# mypy: disable-error-code="operator,dict-item"
from typing import Optional, Union, Annotated
from caskade import forward, Param
from ..backend_obj import backend, ArrayLike
from .base import ThinLens, CosmologyType, NameType, ZType
from . import func
__all__ = ("Multipole",)
[docs]
class Multipole(ThinLens):
"""
Represents a multipole effect in a gravitational lensing system.
Attributes
----------
name: str
Identifier for the lens instance.
cosmology: Cosmology
The cosmological model used for lensing calculations.
m: Union[ArrayLike, int, tuple[int]]
Order of multipole(s).
z_l: Optional[Union[ArrayLike, float]]
The redshift of the lens.
x0, y0: Optional[Union[ArrayLike, float]]
Coordinates of the shear center in the lens plane.
a_m: Optional[Union[ArrayLike, float]]
Strength of multipole.
phi_m: Optional[Union[ArrayLike, float]]
Orientation of multipole.
"""
_null_params = {"x0": 0.0, "y0": 0.0, "a_m": 1.0, "phi_m": 0.0, "m": 2}
def __init__(
self,
cosmology: CosmologyType,
m: Annotated[Union[ArrayLike, int, tuple[int]], "The Multipole moment(s) m"],
z_l: ZType = None,
z_s: ZType = None,
x0: Annotated[
Optional[Union[ArrayLike, float]],
"The x-coordinate of the lens center",
True,
] = None,
y0: Annotated[
Optional[Union[ArrayLike, float]],
"The y-coordinate of the lens center",
True,
] = None,
a_m: Annotated[
Optional[Union[ArrayLike, float]], "The amplitude of the multipole", True
] = None,
phi_m: Annotated[
Optional[Union[ArrayLike, float]],
"The orientation angle of the multipole",
True,
] = None,
name: NameType = None,
):
super().__init__(cosmology, z_l, name=name, z_s=z_s)
self.x0 = Param("x0", x0, shape=(), units="arcsec")
self.y0 = Param("y0", y0, shape=(), units="arcsec")
self.m = backend.as_array(m, dtype=backend.int32)
assert backend.all(self.m >= 2).item(), "Multipole order must be >= 2"
self.a_m = Param("a_m", a_m, self.m.shape, units="unitless")
self.phi_m = Param(
"phi_m",
phi_m,
self.m.shape,
units="radians",
valid=(0, 2 * backend.pi),
cyclic=True,
)
[docs]
def to(self, device=None, dtype=None):
"""
Move the lens to the specified device.
Parameters
----------
device: optional
The device to move the lens to.
dtype: optional
The data type to cast the lens to.
Returns
-------
Multipole
The lens object.
"""
super().to(device, dtype)
self.m = backend.to(self.m, device=device, dtype=backend.int32)
return self
[docs]
@forward
def reduced_deflection_angle(
self,
x: ArrayLike,
y: ArrayLike,
x0: Annotated[ArrayLike, "Param"],
y0: Annotated[ArrayLike, "Param"],
a_m: Annotated[ArrayLike, "Param"],
phi_m: Annotated[ArrayLike, "Param"],
) -> tuple[ArrayLike, ArrayLike]:
"""
Calculate the deflection angle of the multipole.
Parameters
----------
x: ArrayLike
The x-coordinate of the lens.
*Unit: arcsec*
y: ArrayLike
The y-coordinate of the lens.
*Unit: arcsec*
Returns
-------
x_component: ArrayLike
Deflection Angle
*Unit: arcsec*
y_component: ArrayLike
Deflection Angle
*Unit: arcsec*
Equation (B11) and (B12) https://arxiv.org/pdf/1307.4220, Xu et al. 2014
"""
return func.reduced_deflection_angle_multipole(x0, y0, self.m, a_m, phi_m, x, y)
[docs]
@forward
def potential(
self,
x: ArrayLike,
y: ArrayLike,
x0: Annotated[ArrayLike, "Param"],
y0: Annotated[ArrayLike, "Param"],
a_m: Annotated[ArrayLike, "Param"],
phi_m: Annotated[ArrayLike, "Param"],
) -> ArrayLike:
"""
Compute the lensing potential of the multiplane.
Parameters
----------
x: ArrayLike
The x-coordinate of the lens.
*Unit: arcsec*
y: ArrayLike
The y-coordinate of the lens.
*Unit: arcsec*
Returns
-------
ArrayLike
The lensing potential.
*Unit: arcsec^2*
Equation (B11) and (B3) https://arxiv.org/pdf/1307.4220, Xu et al. 2014
"""
return func.potential_multipole(x0, y0, self.m, a_m, phi_m, x, y)
[docs]
@forward
def convergence(
self,
x: ArrayLike,
y: ArrayLike,
x0: Annotated[ArrayLike, "Param"],
y0: Annotated[ArrayLike, "Param"],
a_m: Annotated[ArrayLike, "Param"],
phi_m: Annotated[ArrayLike, "Param"],
) -> ArrayLike:
"""
Calculate the projected mass density of the multipole.
Parameters
----------
x: ArrayLike
The x-coordinate of the lens.
*Unit: arcsec*
y: ArrayLike
The y-coordinate of the lens.
*Unit: arcsec*
Returns
-------
ArrayLike
The projected mass density.
*Unit: unitless*
Equation (B10) and (B3) https://arxiv.org/pdf/1307.4220, Xu et al. 2014
"""
return func.convergence_multipole(x0, y0, self.m, a_m, phi_m, x, y)
