def cal_lensing_signals(kap, bzz, ncc):
dsx_arc = bzz / ncc
# deflection maps
alpha1, alpha2 = cf.call_cal_alphas(kap, bzz, ncc)
# shear maps
npad = 5
al11 = 1 - np.gradient(alpha1, dsx_arc, axis=0)
al12 = -np.gradient(alpha1, dsx_arc, axis=1)
al21 = -np.gradient(alpha2, dsx_arc, axis=0)
al22 = 1 - np.gradient(alpha2, dsx_arc, axis=1)
detA = al11 * al22 - al12 * al21
kappa0 = 1 - 0.5 * (al11 + al22)
shear1 = 0.5 * (al11 - al22)
shear2 = 0.5 * (al21 + al12)
shear0 = (shear1**2 + shear2**2)**0.5
# magnification maps
mu = 1.0 / ((1.0 - kap)**2.0 - shear1 * shear1 - shear2 * shear2)
lambda_t = 1 - kappa0 - shear0 # tangential eigenvalue, page 115
# lensing potential
phi = cf.call_cal_phi(kap, bzz, ncc)
return alpha1, alpha2, mu, phi, detA, lambda_t
def cal_lensing_signals(kap, bzz, ncc, coord):
dsx_arc = bzz / ncc
# deflection maps
alpha1, alpha2 = cf.call_cal_alphas(kap, bzz, ncc)
#TODO: map to finer grid
alpha1_spline = RectBivariateSpline(coord, coord, alpha1)
alpha2_spline = RectBivariateSpline(coord, coord, alpha2)
lencoord = len(coord)
centre_coord = np.linspace(coord[int(lencoord / 3)],
coord[int(2 * lencoord / 3)], 256)
coord = np.concatenate((coord[:int(lencoord / 3)], centre_coord,
coord[int(2 * lencoord / 3 + 1):]))
alpha1 = alpha1_spline(coord, coord)
alpha2 = alpha2_spline(coord, coord)
# shear maps
al11 = 1 - np.gradient(alpha1, coord, axis=0)
al12 = -np.gradient(alpha1, coord, axis=1)
al21 = -np.gradient(alpha2, coord, axis=0)
al22 = 1 - np.gradient(alpha2, coord, axis=1)
detA = al11 * al22 - al12 * al21 # = (1-kappa0-shear0)*(1-kappa0+shear0)
kappa0 = 1 - 0.5 * (al11 + al22)
shear1 = 0.5 * (al11 - al22)
shear2 = 0.5 * (al21 + al12)
shear0 = (shear1**2 + shear2**2)**0.5
# magnification maps
mu = 1 / detA # = 1.0/((1.0-kappa0)**2.0-shear1*shear1-shear2*shear2)
lambda_t = 1 - kappa0 - shear0 # tangential eigenvalue, page 115
# lensing potential
phi = cf.call_cal_phi(kap, bzz, ncc)
return alpha1, alpha2, mu, phi, detA, lambda_t, coord