** 2 / (1. + q) ** 2) s_scale_2 = np.sqrt(4 * w_t ** 2 / (1. + q) ** 2) return theta_E_convert, w_c, w_t, s_scale_1, s_scale_2
[docs] def set_static(self, alpha_1, w_c, w_t, e1, e2, center_x=0, center_y=0): """ :param alpha_1: :param w_c: :param w_t: :param e1: :param e2: :param center_x: :param center_y: :return: """ self._static = True self._theta_convert_static, self._w_c_static, self._w_t_stactic, self._s_scale_1_static, self._s_scale_2_static = self._param_convert(alpha_1, w_c, w_t, e1, e2) self._nie_1.set_static(self._theta_convert_static, e1, e2, self._s_scale_1_static, center_x, center_y) self._nie_2.set_static(self._theta_convert_static, e1, e2, self._s_scale_2_static, center_x, center_y)
[docs] def set_dynamic(self): """ :return: """ self._static = False if hasattr(self, '_theta_convert_static'): del self._theta_convert_static if hasattr(self, '_w_c_static'): del self._w_c_static if hasattr(self, '_w_t_stactic'): del self._w_t_stactic if hasattr(self, '_s_scale_1_static'): del self._s_scale_1_static if hasattr(self, '_s_scale_2_static'): del self._s_scale_2_static self._nie_1.set_dynamic() self._nie_2.set_dynamic()
[docs]@export class DoubleChameleon(LensProfileBase): """ class of the Chameleon model (See Suyu+2014) an elliptical truncated double isothermal profile """ param_names = ['alpha_1', 'ratio', 'w_c1', 'w_t1', 'e11', 'e21', 'w_c2', 'w_t2', 'e12', 'e22', 'center_x', 'center_y'] lower_limit_default = {'alpha_1': 0, 'ratio': 0, 'w_c1': 0, 'w_t1': 0, 'e11': -0.8, 'e21': -0.8, 'w_c2': 0, 'w_t2': 0, 'e12': -0.8, 'e22': -0.8, 'center_x': -100, 'center_y': -100} upper_limit_default = {'alpha_1': 100, 'ratio': 100, 'w_c1': 100, 'w_t1': 100, 'e11': 0.8, 'e21': 0.8, 'w_c2': 100, 'w_t2': 100, 'e12': 0.8, 'e22': 0.8, 'center_x': 100, 'center_y': 100} def __init__(self): self._chameleon_1 = Chameleon() self._chameleon_2 = Chameleon() super(DoubleChameleon, self).__init__()
[docs] def function(self, x, y, alpha_1, ratio, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x=0, center_y=0): """ :param x: ra-coordinate :param y: dec-coordinate :param alpha_1: deflection angle at 1 (arcseconds) from the center :param ratio: ratio of deflection amplitude at radius = 1 of the first to second Chameleon profile :param w_c1: Suyu+2014 for first profile :param w_t1: Suyu+2014 for first profile :param e11: ellipticity parameter for first profile :param e21: ellipticity parameter for first profile :param w_c2: Suyu+2014 for second profile :param w_t2: Suyu+2014 for second profile :param e12: ellipticity parameter for second profile :param e22: ellipticity parameter for second profile :param center_x: ra center :param center_y: dec center :return: lensing potential """ f_1 = self._chameleon_1.function(x, y, alpha_1 / (1. + 1. / ratio), w_c1, w_t1, e11, e21, center_x, center_y) f_2 = self._chameleon_2.function(x, y, alpha_1 / (1. + ratio), w_c2, w_t2, e12, e22, center_x, center_y) return f_1 + f_2
[docs] def derivatives(self, x, y, alpha_1, ratio, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x=0, center_y=0): """ :param x: ra-coordinate :param y: dec-coordinate :param alpha_1: deflection angle at 1 (arcseconds) from the center :param ratio: ratio of deflection amplitude at radius = 1 of the first to second Chameleon profile :param w_c1: Suyu+2014 for first profile :param w_t1: Suyu+2014 for first profile :param e11: ellipticity parameter for first profile :param e21: ellipticity parameter for first profile :param w_c2: Suyu+2014 for second profile :param w_t2: Suyu+2014 for second profile :param e12: ellipticity parameter for second profile :param e22: ellipticity parameter for second profile^V :param center_x: ra center :param center_y: dec center :return: deflection angles (RA, DEC) """ f_x1, f_y1 = self._chameleon_1.derivatives(x, y, alpha_1 / (1. + 1. / ratio), w_c1, w_t1, e11, e21, center_x, center_y) f_x2, f_y2 = self._chameleon_2.derivatives(x, y, alpha_1 / (1. + ratio), w_c2, w_t2, e12, e22, center_x, center_y) return f_x1 + f_x2, f_y1 + f_y2
[docs] def hessian(self, x, y, alpha_1, ratio, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x=0, center_y=0): """ :param x: ra-coordinate :param y: dec-coordinate :param alpha_1: deflection angle at 1 (arcseconds) from the center :param ratio: ratio of deflection amplitude at radius = 1 of the first to second Chameleon profile :param w_c1: Suyu+2014 for first profile :param w_t1: Suyu+2014 for first profile :param e11: ellipticity parameter for first profile :param e21: ellipticity parameter for first profile :param w_c2: Suyu+2014 for second profile :param w_t2: Suyu+2014 for second profile :param e12: ellipticity parameter for second profile :param e22: ellipticity parameter for second profile :param center_x: ra center :param center_y: dec center :return: second derivatives of the lensing potential (Hessian: f_xx, f_yy, f_xy) """ f_xx1, f_xy1, f_yx1, f_yy1, = self._chameleon_1.hessian(x, y, alpha_1 / (1. + 1. / ratio), w_c1, w_t1, e11, e21, center_x, center_y) f_xx2, f_xy2, f_yx2, f_yy2 = self._chameleon_2.hessian(x, y, alpha_1 / (1. + ratio), w_c2, w_t2, e12, e22, center_x, center_y) return f_xx1 + f_xx2, f_xy1 + f_xy2, f_xy1 + f_xy2, f_yy1 + f_yy2
[docs] def density_lens(self, r, alpha_1, ratio, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x=0, center_y=0): """ :param r: 3d radius :param alpha_1: deflection angle at 1 (arcseconds) from the center :param ratio: ratio of deflection amplitude at radius = 1 of the first to second Chameleon profile :param w_c1: Suyu+2014 for first profile :param w_t1: Suyu+2014 for first profile :param e11: ellipticity parameter for first profile :param e21: ellipticity parameter for first profile :param w_c2: Suyu+2014 for second profile :param w_t2: Suyu+2014 for second profile :param e12: ellipticity parameter for second profile :param e22: ellipticity parameter for second profile :param center_x: ra center :param center_y: dec center :return: 3d density at radius r """ f_1 = self._chameleon_1.density_lens(r, alpha_1 / (1. + 1. / ratio), w_c1, w_t1, e11, e21, center_x, center_y) f_2 = self._chameleon_2.density_lens(r, alpha_1 / (1. + ratio), w_c2, w_t2, e12, e22, center_x, center_y) return f_1 + f_2
[docs] def mass_3d_lens(self, r, alpha_1, ratio, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x=0, center_y=0): """ :param r: 3d radius :param alpha_1: deflection angle at 1 (arcseconds) from the center :param ratio: ratio of deflection amplitude at radius = 1 of the first to second Chameleon profile :param w_c1: Suyu+2014 for first profile :param w_t1: Suyu+2014 for first profile :param e11: ellipticity parameter for first profile :param e21: ellipticity parameter for first profile :param w_c2: Suyu+2014 for second profile :param w_t2: Suyu+2014 for second profile :param e12: ellipticity parameter for second profile :param e22: ellipticity parameter for second profile :param center_x: ra center :param center_y: dec center :return: mass enclosed 3d radius """ m_1 = self._chameleon_1.mass_3d_lens(r, alpha_1 / (1. + 1. / ratio), w_c1, w_t1, e11, e21, center_x, center_y) m_2 = self._chameleon_2.mass_3d_lens(r, alpha_1 / (1. + ratio), w_c2, w_t2, e12, e22, center_x, center_y) return m_1 + m_2
[docs] def set_static(self, alpha_1, ratio, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x=0, center_y=0): self._chameleon_1.set_static(alpha_1 / (1. + 1. / ratio), w_c1, w_t1, e11, e21, center_x, center_y) self._chameleon_2.set_static(alpha_1 / (1. + ratio), w_c2, w_t2, e12, e22, center_x, center_y)
[docs] def set_dynamic(self): self._chameleon_1.set_dynamic() self._chameleon_2.set_dynamic()
[docs]@export class TripleChameleon(LensProfileBase): """ class of the Chameleon model (See Suyu+2014) an elliptical truncated double isothermal profile """ param_names = ['alpha_1', 'ratio12', 'ratio13', 'w_c1', 'w_t1', 'e11', 'e21', 'w_c2', 'w_t2', 'e12', 'e22', 'w_c3', 'w_t3', 'e13', 'e23', 'center_x', 'center_y'] lower_limit_default = {'alpha_1': 0, 'ratio12': 0, 'ratio13': 0, 'w_c1': 0, 'w_t1': 0, 'e11': -0.8, 'e21': -0.8, 'w_c2': 0, 'w_t2': 0, 'e12': -0.8, 'e22': -0.8, 'w_c3': 0, 'w_t3': 0, 'e13': -0.8, 'e23': -0.8, 'center_x': -100, 'center_y': -100} upper_limit_default = {'alpha_1': 100, 'ratio12': 100, 'ratio13': 100, 'w_c1': 100, 'w_t1': 100, 'e11': 0.8, 'e21': 0.8, 'w_c2': 100, 'w_t2': 100, 'e12': 0.8, 'e22': 0.8, 'w_c3': 100, 'w_t3': 100, 'e13': 0.8, 'e23': 0.8, 'center_x': 100, 'center_y': 100} def __init__(self): self._chameleon_1 = Chameleon() self._chameleon_2 = Chameleon() self._chameleon_3 = Chameleon() super(TripleChameleon, self).__init__() @staticmethod def _ratio_definition(alpha_1, ratio12, ratio13): """ :param alpha_1: deflection angle at 1 arcsecond :param ratio12: ratio of first to second amplitude :param ratio13: ratio of first to third amplitude :return: amplitudes of individual chameleon profiles """ amp1 = alpha_1 / (1. + 1. / ratio12 + 1. / ratio13) amp2 = amp1 / ratio12 amp3 = amp1 / ratio13 return amp1, amp2, amp3
[docs] def function(self, x, y, alpha_1, ratio12, ratio13, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, w_c3, w_t3, e13, e23, center_x=0, center_y=0): """ :param alpha_1: :param ratio12: ratio of first to second amplitude :param ratio13: ratio of first to third amplitude :param w_c1: :param w_t1: :param e11: :param e21: :param w_c2: :param w_t2: :param e12: :param e22: :param center_x: :param center_y: :return: """ amp1, amp2, amp3 = self._ratio_definition(alpha_1, ratio12, ratio13) f_1 = self._chameleon_1.function(x, y, amp1, w_c1, w_t1, e11, e21, center_x, center_y) f_2 = self._chameleon_2.function(x, y, amp2, w_c2, w_t2, e12, e22, center_x, center_y) f_3 = self._chameleon_3.function(x, y, amp3, w_c3, w_t3, e13, e23, center_x, center_y) return f_1 + f_2 + f_3
[docs] def derivatives(self, x, y, alpha_1, ratio12, ratio13, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, w_c3, w_t3, e13, e23, center_x=0, center_y=0): """ :param alpha_1: :param ratio12: ratio of first to second amplitude :param ratio13: ratio of first to third amplidute :param w_c1: :param w_t1: :param e11: :param e21: :param w_c2: :param w_t2: :param e12: :param e22: :param center_x: :param center_y: :return: """ amp1, amp2, amp3 = self._ratio_definition(alpha_1, ratio12, ratio13) f_x1, f_y1 = self._chameleon_1.derivatives(x, y, amp1, w_c1, w_t1, e11, e21, center_x, center_y) f_x2, f_y2 = self._chameleon_2.derivatives(x, y, amp2, w_c2, w_t2, e12, e22, center_x, center_y) f_x3, f_y3 = self._chameleon_3.derivatives(x, y, amp3, w_c3, w_t3, e13, e23, center_x, center_y) return f_x1 + f_x2 + f_x3, f_y1 + f_y2 + f_y3
[docs] def hessian(self, x, y, alpha_1, ratio12, ratio13, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, w_c3, w_t3, e13, e23, center_x=0, center_y=0): """ :param alpha_1: :param ratio12: ratio of first to second amplitude :param ratio13: ratio of first to third amplidute :param w_c1: :param w_t1: :param e11: :param e21: :param w_c2: :param w_t2: :param e12: :param e22: :param center_x: :param center_y: :return: """ amp1, amp2, amp3 = self._ratio_definition(alpha_1, ratio12, ratio13) f_xx1, f_xy1, f_yx1, f_yy1 = self._chameleon_1.hessian(x, y, amp1, w_c1, w_t1, e11, e21, center_x, center_y) f_xx2, f_xy2, f_yx2, f_yy2 = self._chameleon_2.hessian(x, y, amp2, w_c2, w_t2, e12, e22, center_x, center_y) f_xx3, f_xy3, f_yx3, f_yy3 = self._chameleon_3.hessian(x, y, amp3, w_c3, w_t3, e13, e23, center_x, center_y) return f_xx1 + f_xx2 + f_xx3, f_xy1 + f_xy2 + f_xy3, f_yx1 + f_yx2 + f_yx3, f_yy1 + f_yy2 + f_yy3
[docs] def density_lens(self, r, alpha_1, ratio12, ratio13, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, w_c3, w_t3, e13, e23, center_x=0, center_y=0): """ :param r: 3d radius :param alpha_1: :param ratio12: ratio of first to second amplitude :param ratio13: ratio of first to third amplitude :param w_c1: :param w_t1: :param e11: :param e21: :param w_c2: :param w_t2: :param e12: :param e22: :param center_x: :param center_y: :return: density at radius r (spherical average) """ amp1, amp2, amp3 = self._ratio_definition(alpha_1, ratio12, ratio13) f_1 = self._chameleon_1.density_lens(r, amp1, w_c1, w_t1, e11, e21, center_x, center_y) f_2 = self._chameleon_2.density_lens(r, amp2, w_c2, w_t2, e12, e22, center_x, center_y) f_3 = self._chameleon_3.density_lens(r, amp3, w_c3, w_t3, e13, e23, center_x, center_y) return f_1 + f_2 + f_3
[docs] def mass_3d_lens(self, r, alpha_1, ratio12, ratio13, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, w_c3, w_t3, e13, e23, center_x=0, center_y=0): """ :param r: 3d radius :param alpha_1: :param ratio12: ratio of first to second amplitude :param ratio13: ratio of first to third amplitude :param w_c1: :param w_t1: :param e11: :param e21: :param w_c2: :param w_t2: :param e12: :param e22: :param center_x: :param center_y: :return: mass enclosed 3d radius """ amp1, amp2, amp3 = self._ratio_definition(alpha_1, ratio12, ratio13) m_1 = self._chameleon_1.mass_3d_lens(r, amp1, w_c1, w_t1, e11, e21, center_x, center_y) m_2 = self._chameleon_2.mass_3d_lens(r, amp2, w_c2, w_t2, e12, e22, center_x, center_y) m_3 = self._chameleon_3.mass_3d_lens(r, amp3, w_c3, w_t3, e13, e23, center_x, center_y) return m_1 + m_2 + m_3
[docs] def set_static(self, alpha_1, ratio12, ratio13, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, w_c3, w_t3, e13, e23, center_x=0, center_y=0): amp1, amp2, amp3 = self._ratio_definition(alpha_1, ratio12, ratio13) self._chameleon_1.set_static(amp1, w_c1, w_t1, e11, e21, center_x, center_y) self._chameleon_2.set_static(amp2, w_c2, w_t2, e12, e22, center_x, center_y) self._chameleon_3.set_static(amp3, w_c3, w_t3, e13, e23, center_x, center_y)
[docs] def set_dynamic(self): self._chameleon_1.set_dynamic() self._chameleon_2.set_dynamic() self._chameleon_3.set_dynamic()
[docs]@export class DoubleChameleonPointMass(LensProfileBase): """ class of the Chameleon model (See Suyu+2014) an elliptical truncated double isothermal profile """ param_names = ['alpha_1', 'ratio_chameleon', 'ratio_pointmass', 'w_c1', 'w_t1', 'e11', 'e21', 'w_c2', 'w_t2', 'e12', 'e22', 'center_x', 'center_y'] lower_limit_default = {'alpha_1': 0, 'ratio_chameleon': 0, 'ratio_pointmass': 0, 'w_c1': 0, 'w_t1': 0, 'e11': -0.8, 'e21': -0.8, 'w_c2': 0, 'w_t2': 0, 'e12': -0.8, 'e22': -0.8, 'center_x': -100, 'center_y': -100} upper_limit_default = {'alpha_1': 100, 'ratio_chameleon': 100, 'ratio_pointmass': 100, 'w_c1': 100, 'w_t1': 100, 'e11': 0.8, 'e21': 0.8, 'w_c2': 100, 'w_t2': 100, 'e12': 0.8, 'e22': 0.8, 'center_x': 100, 'center_y': 100} def __init__(self): self.chameleon = DoubleChameleon() self.pointMass = PointMass() super(DoubleChameleonPointMass, self).__init__()
[docs] def function(self, x, y, alpha_1, ratio_pointmass, ratio_chameleon, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x=0, center_y=0): """ #TODO chose better parameterization for combining point mass and Chameleon profiles :param x: ra-coordinate :param y: dec-coordinate :param alpha_1: deflection angle at 1 (arcseconds) from the center :param ratio_pointmass: ratio of point source Einstein radius to combined Chameleon deflection angle at r=1 :param ratio_chameleon: ratio in deflection angles at r=1 for the two Chameleon profiles :param w_c1: Suyu+2014 for first profile :param w_t1: Suyu+2014 for first profile :param e11: ellipticity parameter for first profile :param e21: ellipticity parameter for first profile :param w_c2: Suyu+2014 for second profile :param w_t2: Suyu+2014 for second profile :param e12: ellipticity parameter for second profile :param e22: ellipticity parameter for second profile :param center_x: ra center :param center_y: dec center :return: """ f_1 = self.pointMass.function(x, y, alpha_1 / (1. + 1. / ratio_pointmass), center_x, center_y) f_2 = self.chameleon.function(x, y, alpha_1 / (1. + ratio_pointmass), ratio_chameleon, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x, center_y) return f_1 + f_2
[docs] def derivatives(self, x, y, alpha_1, ratio_pointmass, ratio_chameleon, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x=0, center_y=0): """ :param x: :param y: :param alpha_1: :param ratio_pointmass: ratio of point source Einstein radius to combined Chameleon deflection angle at r=1 :param ratio_chameleon: ratio in deflection angles at r=1 for the two Chameleon profiles :param w_c1: Suyu+2014 for first profile :param w_t1: Suyu+2014 for first profile :param e11: ellipticity parameter for first profile :param e21: ellipticity parameter for first profile :param w_c2: Suyu+2014 for second profile :param w_t2: Suyu+2014 for second profile :param e12: ellipticity parameter for second profile :param e22: ellipticity parameter for second profile :param center_x: ra center :param center_y: dec center :return: """ f_x1, f_y1 = self.pointMass.derivatives(x, y, alpha_1 / (1. + 1. / ratio_pointmass), center_x, center_y) f_x2, f_y2 = self.chameleon.derivatives(x, y, alpha_1 / (1. + ratio_pointmass), ratio_chameleon, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x, center_y) return f_x1 + f_x2, f_y1 + f_y2
[docs] def hessian(self, x, y, alpha_1, ratio_pointmass, ratio_chameleon, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x=0, center_y=0): """ :param x: :param y: :param alpha_1: :param ratio_pointmass: ratio of point source Einstein radius to combined Chameleon deflection angle at r=1 :param ratio_chameleon: ratio in deflection angles at r=1 for the two Chameleon profiles :param w_c1: Suyu+2014 for first profile :param w_t1: Suyu+2014 for first profile :param e11: ellipticity parameter for first profile :param e21: ellipticity parameter for first profile :param w_c2: Suyu+2014 for second profile :param w_t2: Suyu+2014 for second profile :param e12: ellipticity parameter for second profile :param e22: ellipticity parameter for second profile :param center_x: ra center :param center_y: dec center :return: """ f_xx1, f_xy1, f_yx1, f_yy1 = self.pointMass.hessian(x, y, alpha_1 / (1. + 1. / ratio_pointmass), center_x, center_y) f_xx2, f_xy2, f_yx2, f_yy2 = self.chameleon.hessian(x, y, alpha_1 / (1. + ratio_pointmass), ratio_chameleon, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x, center_y) return f_xx1 + f_xx2, f_xy1 + f_xy2, f_yx1 + f_yx2, f_yy1 + f_yy2