class Hernquist(object):
"""
class for pseudo Jaffe lens light (2d projected light/mass distribution
"""
def __init__(self):
from lenstronomy.LensModel.Profiles.hernquist import Hernquist as Hernquist_lens
self.lens = Hernquist_lens()
self.param_names = ['amp', 'Rs', 'center_x', 'center_y']
self.lower_limit_default = {'amp': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}
self.upper_limit_default = {'amp': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}
def function(self, x, y, amp, Rs, center_x=0, center_y=0):
"""
:param x:
:param y:
:param amp:
:param Rs: scale radius: half-light radius = Rs / 0.551
:param center_x:
:param center_y:
:return:
"""
rho0 = self.lens.sigma2rho(amp, Rs)
return self.lens.density_2d(x, y, rho0, Rs, center_x, center_y)
def light_3d(self, r, amp, Rs):
"""
:param r:
:param amp:
:param Rs:
:return:
"""
rho0 = self.lens.sigma2rho(amp, Rs)
return self.lens.density(r, rho0, Rs)
class Hernquist(object):
"""
class for pseudo Jaffe lens light (2d projected light/mass distribution
"""
def __init__(self):
from lenstronomy.LensModel.Profiles.hernquist import Hernquist as Hernquist_lens
self.lens = Hernquist_lens()
def function(self, x, y, sigma0, Rs, center_x=0, center_y=0):
"""
:param x:
:param y:
:param sigma0:
:param a:
:param s:
:param center_x:
:param center_y:
:return:
"""
rho0 = self.lens.sigma2rho(sigma0, Rs)
return self.lens.density_2d(x, y, rho0, Rs, center_x, center_y)
def light_3d(self, r, sigma0, Rs):
"""
:param y:
:param sigma0:
:param Rs:
:param center_x:
:param center_y:
:return:
"""
rho0 = self.lens.sigma2rho(sigma0, Rs)
return self.lens.density(r, rho0, Rs)
class Hernquist_Ellipse(LensProfileBase):
"""
this class contains functions for the elliptical Hernquist profile. Ellipticity is defined in the potential.
"""
param_names = ['sigma0', 'Rs', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {
'sigma0': 0,
'Rs': 0,
'e1': -0.5,
'e2': -0.5,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'sigma0': 100,
'Rs': 100,
'e1': 0.5,
'e2': 0.5,
'center_x': 100,
'center_y': 100
}
def __init__(self):
self.spherical = Hernquist()
self._diff = 0.0000000001
super(Hernquist_Ellipse, self).__init__()
def function(self, x, y, sigma0, 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 = abs(1 - q)
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, Rs)
return f_
def derivatives(self, x, y, sigma0, 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 = abs(1 - q)
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, Rs)
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
def hessian(self, x, y, sigma0, Rs, e1, e2, center_x=0, center_y=0):
"""
returns Hessian matrix of function d^2f/dx^2, d^f/dy^2, d^2/dxdy
"""
alpha_ra, alpha_dec = self.derivatives(x, y, sigma0, Rs, e1, e2,
center_x, center_y)
diff = self._diff
alpha_ra_dx, alpha_dec_dx = self.derivatives(x + diff, y, sigma0, Rs,
e1, e2, center_x,
center_y)
alpha_ra_dy, alpha_dec_dy = self.derivatives(x, y + diff, sigma0, 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_yy, f_xy
def density(self, r, rho0, Rs, e1=0, e2=0):
"""
computes the 3-d density
:param r: 3-d radius
:param rho0: density normalization
:param Rs: Hernquist radius
:return: density at radius r
"""
return self.spherical.density(r, rho0, Rs)
def density_lens(self, r, sigma0, Rs, e1=0, e2=0):
"""
Density as a function of 3d radius in lensing parameters
This function converts the lensing definition sigma0 into the 3d density
:param r: 3d radius
:param sigma0: rho0 * Rs (units of projected density)
:param Rs: Hernquist radius
:return: enclosed mass in 3d
"""
return self.spherical.density_lens(r, sigma0, Rs)
def density_2d(self, x, y, rho0, Rs, e1=0, e2=0, center_x=0, center_y=0):
"""
projected density along the line of sight at coordinate (x, y)
:param x: x-coordinate
:param y: y-coordinate
:param rho0: density normalization
:param Rs: Hernquist radius
:param center_x: x-center of the profile
:param center_y: y-center of the profile
:return: projected density
"""
return self.spherical.density_2d(x, y, rho0, Rs, center_x, center_y)
def mass_2d_lens(self, r, sigma0, Rs, e1=0, e2=0):
"""
mass enclosed projected 2d sphere of radius r
Same as mass_2d but with input normalization in units of projected density
:param r: projected radius
:param sigma0: rho0 * Rs (units of projected density)
:param Rs: Hernquist radius
:return: mass enclosed 2d projected radius
"""
return self.spherical.mass_2d_lens(r, sigma0, Rs)
def mass_2d(self, r, rho0, Rs, e1=0, e2=0):
"""
mass enclosed projected 2d sphere of radius r
:param r: projected radius
:param rho0: density normalization
:param Rs: Hernquist radius
:return: mass enclosed 2d projected radius
"""
return self.spherical.mass_2d(r, rho0, Rs)
def mass_3d(self, r, rho0, Rs, e1=0, e2=0):
"""
mass enclosed a 3d sphere or radius r
:param r: 3-d radius within the mass is integrated (same distance units as density definition)
:param rho0: density normalization
:param Rs: Hernquist radius
:return: enclosed mass
"""
return self.spherical.mass_3d(r, rho0, Rs)