from lenstronomy.LensModel.Profiles.p_jaffe import PJaffe
import lenstronomy.Util.param_util as param_util
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
import numpy as np
__all__ = ['PJaffe_Ellipse']
[docs]class PJaffe_Ellipse(LensProfileBase):
"""
this class contains functions concerning the NFW profile
relation are: R_200 = c * Rs
"""
param_names = ['sigma0', 'Ra', 'Rs', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {'sigma0': 0, 'Ra': 0, 'Rs': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100}
upper_limit_default = {'sigma0': 10, 'Ra': 100, 'Rs': 100, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100}
def __init__(self):
self.spherical = PJaffe()
self._diff = 0.000001
super(PJaffe_Ellipse, self).__init__()
[docs] def function(self, x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0):
"""
returns double integral of NFW profile
"""
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
x_shift = x - center_x
y_shift = y - center_y
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
e = min(abs(1. - q), 0.99)
x_ = (cos_phi*x_shift+sin_phi*y_shift)*np.sqrt(1 - e)
y_ = (-sin_phi*x_shift+cos_phi*y_shift)*np.sqrt(1 + e)
f_ = self.spherical.function(x_, y_, sigma0, Ra, Rs)
return f_
[docs] def derivatives(self, x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0):
"""
returns df/dx and df/dy of the function (integral of NFW)
"""
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
x_shift = x - center_x
y_shift = y - center_y
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
e = min(abs(1. - q), 0.99)
x_ = (cos_phi*x_shift+sin_phi*y_shift)*np.sqrt(1 - e)
y_ = (-sin_phi*x_shift+cos_phi*y_shift)*np.sqrt(1 + e)
f_x_prim, f_y_prim = self.spherical.derivatives(x_, y_, sigma0, Ra, Rs, center_x=0, center_y=0)
f_x_prim *= np.sqrt(1 - e)
f_y_prim *= np.sqrt(1 + e)
f_x = cos_phi*f_x_prim-sin_phi*f_y_prim
f_y = sin_phi*f_x_prim+cos_phi*f_y_prim
return f_x, f_y
[docs] def hessian(self, x, y, sigma0, Ra, Rs, e1, e2, center_x=0, center_y=0):
"""
returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
"""
alpha_ra, alpha_dec = self.derivatives(x, y, sigma0, Ra, Rs, e1, e2, center_x, center_y)
diff = self._diff
alpha_ra_dx, alpha_dec_dx = self.derivatives(x + diff, y, sigma0, Ra, Rs, e1, e2, center_x, center_y)
alpha_ra_dy, alpha_dec_dy = self.derivatives(x, y + diff, sigma0, Ra, Rs, e1, e2, center_x, center_y)
f_xx = (alpha_ra_dx - alpha_ra)/diff
f_xy = (alpha_ra_dy - alpha_ra)/diff
f_yx = (alpha_dec_dx - alpha_dec)/diff
f_yy = (alpha_dec_dy - alpha_dec)/diff
return f_xx, f_xy, f_yx, f_yy
[docs] def mass_3d_lens(self, r, sigma0, Ra, Rs, e1=0, e2=0):
"""
:param r:
:param sigma0:
:param Ra:
:param Rs:
:param q:
:param phi_G:
:return:
"""
return self.spherical.mass_3d_lens(r, sigma0, Ra, Rs)