__author__ = "sibirrer"
import numpy as np
from lenstronomy.LensModel.profile_list_base import ProfileListBase
__all__ = ["SinglePlane"]
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class SinglePlane(ProfileListBase):
"""Class to handle an arbitrary list of lens models in a single lensing plane."""
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def ray_shooting(self, x, y, kwargs, k=None):
"""Maps image to source position (inverse deflection).
:param x: x-position (preferentially arcsec)
:type x: numpy array
:param y: y-position (preferentially arcsec)
:type y: numpy array
:param kwargs: list of keyword arguments of lens model parameters matching the
lens model classes
:param k: only evaluate the k-th lens model
:return: source plane positions corresponding to (x, y) in the image plane
"""
dx, dy = self.alpha(x, y, kwargs, k=k)
return x - dx, y - dy
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def fermat_potential(
self, x_image, y_image, kwargs_lens, x_source=None, y_source=None, k=None
):
"""Fermat potential (negative sign means earlier arrival time)
:param x_image: image position
:param y_image: image position
:param x_source: source position
:param y_source: source position
:param kwargs_lens: list of keyword arguments of lens model parameters matching
the lens model classes
:param k:
:return: fermat potential in arcsec**2 without geometry term (second part of Eqn
1 in Suyu et al. 2013) as a list
"""
potential = self.potential(x_image, y_image, kwargs_lens, k=k)
if x_source is None or y_source is None:
x_source, y_source = self.ray_shooting(x_image, y_image, kwargs_lens, k=k)
geometry = ((x_image - x_source) ** 2 + (y_image - y_source) ** 2) / 2.0
return geometry - potential
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def potential(self, x, y, kwargs, k=None):
"""Lensing potential.
:param x: x-position (preferentially arcsec)
:type x: numpy array
:param y: y-position (preferentially arcsec)
:type y: numpy array
:param kwargs: list of keyword arguments of lens model parameters matching the
lens model classes
:param k: only evaluate the k-th lens model
:return: lensing potential in units of arcsec^2
"""
x = np.array(x, dtype=float)
y = np.array(y, dtype=float)
if isinstance(k, int):
return self.func_list[k].function(x, y, **kwargs[k])
bool_list = self._bool_list(k)
potential = np.zeros_like(x)
for i, func in enumerate(self.func_list):
if bool_list[i] is True:
potential += func.function(x, y, **kwargs[i])
return potential
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def alpha(self, x, y, kwargs, k=None):
"""Deflection angles.
:param x: x-position (preferentially arcsec)
:type x: numpy array
:param y: y-position (preferentially arcsec)
:type y: numpy array
:param kwargs: list of keyword arguments of lens model parameters matching the
lens model classes
:param k: only evaluate the k-th lens model
:return: deflectionangles in units of arcsec
"""
x = np.array(x, dtype=float)
y = np.array(y, dtype=float)
if isinstance(k, int):
return self.func_list[k].derivatives(x, y, **kwargs[k])
bool_list = self._bool_list(k)
f_x, f_y = np.zeros_like(x), np.zeros_like(x)
for i, func in enumerate(self.func_list):
if bool_list[i] is True:
f_x_i, f_y_i = func.derivatives(x, y, **kwargs[i])
f_x += f_x_i
f_y += f_y_i
return f_x, f_y
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def hessian(self, x, y, kwargs, k=None):
"""Hessian matrix.
:param x: x-position (preferentially arcsec)
:type x: numpy array
:param y: y-position (preferentially arcsec)
:type y: numpy array
:param kwargs: list of keyword arguments of lens model parameters matching the
lens model classes
:param k: only evaluate the k-th lens model
:return: f_xx, f_xy, f_yx, f_yy components
"""
x = np.array(x, dtype=float)
y = np.array(y, dtype=float)
if isinstance(k, int):
f_xx, f_xy, f_yx, f_yy = self.func_list[k].hessian(x, y, **kwargs[k])
return f_xx, f_xy, f_yx, f_yy
bool_list = self._bool_list(k)
f_xx, f_xy, f_yx, f_yy = (
np.zeros_like(x),
np.zeros_like(x),
np.zeros_like(x),
np.zeros_like(x),
)
for i, func in enumerate(self.func_list):
if bool_list[i] is True:
f_xx_i, f_xy_i, f_yx_i, f_yy_i = func.hessian(x, y, **kwargs[i])
f_xx += f_xx_i
f_xy += f_xy_i
f_yx += f_yx_i
f_yy += f_yy_i
return f_xx, f_xy, f_yx, f_yy
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def mass_3d(self, r, kwargs, bool_list=None):
"""Computes the mass within a 3d sphere of radius r.
if you want to have physical units of kg, you need to multiply by this factor:
const.arcsec ** 2 * self._cosmo.dd * self._cosmo.ds / self._cosmo.dds *
const.Mpc * const.c ** 2 / (4 * np.pi * const.G) grav_pot = -const.G * mass_dim
/ (r * const.arcsec * self._cosmo.dd * const.Mpc)
:param r: radius (in angular units)
:param kwargs: list of keyword arguments of lens model parameters matching the
lens model classes
:param bool_list: list of bools that are part of the output
:return: mass (in angular units, modulo epsilon_crit)
"""
bool_list = self._bool_list(bool_list)
mass_3d = 0
for i, func in enumerate(self.func_list):
if bool_list[i] is True:
kwargs_i = {
k: v
for k, v in kwargs[i].items()
if k not in ["center_x", "center_y"]
}
mass_3d_i = func.mass_3d_lens(r, **kwargs_i)
mass_3d += mass_3d_i
return mass_3d
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def mass_2d(self, r, kwargs, bool_list=None):
"""Computes the mass enclosed a projected (2d) radius r.
The mass definition is such that:
.. math::
\\alpha = mass_2d / r / \\pi
with alpha is the deflection angle
:param r: radius (in angular units)
:param kwargs: list of keyword arguments of lens model parameters matching the
lens model classes
:param bool_list: list of bools that are part of the output
:return: projected mass (in angular units, modulo epsilon_crit)
"""
bool_list = self._bool_list(bool_list)
mass_2d = 0
for i, func in enumerate(self.func_list):
if bool_list[i] is True:
kwargs_i = {
k: v
for k, v in kwargs[i].items()
if k not in ["center_x", "center_y"]
}
mass_2d_i = func.mass_2d_lens(r, **kwargs_i)
mass_2d += mass_2d_i
return mass_2d
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def density(self, r, kwargs, bool_list=None):
"""3d mass density at radius r The integral in the LOS projection of this
quantity results in the convergence quantity.
:param r: radius (in angular units)
:param kwargs: list of keyword arguments of lens model parameters matching the
lens model classes
:param bool_list: list of bools that are part of the output
:return: mass density at radius r (in angular units, modulo epsilon_crit)
"""
bool_list = self._bool_list(bool_list)
density = 0
for i, func in enumerate(self.func_list):
if bool_list[i] is True:
kwargs_i = {
k: v
for k, v in kwargs[i].items()
if k not in ["center_x", "center_y"]
}
density_i = func.density_lens(r, **kwargs_i)
density += density_i
return density