-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:
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:param ratio12: ratio of first to second amplitude
-
:param ratio13: ratio of first to third amplidute
-
:param w_c1:
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:param w_t1:
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:param e11:
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:param e21:
-
:param w_c2:
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:param w_t2:
-
:param e12:
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:param e22:
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:param center_x:
-
:param center_y:
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:return:
-
"""
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amp1, amp2, amp3 = self._ratio_definition(alpha_1, ratio12, ratio13)
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f_x1, f_y1 = self._chameleon_1.derivatives(x, y, amp1, w_c1, w_t1, e11, e21, center_x, center_y)
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f_x2, f_y2 = self._chameleon_2.derivatives(x, y, amp2, w_c2, w_t2, e12, e22, center_x, center_y)
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f_x3, f_y3 = self._chameleon_3.derivatives(x, y, amp3, w_c3, w_t3, e13, e23, center_x, center_y)
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return f_x1 + f_x2 + f_x3, f_y1 + f_y2 + f_y3
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[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,
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center_x=0, center_y=0):
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"""
-
-
:param alpha_1:
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:param ratio12: ratio of first to second amplitude
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:param ratio13: ratio of first to third amplidute
-
:param w_c1:
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:param w_t1:
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:param e11:
-
:param e21:
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:param w_c2:
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:param w_t2:
-
:param e12:
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:param e22:
-
:param center_x:
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:param center_y:
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:return:
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"""
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amp1, amp2, amp3 = self._ratio_definition(alpha_1, ratio12, ratio13)
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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)
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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)
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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)
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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
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[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,
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center_x=0, center_y=0):
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"""
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-
:param r: 3d radius
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:param alpha_1:
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:param ratio12: ratio of first to second amplitude
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:param ratio13: ratio of first to third amplitude
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:param w_c1:
-
:param w_t1:
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:param e11:
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:param e21:
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:param w_c2:
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:param w_t2:
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:param e12:
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:param e22:
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:param center_x:
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:param center_y:
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:return: density at radius r (spherical average)
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"""
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amp1, amp2, amp3 = self._ratio_definition(alpha_1, ratio12, ratio13)
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f_1 = self._chameleon_1.density_lens(r, amp1, w_c1, w_t1, e11, e21, center_x, center_y)
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f_2 = self._chameleon_2.density_lens(r, amp2, w_c2, w_t2, e12, e22, center_x, center_y)
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f_3 = self._chameleon_3.density_lens(r, amp3, w_c3, w_t3, e13, e23, center_x, center_y)
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return f_1 + f_2 + f_3
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[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,
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center_x=0, center_y=0):
-
"""
-
-
:param r: 3d radius
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:param alpha_1:
-
:param ratio12: ratio of first to second amplitude
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: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
-
"""
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amp1, amp2, amp3 = self._ratio_definition(alpha_1, ratio12, ratio13)
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m_1 = self._chameleon_1.mass_3d_lens(r, amp1, w_c1, w_t1, e11, e21, center_x, center_y)
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m_2 = self._chameleon_2.mass_3d_lens(r, amp2, w_c2, w_t2, e12, e22, center_x, center_y)
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m_3 = self._chameleon_3.mass_3d_lens(r, amp3, w_c3, w_t3, e13, e23, center_x, center_y)
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return m_1 + m_2 + m_3
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-
[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)
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self._chameleon_1.set_static(amp1, w_c1, w_t1, e11, e21, center_x, center_y)
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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']
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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
-
