class NFW_ELLIPSE(object):
"""
this class contains functions concerning the NFW profile
relation are: R_200 = c * Rs
"""
param_names = ['Rs', 'alpha_Rs', 'e1', 'e2', 'center_x', 'center_y']
lower_limit_default = {
'Rs': 0,
'alpha_Rs': 0,
'e1': -0.5,
'e2': -0.5,
'center_x': -100,
'center_y': -100
}
upper_limit_default = {
'Rs': 100,
'alpha_Rs': 10,
'e1': 0.5,
'e2': 0.5,
'center_x': 100,
'center_y': 100
}
def __init__(self, interpol=False, num_interp_X=1000, max_interp_X=10):
self.nfw = NFW(interpol=interpol,
num_interp_X=num_interp_X,
max_interp_X=max_interp_X)
self._diff = 0.0000000001
def function(self, x, y, Rs, alpha_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)
xt1 = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e)
xt2 = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e)
R_ = np.sqrt(xt1**2 + xt2**2)
rho0_input = self.nfw._alpha2rho0(alpha_Rs=alpha_Rs, Rs=Rs)
if Rs < 0.0000001:
Rs = 0.0000001
f_ = self.nfw.nfwPot(R_, Rs, rho0_input)
return f_
def derivatives(self, x, y, Rs, alpha_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)
xt1 = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e)
xt2 = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e)
R_ = np.sqrt(xt1**2 + xt2**2)
rho0_input = self.nfw._alpha2rho0(alpha_Rs=alpha_Rs, Rs=Rs)
if Rs < 0.0000001:
Rs = 0.0000001
f_x_prim, f_y_prim = self.nfw.nfwAlpha(R_, Rs, rho0_input, xt1, xt2)
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, Rs, alpha_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, Rs, alpha_Rs, e1, e2,
center_x, center_y)
diff = self._diff
alpha_ra_dx, alpha_dec_dx = self.derivatives(x + diff, y, Rs, alpha_Rs,
e1, e2, center_x,
center_y)
alpha_ra_dy, alpha_dec_dy = self.derivatives(x, y + diff, Rs, alpha_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 mass_3d_lens(self, R, Rs, alpha_Rs, e1=1, e2=0):
"""
:param R:
:param Rs:
:param alpha_Rs:
:param q:
:param phi_G:
:return:
"""
return self.nfw.mass_3d(R, Rs, alpha_Rs)
class NFW_ELLIPSE(object):
"""
this class contains functions concerning the NFW profile
relation are: R_200 = c * Rs
"""
def __init__(self):
self.nfw = NFW()
self._diff = 0.000001
def function(self, x, y, Rs, theta_Rs, q, phi_G, center_x=0, center_y=0):
"""
returns double integral of NFW profile
"""
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)
xt1 = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e)
xt2 = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e)
R_ = np.sqrt(xt1**2 + xt2**2)
rho0_input = self.nfw._alpha2rho0(theta_Rs=theta_Rs, Rs=Rs)
if Rs < 0.0001:
Rs = 0.0001
f_ = self.nfw.nfwPot(R_, Rs, rho0_input)
return f_
def derivatives(self,
x,
y,
Rs,
theta_Rs,
q,
phi_G,
center_x=0,
center_y=0):
"""
returns df/dx and df/dy of the function (integral of NFW)
"""
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)
xt1 = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e)
xt2 = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e)
R_ = np.sqrt(xt1**2 + xt2**2)
rho0_input = self.nfw._alpha2rho0(theta_Rs=theta_Rs, Rs=Rs)
if Rs < 0.0001:
Rs = 0.0001
f_x_prim, f_y_prim = self.nfw.nfwAlpha(R_, Rs, rho0_input, xt1, xt2)
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, Rs, theta_Rs, q, phi_G, 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, Rs, theta_Rs, q, phi_G,
center_x, center_y)
diff = self._diff
alpha_ra_dx, alpha_dec_dx = self.derivatives(x + diff, y, Rs, theta_Rs,
q, phi_G, center_x,
center_y)
alpha_ra_dy, alpha_dec_dy = self.derivatives(x, y + diff, Rs, theta_Rs,
q, phi_G, 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 mass_3d_lens(self, R, Rs, theta_Rs, q=1, phi_G=0):
"""
:param R:
:param Rs:
:param theta_Rs:
:param q:
:param phi_G:
:return:
"""
return self.nfw.mass_3d(R, Rs, theta_Rs)
