import torch
import numpy as np
from ...param import forward
from ...backend_obj import ArrayLike
from ...utils.decorators import ignore_numpy_warnings
from ...utils.parametric_profiles import king_np
from .._shared_methods import parametric_initialize, parametric_segment_initialize
from .. import func
[docs]
def x0_func(model_params, R, F):
return R[2], R[5], 2, 10 ** F[0]
[docs]
class KingMixin:
"""Empirical King radial light profile (Elson 1999).
Often used for star clusters. By default the profile has `alpha = 2` but we
allow the parameter to vary freely for fitting. The functional form of the
Empirical King profile is defined as:
$$I(R) = I_0\\left[\\frac{1}{(1 + (R/R_c)^2)^{1/\\alpha}} - \\frac{1}{(1 + (R_t/R_c)^2)^{1/\\alpha}}\\right]^{\\alpha}\\left[1 - \\frac{1}{(1 + (R_t/R_c)^2)^{1/\\alpha}}\\right]^{-\\alpha}$$
where `R_c` is the core radius, `R_t` is the truncation radius, and `I_0` is
the intensity at the center of the profile. `alpha` is the concentration
index which controls the shape of the profile.
**Parameters:**
- `Rc`: core radius
- `Rt`: truncation radius
- `alpha`: concentration index which controls the shape of the brightness profile
- `I0`: intensity at the center of the profile
"""
_model_type = "king"
_parameter_specs = {
"Rc": {"units": "arcsec", "valid": (0.0, None), "shape": (), "dynamic": True},
"Rt": {"units": "arcsec", "valid": (0.0, None), "shape": (), "dynamic": True},
"alpha": {
"units": "unitless",
"valid": (0, 10),
"shape": (),
"value": 2.0,
"dynamic": False,
},
"I0": {"units": "flux/arcsec^2", "valid": (0, None), "shape": (), "dynamic": True},
}
[docs]
@torch.no_grad()
@ignore_numpy_warnings
def initialize(self):
super().initialize()
parametric_initialize(
self,
self.target[self.window],
lambda r, *x: king_np(r, x[0], x[1], 2.0, x[2]),
("Rc", "Rt", "I0"),
x0_func,
)
[docs]
@forward
def radial_model(
self, R: ArrayLike, Rc: ArrayLike, Rt: ArrayLike, alpha: ArrayLike, I0: ArrayLike
) -> ArrayLike:
return func.king(R, Rc, Rt, alpha, I0)
[docs]
class iKingMixin:
"""Empirical King radial light profile (Elson 1999).
Often used for star clusters. By default the profile has `alpha = 2` but we
allow the parameter to vary freely for fitting. The functional form of the
Empirical King profile is defined as:
$$I(R) = I_0\\left[\\frac{1}{(1 + (R/R_c)^2)^{1/\\alpha}} - \\frac{1}{(1 + (R_t/R_c)^2)^{1/\\alpha}}\\right]^{\\alpha}\\left[1 - \\frac{1}{(1 + (R_t/R_c)^2)^{1/\\alpha}}\\right]^{-\\alpha}$$
where `R_c` is the core radius, `R_t` is the truncation radius, and `I_0` is
the intensity at the center of the profile. `alpha` is the concentration
index which controls the shape of the profile.
`Rc`, `Rt`, `alpha`, and `I0` are batched by their first dimension, allowing
for multiple King profiles to be defined at once.
**Parameters:**
- `Rc`: core radius
- `Rt`: truncation radius
- `alpha`: concentration index which controls the shape of the brightness profile
- `I0`: intensity at the center of the profile
"""
_model_type = "king"
_parameter_specs = {
"Rc": {"units": "arcsec", "valid": (0.0, None), "shape": (None,), "dynamic": True},
"Rt": {"units": "arcsec", "valid": (0.0, None), "shape": (None,), "dynamic": True},
"alpha": {"units": "unitless", "valid": (0, 10), "shape": (None,), "dynamic": False},
"I0": {"units": "flux/arcsec^2", "valid": (0, None), "shape": (None,), "dynamic": True},
}
[docs]
@torch.no_grad()
@ignore_numpy_warnings
def initialize(self):
super().initialize()
if not self.alpha.initialized:
self.alpha.value = 2.0 * np.ones(self.segments)
parametric_segment_initialize(
model=self,
target=self.target[self.window],
prof_func=lambda r, *x: king_np(r, x[0], x[1], 2.0, x[2]),
params=("Rc", "Rt", "I0"),
x0_func=x0_func,
segments=self.segments,
)
[docs]
@forward
def iradial_model(
self, i: int, R: ArrayLike, Rc: ArrayLike, Rt: ArrayLike, alpha: ArrayLike, I0: ArrayLike
) -> ArrayLike:
return func.king(R, Rc[i], Rt[i], alpha[i], I0[i])
[docs]
class KingPSFMixin:
"""Empirical King radial light profile (Elson 1999).
Often used for star clusters. By default the profile has `alpha = 2` but we
allow the parameter to vary freely for fitting. The functional form of the
Empirical King profile is defined as:
$$I(R) = I_0\\left[\\frac{1}{(1 + (R/R_c)^2)^{1/\\alpha}} - \\frac{1}{(1 + (R_t/R_c)^2)^{1/\\alpha}}\\right]^{\\alpha}\\left[1 - \\frac{1}{(1 + (R_t/R_c)^2)^{1/\\alpha}}\\right]^{-\\alpha}$$
where `R_c` is the core radius, `R_t` is the truncation radius, and `I_0` is
the intensity at the center of the profile. `alpha` is the concentration
index which controls the shape of the profile.
**Parameters:**
- `Rc`: core radius [pix]
- `Rt`: truncation radius [pix]
- `alpha`: concentration index which controls the shape of the brightness profile
- `I0`: intensity at the center of the profile [flux/pix^2]
"""
_model_type = "king"
_parameter_specs = {
"Rc": {"units": "pix", "valid": (0.0, None), "shape": (), "dynamic": True},
"Rt": {"units": "pix", "valid": (0.0, None), "shape": (), "dynamic": True},
"alpha": {
"units": "unitless",
"valid": (0, 10),
"shape": (),
"value": 2.0,
"dynamic": False,
},
"I0": {
"units": "flux/pix^2",
"valid": (0, None),
"shape": (),
"dynamic": False,
"value": 1.0,
},
}
[docs]
@torch.no_grad()
@ignore_numpy_warnings
def initialize(self):
super().initialize()
parametric_initialize(
self,
self.target[self.window],
lambda r, *x: king_np(r, x[0], x[1], 2.0, x[2]),
("Rc", "Rt", "I0"),
x0_func,
)
[docs]
@forward
def radial_model(
self, R: ArrayLike, Rc: ArrayLike, Rt: ArrayLike, alpha: ArrayLike, I0: ArrayLike
) -> ArrayLike:
return func.king(R, Rc, Rt, alpha, I0)
