from lenstronomy.LensModel.Profiles.p_jaffe import PJaffe
import lenstronomy.Util.param_util as param_util
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
import numpy as np
__all__ = ["PJaffe_Ellipse"]
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class PJaffe_Ellipse(LensProfileBase):
"""
class to compute the DUAL PSEUDO ISOTHERMAL ELLIPTICAL MASS DISTRIBUTION
based on Eliasdottir (2007) https://arxiv.org/pdf/0710.5636.pdf Appendix A
with the ellipticity implemented in the potential
Module name: 'PJAFFE_ELLIPSE';
An alternative name is dPIED.
The 3D density distribution is
.. math::
\\rho(r) = \\frac{\\rho_0}{(1+r^2/Ra^2)(1+r^2/Rs^2)}
with :math:`Rs > Ra`.
The projected density is
.. math::
\\Sigma(R) = \\Sigma_0 \\frac{Ra Rs}{Rs-Ra}\\left(\\frac{1}{\\sqrt{Ra^2+R^2}} - \\frac{1}{\\sqrt{Rs^2+R^2}} \\right)
with
.. math::
\\Sigma_0 = \\pi \\rho_0 \\frac{Ra Rs}{Rs + Ra}
In the lensing parameterization,
.. math::
\\sigma_0 = \\frac{\\Sigma_0}{\\Sigma_{\\rm crit}}
"""
param_names = ["sigma0", "Ra", "Rs", "e1", "e2", "center_x", "center_y"]
lower_limit_default = {
"sigma0": 0,
"Ra": 0,
"Rs": 0,
"e1": -0.5,
"e2": -0.5,
"center_x": -100,
"center_y": -100,
}
upper_limit_default = {
"sigma0": 10,
"Ra": 100,
"Rs": 100,
"e1": 0.5,
"e2": 0.5,
"center_x": 100,
"center_y": 100,
}
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def __init__(self):
self.spherical = PJaffe()
self._diff = 0.000001
super(PJaffe_Ellipse, self).__init__()
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def function(self, x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0):
"""Returns double integral of NFW profile."""
x_, y_ = param_util.transform_e1e2_square_average(
x, y, e1, e2, center_x, center_y
)
f_ = self.spherical.function(x_, y_, sigma0, Ra, Rs)
return f_
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def derivatives(self, x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0):
"""Returns df/dx and df/dy of the function (integral of NFW)"""
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
x_, y_ = param_util.transform_e1e2_square_average(
x, y, e1, e2, center_x, center_y
)
e = param_util.q2e(q)
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
f_x_prim, f_y_prim = self.spherical.derivatives(
x_, y_, sigma0, Ra, Rs, center_x=0, center_y=0
)
f_x_prim *= np.sqrt(1 - e)
f_y_prim *= np.sqrt(1 + e)
f_x = cos_phi * f_x_prim - sin_phi * f_y_prim
f_y = sin_phi * f_x_prim + cos_phi * f_y_prim
return f_x, f_y
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def hessian(self, x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0):
"""Returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx,
d^f/dy^2."""
alpha_ra, alpha_dec = self.derivatives(
x, y, sigma0, Ra, Rs, e1, e2, center_x, center_y
)
diff = self._diff
alpha_ra_dx, alpha_dec_dx = self.derivatives(
x + diff, y, sigma0, Ra, Rs, e1, e2, center_x, center_y
)
alpha_ra_dy, alpha_dec_dy = self.derivatives(
x, y + diff, sigma0, Ra, Rs, e1, e2, center_x, center_y
)
f_xx = (alpha_ra_dx - alpha_ra) / diff
f_xy = (alpha_ra_dy - alpha_ra) / diff
f_yx = (alpha_dec_dx - alpha_dec) / diff
f_yy = (alpha_dec_dy - alpha_dec) / diff
return f_xx, f_xy, f_yx, f_yy
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def mass_3d_lens(self, r, sigma0, Ra, Rs, e1=0, e2=0):
"""
:param r:
:param sigma0:
:param Ra:
:param Rs:
:param e1:
:param e2:
:return:
"""
return self.spherical.mass_3d_lens(r, sigma0, Ra, Rs)