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 nuker_np
from .. import func
def _x0_func(model_params, R, F):
return R[4], 10 ** F[4], 1.0, 2.0, 0.5
[docs]
class NukerMixin:
"""Nuker radial light profile (Lauer et al. 1995).
This is a classic profile used widely in galaxy modelling. The functional
form of the Nuker profile is defined as:
$$I(R) = I_b2^{\\frac{\\beta - \\gamma}{\\alpha}}\\left(\\frac{R}{R_b}\\right)^{-\\gamma}\\left[1 + \\left(\\frac{R}{R_b}\\right)^{\\alpha}\\right]^{\\frac{\\gamma-\\beta}{\\alpha}}$$
It is effectively a double power law profile. $\\gamma$ gives the inner
slope, $\\beta$ gives the outer slope, $\\alpha$ is somewhat degenerate with
the other slopes.
**Parameters:**
- `Rb`: scale length radius
- `Ib`: intensity at the scale length
- `alpha`: sharpness of transition between power law slopes
- `beta`: outer power law slope
- `gamma`: inner power law slope
"""
_model_type = "nuker"
_parameter_specs = {
"Rb": {"units": "arcsec", "valid": (0, None), "shape": (), "dynamic": True},
"Ib": {"units": "flux/arcsec^2", "valid": (0, None), "shape": (), "dynamic": True},
"alpha": {"units": "none", "valid": (0, None), "shape": (), "dynamic": True},
"beta": {"units": "none", "valid": (0, None), "shape": (), "dynamic": True},
"gamma": {"units": "none", "shape": (), "dynamic": True},
}
[docs]
@torch.no_grad()
@ignore_numpy_warnings
def initialize(self):
super().initialize()
parametric_initialize(
self,
self.target[self.window],
nuker_np,
("Rb", "Ib", "alpha", "beta", "gamma"),
_x0_func,
)
[docs]
@forward
def radial_model(
self,
R: ArrayLike,
Rb: ArrayLike,
Ib: ArrayLike,
alpha: ArrayLike,
beta: ArrayLike,
gamma: ArrayLike,
) -> ArrayLike:
return func.nuker(R, Rb, Ib, alpha, beta, gamma)
[docs]
class iNukerMixin:
"""Nuker radial light profile (Lauer et al. 1995).
This is a classic profile used widely in galaxy modelling. The functional
form of the Nuker profile is defined as:
$$I(R) = I_b2^{\\frac{\\beta - \\gamma}{\\alpha}}\\left(\\frac{R}{R_b}\\right)^{-\\gamma}\\left[1 + \\left(\\frac{R}{R_b}\\right)^{\\alpha}\\right]^{\\frac{\\gamma-\\beta}{\\alpha}}$$
It is effectively a double power law profile. $\\gamma$ gives the inner
slope, $\\beta$ gives the outer slope, $\\alpha$ is somewhat degenerate with
the other slopes.
`Rb`, `Ib`, `alpha`, `beta`, and `gamma` are batched by their first
dimension, allowing for multiple Nuker profiles to be defined at once.
**Parameters:**
- `Rb`: scale length radius
- `Ib`: intensity at the scale length
- `alpha`: sharpness of transition between power law slopes
- `beta`: outer power law slope
- `gamma`: inner power law slope
"""
_model_type = "nuker"
_parameter_specs = {
"Rb": {"units": "arcsec", "valid": (0, None), "shape": (None,), "dynamic": True},
"Ib": {"units": "flux/arcsec^2", "valid": (0, None), "shape": (None,), "dynamic": True},
"alpha": {"units": "none", "valid": (0, None), "shape": (None,), "dynamic": True},
"beta": {"units": "none", "valid": (0, None), "shape": (None,), "dynamic": True},
"gamma": {"units": "none", "shape": (None,), "dynamic": True},
}
[docs]
@torch.no_grad()
@ignore_numpy_warnings
def initialize(self):
super().initialize()
parametric_segment_initialize(
model=self,
target=self.target[self.window],
prof_func=nuker_np,
params=("Rb", "Ib", "alpha", "beta", "gamma"),
x0_func=_x0_func,
segments=self.segments,
)
[docs]
@forward
def iradial_model(
self,
i: int,
R: ArrayLike,
Rb: ArrayLike,
Ib: ArrayLike,
alpha: ArrayLike,
beta: ArrayLike,
gamma: ArrayLike,
) -> ArrayLike:
return func.nuker(R, Rb[i], Ib[i], alpha[i], beta[i], gamma[i])
[docs]
class NukerPSFMixin:
"""Nuker radial light profile (Lauer et al. 1995).
This is a classic profile used widely in galaxy modelling. The functional
form of the Nuker profile is defined as:
$$I(R) = I_b2^{\\frac{\\beta - \\gamma}{\\alpha}}\\left(\\frac{R}{R_b}\\right)^{-\\gamma}\\left[1 + \\left(\\frac{R}{R_b}\\right)^{\\alpha}\\right]^{\\frac{\\gamma-\\beta}{\\alpha}}$$
It is effectively a double power law profile. $\\gamma$ gives the inner
slope, $\\beta$ gives the outer slope, $\\alpha$ is somewhat degenerate with
the other slopes.
**Parameters:**
- `Rb`: scale length radius [pix]
- `Ib`: intensity at the scale length [flux/pix^2]
- `alpha`: sharpness of transition between power law slopes
- `beta`: outer power law slope
- `gamma`: inner power law slope
"""
_model_type = "nuker"
_parameter_specs = {
"Rb": {"units": "pix", "valid": (0, None), "shape": (), "dynamic": True},
"Ib": {
"units": "flux/pix^2",
"valid": (0, None),
"shape": (),
"dynamic": False,
"value": 1.0,
},
"alpha": {"units": "none", "valid": (0, None), "shape": (), "dynamic": True},
"beta": {"units": "none", "valid": (0, None), "shape": (), "dynamic": True},
"gamma": {"units": "none", "shape": (), "dynamic": True},
}
[docs]
@torch.no_grad()
@ignore_numpy_warnings
def initialize(self):
super().initialize()
parametric_initialize(
self,
self.target[self.window],
nuker_np,
("Rb", "Ib", "alpha", "beta", "gamma"),
_x0_func,
)
[docs]
@forward
def radial_model(
self,
R: ArrayLike,
Rb: ArrayLike,
Ib: ArrayLike,
alpha: ArrayLike,
beta: ArrayLike,
gamma: ArrayLike,
) -> ArrayLike:
return func.nuker(R, Rb, Ib, alpha, beta, gamma)
