__author__ = 'sibirrer'
from lenstronomy.LensModel.Profiles.spp import SPP
from lenstronomy.LensModel.Profiles.spemd import SPEMD
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
__all__ = ['PEMD']
[docs]class PEMD(LensProfileBase):
"""
class for power law ellipse mass density profile.
This class effectively calls the class SPEMD_SMOOTH with a fixed and very small central smoothing scale
to perform the numerical integral using the FASTELL code by Renan Barkana.
.. math::
\\kappa(x, y) = \\frac{3-\\gamma}{2} \\left(\\frac{\\theta_{E}}{\\sqrt{q x^2 + y^2/q}} \\right)^{\\gamma-1}
with :math:`\\theta_{E}` is the (circularized) Einstein radius,
:math:`\\gamma` is the negative power-law slope of the 3D mass distributions,
:math:`q` is the minor/major axis ratio,
and :math:`x` and :math:`y` are defined in a coordinate system aligned with the major and minor axis of the lens.
In terms of eccentricities, this profile is defined as
.. math::
\\kappa(r) = \\frac{3-\\gamma}{2} \\left(\\frac{\\theta'_{E}}{r \\sqrt{1 − e*\\cos(2*\\phi)}} \\right)^{\\gamma-1}
with :math:`\\epsilon` is the ellipticity defined as
.. math::
\\epsilon = \\frac{1-q^2}{1+q^2}
And an Einstein radius :math:`\\theta'_{\\rm E}` related to the definition used is
.. math::
\\left(\\frac{\\theta'_{\\rm E}}{\\theta_{\\rm E}}\\right)^{2} = \\frac{2q}{1+q^2}.
"""
param_names = ['theta_E', 'gamma', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {'theta_E': 0, 'gamma': 1.5, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100}
upper_limit_default = {'theta_E': 100, 'gamma': 2.5, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100}
def __init__(self, suppress_fastell=False):
"""
:param suppress_fastell: bool, if True, does not raise if fastell4py is not installed
"""
self._s_scale = 0.0001 # smoothing scale as used to numerically compute a power-law profile
self.spp = SPP()
self.spemd_smooth = SPEMD(suppress_fastell=suppress_fastell)
super(PEMD, self).__init__()
[docs] def function(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate (angle)
:param y: y-coordinate (angle)
:param theta_E: Einstein radius (angle), pay attention to specific definition!
:param gamma: logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: x-position of lens center
:param center_y: y-position of lens center
:return: lensing potential
"""
return self.spemd_smooth.function(x, y, theta_E, gamma, e1, e2, self._s_scale, center_x, center_y)
[docs] def derivatives(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate (angle)
:param y: y-coordinate (angle)
:param theta_E: Einstein radius (angle), pay attention to specific definition!
:param gamma: logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: x-position of lens center
:param center_y: y-position of lens center
:return: deflection angles alpha_x, alpha_y
"""
return self.spemd_smooth.derivatives(x, y, theta_E, gamma, e1, e2, self._s_scale, center_x, center_y)
[docs] def hessian(self, x, y, theta_E, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: x-coordinate (angle)
:param y: y-coordinate (angle)
:param theta_E: Einstein radius (angle), pay attention to specific definition!
:param gamma: logarithmic slope of the power-law profile. gamma=2 corresponds to isothermal
:param e1: eccentricity component
:param e2: eccentricity component
:param center_x: x-position of lens center
:param center_y: y-position of lens center
:return: Hessian components f_xx, f_xy, f_yx, f_yy
"""
return self.spemd_smooth.hessian(x, y, theta_E, gamma, e1, e2, self._s_scale, center_x, center_y)
[docs] def mass_3d_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the spherical power-law mass enclosed (with SPP routine)
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.mass_3d_lens(r, theta_E, gamma)
[docs] def density_lens(self, r, theta_E, gamma, e1=None, e2=None):
"""
computes the density at 3d radius r given lens model parameterization.
The integral in the LOS projection of this quantity results in the convergence quantity.
:param r: radius within the mass is computed
:param theta_E: Einstein radius
:param gamma: power-law slope
:param e1: eccentricity component (not used)
:param e2: eccentricity component (not used)
:return: mass enclosed a 3D radius r
"""
return self.spp.density_lens(r, theta_E, gamma)