def hankel_spline_lognormal_cl(ells, cl, plot=False, ell_min=90, ell_max=1e5):
ft = SymmetricFourierTransform(ndim=2, N=200, h=0.03)
# transform to angular correlation function with inverse hankel transform and spline interpolated C_ell
spline_cl = interpolate.InterpolatedUnivariateSpline(
np.log10(ells), np.log10(cl))
f = lambda ell: 10**(spline_cl(np.log10(ell)))
thetas = np.pi / ells
w_theta = ft.transform(f, thetas, ret_err=False, inverse=True)
# compute lognormal angular correlation function
w_theta_g = np.log(1. + w_theta)
# convert back to multipole space
spline_w_theta_g = interpolate.InterpolatedUnivariateSpline(
np.log10(np.flip(thetas, 0)), np.flip(w_theta_g, 0))
g = lambda theta: spline_w_theta_g(np.log10(theta))
cl_g = ft.transform(g, ells, ret_err=False)
spline_cl_g = interpolate.InterpolatedUnivariateSpline(
np.log10(ells), np.log10(np.abs(cl_g)))
# plotting is just for validation if ever unsure
if plot:
plt.figure()
plt.loglog(ells, cl, label='$C_{\\ell}$', marker='.')
plt.loglog(ells, cl_g, label='$C_{\\ell}^G$', marker='.')
plt.loglog(np.linspace(ell_min, ell_max, 1000),
10**spline_cl_g(
np.log10(np.linspace(ell_min, ell_max, 1000))),
label='spline of $C_{\\ell}^G$')
plt.legend(fontsize=14)
plt.xlabel('$\\ell$', fontsize=16)
plt.title('Angular power spectra', fontsize=16)
plt.show()
return cl_g, spline_cl_g
def _realspace_power(self, nu1, nu2):
r = np.logspace(-3, 3, 1000)
ht1 = SymmetricFourierTransform(ndim=2,
N=1000,
h=0.003,
a=0,
b=2 * np.pi)
gres = ht1.transform(
lambda u: np.sqrt(self.point_source_power_spec(2 * np.pi * u)) * np
.sqrt(self.point_source_power_spec(2 * np.pi * u)),
k=r,
inverse=True,
ret_err=False)
# *nu1*nu2
xir = spline(np.log(r), np.log(gres))
return lambda r: np.exp(xir(np.log(r)))