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_, y_ = param_util.transform_e1e2_square_average(
x, y, e1, e2, center_x, center_y)
e = param_util.q2e(q)
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
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
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, calculated as an elliptically distorted deflection angle of the
spherical NFW profile
:param x: angular position (normally in units of arc seconds)
:param y: angular position (normally in units of arc seconds)
:param Rs: turn over point in the slope of the NFW profile in angular unit
:param alpha_Rs: deflection (angular units) at projected Rs
:param e1: eccentricity component in x-direction
:param e2: eccentricity component in y-direction
:param center_x: center of halo (in angular units)
:param center_y: center of halo (in angular units)
:return: deflection in x-direction, deflection in y-direction
"""
x_, y_ = param_util.transform_e1e2_square_average(
x, y, e1, e2, center_x, center_y)
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
e = abs(1 - q)
R_ = np.sqrt(x_**2 + y_**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, x_, y_)
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 function(self, x, y, sigma0, Rs, e1, e2, center_x=0, center_y=0):
"""
returns double integral of NFW profile
"""
x_, y_ = param_util.transform_e1e2_square_average(x, y, e1, e2, center_x, center_y)
f_ = self.spherical.function(x_, y_, sigma0, Rs)
return f_
def function(self,
x,
y,
Rs,
alpha_Rs,
r_trunc,
e1,
e2,
center_x=0,
center_y=0):
"""
returns elliptically distorted NFW lensing potential
:param x: angular position (normally in units of arc seconds)
:param y: angular position (normally in units of arc seconds)
:param Rs: turn over point in the slope of the NFW profile in angular unit
:param alpha_Rs: deflection (angular units) at projected Rs
:param r_trunc: truncation radius
:param e1: eccentricity component in x-direction
:param e2: eccentricity component in y-direction
:param center_x: center of halo (in angular units)
:param center_y: center of halo (in angular units)
:return: lensing potential
"""
x_, y_ = param_util.transform_e1e2_square_average(
x, y, e1, e2, center_x, center_y)
R_ = np.sqrt(x_**2 + y_**2)
rho0_input = self.tnfw.alpha2rho0(alpha_Rs=alpha_Rs, Rs=Rs)
Rs = np.maximum(Rs, 0.0000001)
#if Rs < 0.0000001:
# Rs = 0.0000001
f_ = self.tnfw.nfwPot(R_, Rs, rho0_input, r_trunc)
return f_
def function(self, x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0):
"""
returns Gaussian
"""
# phi_G, q = param_util.ellipticity2phi_q(e1, e2)
x_, y_ = param_util.transform_e1e2_square_average(x, y, e1, e2, center_x, center_y)
# x_, y_ = self._coord_transf(x, y, q, phi_G, center_x, center_y)
f_ = self.sersic.function(x_, y_, n_sersic, R_sersic, k_eff)
return f_
def function(self, x, y, amp, Ra, Rs, e1, e2, center_x=0, center_y=0):
"""
:param x:
:param y:
:param amp:
:param Ra:
:param Rs:
:param center_x:
:param center_y:
:return:
"""
x_, y_ = param_util.transform_e1e2_square_average(x, y, e1, e2, center_x, center_y)
return self.spherical.function(x_, y_, amp, Ra, Rs)
def test_transform_e1e2_square_average():
x, y = np.array([1, 0]), np.array([0, 1])
e1 = 0.1
e2 = 0
center_x, center_y = 0, 0
x_, y_ = param_util.transform_e1e2_square_average(x,
y,
e1,
e2,
center_x=center_x,
center_y=center_y)
npt.assert_almost_equal(np.sum(x**2 + y**2),
np.sum(x_**2 + y_**2),
decimal=8)
def derivatives(self, x, y, n_sersic, R_sersic, k_eff, e1, e2, center_x=0, center_y=0):
"""
returns df/dx and df/dy of the function
"""
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
e = param_util.q2e(q)
# e = abs(1. - q)
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
x_, y_ = param_util.transform_e1e2_square_average(x, y, e1, e2, center_x, center_y)
# x_, y_ = self._coord_transf(x, y, q, phi_G, center_x, center_y)
f_x_prim, f_y_prim = self.sersic.derivatives(x_, y_, n_sersic, R_sersic, k_eff)
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 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)
"""
x_, y_ = param_util.transform_e1e2_square_average(x, y, e1, e2, center_x, center_y)
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
