Source code for lenstronomy.LightModel.Profiles.power_law
import lenstronomy.Util.param_util as param_util
from lenstronomy.LensModel.Profiles.spp import SPP
import numpy as np
import scipy.special as special
__all__ = ['PowerLaw']
[docs]class PowerLaw(object):
"""
class for power-law elliptical light distribution
"""
param_names = ['amp', 'gamma', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {'amp': 0, 'gamma': 1, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100}
upper_limit_default = {'amp': 100, 'gamma': 3, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100}
def __init__(self):
self.lens = SPP()
[docs] def function(self, x, y, amp, gamma, e1, e2, center_x=0, center_y=0):
"""
:param x: ra-coordinate
:param y: dec-coordinate
:param gamma: projected power-law slope
:param e1: ellipticity
:param e2: ellipticity
:param center_x: center
:param center_y: center
:return: projected flux
"""
x_, y_ = param_util.transform_e1e2_product_average(x, y, e1, e2, center_x, center_y)
P2 = x_ ** 2 + y_ ** 2
if isinstance(P2, int) or isinstance(P2, float):
a = max(0.00000001, P2)
else:
a = np.empty_like(P2)
p2 = P2[P2 > 0] # in the SIS regime
a[P2 == 0] = 0.00000001
a[P2 > 0] = p2
sigma = amp * a ** ((1. - gamma)/2.)
return sigma
[docs] def light_3d(self, r, amp, gamma, e1=0, e2=0):
"""
:param r:
:param amp:
:param gamma:
:param e1:
:param e2:
:return:
"""
rho0 = self._amp2rho(amp, gamma)
rho = rho0 / r ** gamma
return rho
def _amp2rho(self, amp, gamma):
"""
:param amp:
:param gamma:
:return:
"""
factor = np.sqrt(np.pi) * special.gamma(1./2*(-1+gamma))/special.gamma(gamma/2.)
return amp / factor