import torch
from ...param import forward
from ...backend_obj import ArrayLike
from ...utils.decorators import ignore_numpy_warnings
from .._shared_methods import parametric_initialize, parametric_segment_initialize
from ...utils.parametric_profiles import exponential_np
from .. import func
def _x0_func(model_params, R, F):
return R[4], 10 ** F[4]
[docs]
class ExponentialMixin:
"""Exponential radial light profile.
An exponential is a classical radial model used in many contexts. The
functional form of the exponential profile is defined as:
.. math::
I(R) = I_e \\exp\\left(- b_1\\left(\\frac{R}{R_e} - 1\\right)\\right)
Ie is the brightness at the effective radius, and Re is the effective
radius. :math:`b_1` is a constant that ensures :math:`I_e` is the brightness at :math:`R_e`.
:param Re: effective radius, radius enclosing half the total light
:param Ie: effective surface density, brightness at the effective radius
"""
_model_type = "exponential"
_parameter_specs = {
"Re": {
"units": "arcsec",
"valid": (0, None),
"shape": (),
"dynamic": True,
"description": "effective radius, radius enclosing half the total light",
},
"Ie": {
"units": "flux/arcsec^2",
"valid": (0, None),
"shape": (),
"dynamic": True,
"description": "effective surface density, brightness at the effective radius",
},
}
[docs]
@torch.no_grad()
@ignore_numpy_warnings
def initialize(self):
super().initialize()
parametric_initialize(
self,
self.target[self.window],
exponential_np,
("Re", "Ie"),
_x0_func,
)
[docs]
@forward
def radial_model(self, R: ArrayLike, Re: ArrayLike, Ie: ArrayLike) -> ArrayLike:
return func.exponential(R, Re, Ie)
[docs]
class iExponentialMixin:
"""Exponential radial light profile.
An exponential is a classical radial model used in many contexts. The
functional form of the exponential profile is defined as:
.. math::
I(R) = I_e \\exp\\left(- b_1\\left(\\frac{R}{R_e} - 1\\right)\\right)
:math:`I_e` is the brightness at the effective radius, and :math:`R_e` is the effective
radius. :math:`b_1` is a constant that ensures :math:`I_e` is the brightness at :math:`R_e`.
``Re`` and ``Ie`` are batched by their first dimension, allowing for multiple
exponential profiles to be defined at once.
:param Re: effective radius, radius enclosing half the total light
:param Ie: effective surface density, brightness at the effective radius
"""
_model_type = "exponential"
_parameter_specs = {
"Re": {
"units": "arcsec",
"valid": (0, None),
"shape": (None,),
"dynamic": True,
"description": "effective radius, radius enclosing half the total light",
},
"Ie": {
"units": "flux/arcsec^2",
"valid": (0, None),
"shape": (None,),
"dynamic": True,
"description": "effective surface density, brightness at the effective radius",
},
}
[docs]
@torch.no_grad()
@ignore_numpy_warnings
def initialize(self):
super().initialize()
parametric_segment_initialize(
model=self,
target=self.target[self.window],
prof_func=exponential_np,
params=("Re", "Ie"),
x0_func=_x0_func,
segments=self.segments,
)
[docs]
@forward
def iradial_model(self, i: int, R: ArrayLike, Re: ArrayLike, Ie: ArrayLike) -> ArrayLike:
return func.exponential(R, Re[i], Ie[i])
[docs]
class ExponentialPSFMixin:
"""Exponential radial light profile.
An exponential is a classical radial model used in many contexts. The
functional form of the exponential profile is defined as:
.. math::
I(R) = I_e \\exp\\left(- b_1\\left(\\frac{R}{R_e} - 1\\right)\\right)
Ie is the brightness at the effective radius, and Re is the effective
radius. :math:`b_1` is a constant that ensures :math:`I_e` is the brightness at :math:`R_e`.
:param Re: effective radius, radius enclosing half the total light
:param Ie: effective surface density, brightness at the effective radius
"""
_model_type = "exponential"
_parameter_specs = {
"Re": {
"units": "pix",
"valid": (0, None),
"shape": (),
"dynamic": True,
"description": "effective radius, radius enclosing half the total light",
},
"Ie": {
"units": "flux/pix^2",
"valid": (0, None),
"shape": (),
"dynamic": False,
"value": 1.0,
"description": "effective surface density, brightness at the effective radius",
},
}
[docs]
@torch.no_grad()
@ignore_numpy_warnings
def initialize(self):
super().initialize()
parametric_initialize(
self,
self.target[self.window],
exponential_np,
("Re", "Ie"),
_x0_func,
)
[docs]
@forward
def radial_model(self, R: ArrayLike, Re: ArrayLike, Ie: ArrayLike) -> ArrayLike:
return func.exponential(R, Re, Ie)
