__author__ = 'sibirrer'
# this file contains a class to make a Sersic profile
import numpy as np
from lenstronomy.LensModel.Profiles.sersic_utils import SersicUtil
import lenstronomy.Util.param_util as param_util
from lenstronomy.Util.package_util import exporter
export, __all__ = exporter()
[docs]@export
class Sersic(SersicUtil):
"""
this class contains functions to evaluate an spherical Sersic function
.. math::
I(R) = I_0 \\exp \\left[ -b_n (R/R_{\\rm Sersic})^{\\frac{1}{n}}\\right]
with :math:`I_0 = amp`
and
with :math:`b_{n}\\approx 1.999\,n-0.327`
"""
param_names = ['amp', 'R_sersic', 'n_sersic', 'center_x', 'center_y']
lower_limit_default = {'amp': 0, 'R_sersic': 0, 'n_sersic': 0.5, 'center_x': -100, 'center_y': -100}
upper_limit_default = {'amp': 100, 'R_sersic': 100, 'n_sersic': 8, 'center_x': 100, 'center_y': 100}
[docs] def function(self, x, y, amp, R_sersic, n_sersic, center_x=0, center_y=0, max_R_frac=100.0):
"""
:param x:
:param y:
:param amp: surface brightness/amplitude value at the half light radius
:param R_sersic: semi-major axis half light radius
:param n_sersic: Sersic index
:param center_x: center in x-coordinate
:param center_y: center in y-coordinate
:param max_R_frac: maximum window outside of which the mass is zeroed, in units of R_sersic (float)
:return: Sersic profile value at (x, y)
"""
R = self.get_distance_from_center(x, y, phi_G=0.0, q=1.0, center_x=center_x, center_y=center_y)
result = self._r_sersic(R, R_sersic, n_sersic, max_R_frac)
return amp * result
[docs]@export
class SersicElliptic(SersicUtil):
"""
this class contains functions to evaluate an elliptical Sersic function
"""
param_names = ['amp', 'R_sersic', 'n_sersic', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {'amp': 0, 'R_sersic': 0, 'n_sersic': 0.5, 'e1': -0.5, 'e2': -0.5,'center_x': -100, 'center_y': -100}
upper_limit_default = {'amp': 100, 'R_sersic': 100, 'n_sersic': 8, 'e1': 0.5, 'e2': 0.5,'center_x': 100, 'center_y': 100}
[docs] def function(self, x, y, amp, R_sersic, n_sersic, e1, e2, center_x=0, center_y=0, max_R_frac=100.0):
"""
:param x:
:param y:
:param amp: surface brightness/amplitude value at the half light radius
:param R_sersic: semi-major axis half light radius
:param n_sersic: Sersic index
:param e1: eccentricity parameter
:param e2: eccentricity parameter
:param center_x: center in x-coordinate
:param center_y: center in y-coordinate
:param max_R_frac: maximum window outside of which the mass is zeroed, in units of R_sersic (float)
:return: Sersic profile value at (x, y)
"""
R_sersic = np.maximum(0, R_sersic)
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
R = self.get_distance_from_center(x, y, phi_G, q, center_x, center_y)
result = self._r_sersic(R, R_sersic, n_sersic, max_R_frac)
return amp * result
[docs]@export
class CoreSersic(SersicUtil):
"""
this class contains the Core-Sersic function introduced by e.g Trujillo et al. 2004
.. math::
I(R) = I' \\left[1 + (R_b/R)^{\\alpha} \\right]^{\\gamma / \\alpha}
\\exp \\left{ -b_n \\left[(R^{\\alpha} + R_b^{\alpha})/R_e^{\\alpha} \\right]^{1 / (n\\alpha)} \\right}
with
.. math::
I' = I_b 2^{-\\gamma/ \\alpha} \exp \\left[b_n 2^{1 / (n\\alpha)} (R_b/R_e)^{1/n} \\right]
where :math:`I_b` is the intensity at the break radius.
"""
param_names = ['amp', 'R_sersic', 'Rb', 'n_sersic', 'gamma', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {'amp': 0, 'Rb': 0, 'n_sersic': 0.5, 'gamma': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100,
'center_y': -100}
upper_limit_default = {'amp': 100, 'Rb': 100, 'n_sersic': 8, 'gamma': 10, 'e1': 0.5, 'e2': 0.5, 'center_x': 100,
'center_y': 100}
[docs] def function(self, x, y, amp, R_sersic, Rb, n_sersic, gamma, e1, e2, center_x=0, center_y=0, alpha=3.0,
max_R_frac=100.0):
"""
:param x:
:param y:
:param amp: surface brightness/amplitude value at the half light radius
:param R_sersic: semi-major axis half light radius
:param Rb: "break" core radius
:param n_sersic: Sersic index
:param gamma: inner power-law exponent
:param e1: eccentricity parameter
:param e2: eccentricity parameter
:param center_x: center in x-coordinate
:param center_y: center in y-coordinate
:param alpha: sharpness of the transition between the cusp and the outer Sersic profile (float)
:param max_R_frac: maximum window outside of which the mass is zeroed, in units of R_sersic (float)
:return: Cored Sersic profile value at (x, y)
"""
#TODO max_R_frac not implemented
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
R_ = self.get_distance_from_center(x, y, phi_G, q, center_x, center_y)
R = self._R_stable(R_)
bn = self.b_n(n_sersic)
result = amp * (1 + (Rb / R) ** alpha) ** (gamma / alpha) * np.exp(-bn * (((R ** alpha + Rb ** alpha) / R_sersic ** alpha) ** (1. / (alpha * n_sersic)) - 1.))
return np.nan_to_num(result)