def crosscorr_integral_y_rec_coords(
ell, z_i, delta_z
): #This is not working out-don't try this for now. Just leave it.
n = n_points #number of points over which to integrate
Kp_par = np.geomspace(1.e-6, .15, n)
Kp_perp = np.geomspace(1.e-6, 1., n)
Z_min = z_i - delta_z
Z_max = z_i + delta_z
z = np.geomspace(Z_min, Z_max, n)
Kpar = np.geomspace(1.e-6, .15, n)
kp_perp, kp_par, kpar = np.meshgrid(Kp_perp, Kp_par, Kpar)
chi_z = chi(z)
T_mean_zi = uf.T_mean(z_i)
chi_zi = chi(z_i)
f_zi = uf.f(z_i)
f_z = uf.f(z)
D_zi = uf.D_1(z_i)
r_zi = uf.r(z_i)
D_z = uf.D_1(z)
H_zi = uf.H(z_i)
tau_z = uf.tau_inst(z)
kpar = y / uf.r(z)
const = 1.e6 / (
8. * np.pi**3
) * T_rad * T_mean_zi**2 / cc.c_light_Mpc_s * f_zi * D_zi**2 * H_zi / (
chi_zi**2) / (1. + z_i) * x * (sigma_T * rho_g0 / (mu_e * m_p))
kperp = ell / chi_zi
k = np.sqrt(kperp**2 + kpar**2)
kp = np.sqrt(kp_perp**2 + kp_par**2)
cos_theta = kp_par / kp #cos_theta=u, theta is azimuthal angle between k' and z (line of sight) axis
sin_theta = kp_perp / kp
sin_gamma = kpar / k #gamma is measured between k and xy plane, i.e. elevation of k
cos_gamma = kperp / k
zeta = sin_gamma * cos_theta + cos_gamma * sin_theta
k_dot_kp = kperp * kp_perp + kpar * kp_par * zeta
K = np.sqrt(k**2 + kp**2 - 2 * k_dot_kp)
theta_K = kpar / K / k**2 * (
k**2 - k_dot_kp) - kp * kperp * np.sqrt(1 - zeta**2) / k / K
theta_kp = cos_theta
rsd = 1. + f_zi * kpar**2 / k**2
I = theta_kp * (theta_kp / kp**2 + theta_K / K / kp)
z_dep_integ = sp.integrate.trapz(f_z * D_z**2 * (1 + z) * np.exp(-tau_z),
z)
integrand_1 = rsd**2 * Mps_interpf(kp) * Mps_interpf(
K) * theta_kp**2 / kp**2 * kp_perp
integrand_2 = rsd**2 * Mps_interpf(kp) * Mps_interpf(
K) * theta_kp * theta_K / kp / K * kp_perp
integral_1 = const * z_dep_integ * sp.integrate.trapz(sp.integrate.trapz(
sp.integrate.trapz(integrand_1, Kp_perp, axis=0), Kp_par, axis=0),
Kpar,
axis=0)
integral_2 = const * z_dep_integ * sp.integrate.trapz(sp.integrate.trapz(
sp.integrate.trapz(integrand_2, Kp_perp, axis=0), Kp_par, axis=0),
Kpar,
axis=0)
return integral_1 + integral_2
def crosscorr_rec_coords(
ell, z_i, y, delta_z
): #with the assumption that zi=z so no cos factor, and we have dz=redshift bin width=2*delta_z defined above
n = n_points #number of points over which to integrate
Kp_par = np.geomspace(1.e-6, .15, n)
Kp_perp = np.geomspace(1.e-6, 1., n)
Z_min = z_i - delta_z
Z_max = z_i + delta_z
Z = np.geomspace(Z_min, Z_max, n)
kp_perp, kp_par, z = np.meshgrid(Kp_perp, Kp_par, Z)
chi_z = chi(z)
T_mean_zi = uf.T_mean(z_i)
chi_zi = chi(z_i)
chi_z = chi(z)
f_zi = uf.f(z_i)
f_z = uf.f(z)
D_zi = uf.D_1(z_i)
r_zi = uf.r(z_i)
D_z = uf.D_1(z)
H_zi = uf.H(z_i)
tau_z = uf.tau_inst(z)
kpar = y / uf.r(z)
const = 1.e6 / (
4. * np.pi**2
) * T_rad * T_mean_zi**2 / cc.c_light_Mpc_s * f_zi * D_zi**2 * H_zi / (
chi_zi**2 * r_zi) / (1. + z_i) * x * (sigma_T * rho_g0 / (mu_e * m_p))
kperp = ell / chi_z
k = np.sqrt(kperp**2 + kpar**2)
kp = np.sqrt(kp_perp**2 + kp_par**2)
cos_theta = kp_par / kp #cos_theta=u, theta is azimuthal angle between k' and z (line of sight) axis
sin_theta = kp_perp / kp
sin_gamma = kpar / k #gamma is measured between k and xy plane, i.e. elevation of k
cos_gamma = kperp / k
zeta = sin_gamma * cos_theta + cos_gamma * sin_theta
k_dot_kp = kperp * kp_perp + kpar * kp_par * zeta
K = np.sqrt(k**2 + kp**2 - 2 * k_dot_kp)
theta_K = kpar / K / k**2 * (
k**2 - k_dot_kp) - kp * kperp * np.sqrt(1 - zeta**2) / k / K
theta_kp = cos_theta
rsd = 1. + f_zi * kpar**2 / k**2
I = theta_kp * (theta_kp / kp**2 + theta_K / K / kp)
integrand_1 = f_z * D_z**2 * (
1 + z) * np.exp(-tau_z) * rsd**2 * Mps_interpf(kp) * Mps_interpf(
K) * theta_kp**2 / kp**2
integrand_2 = f_z * D_z**2 * (
1 + z) * np.exp(-tau_z) * rsd**2 * Mps_interpf(kp) * Mps_interpf(
K) * theta_kp * theta_K / kp / K
integral_1 = const * sp.integrate.trapz(sp.integrate.trapz(
sp.integrate.trapz(integrand_1, Kp_perp, axis=0), Kp_par, axis=0),
Z,
axis=0)
integral_2 = const * sp.integrate.trapz(sp.integrate.trapz(
sp.integrate.trapz(integrand_2, Kp_perp, axis=0), Kp_par, axis=0),
Z,
axis=0)
return integral_1 + integral_2
def crosscorr_squeezedlim(
ell, z_i, y, delta_z
): #with the assumption that zi=z so no cos factor, and we have dz=redshift bin width=2*delta_z defined above
n = n_points #number of points over which to integrate
#y=np.geomspace(1.,3000.,n)
U = np.linspace(-.9999, .9999, n)
Kp = np.geomspace(1.e-6, .1, n)
Z_min = z_i - delta_z
Z_max = z_i + delta_z
z = np.geomspace(Z_min, Z_max, n)
u, kp = np.meshgrid(U, Kp)
T_mean_zi = uf.T_mean(z_i)
chi_zi = chi(z_i)
chi_z = chi(z)
f_zi = uf.f(z_i)
f_z = uf.f(z)
D_zi = uf.D_1(z_i)
r_zi = uf.r(z_i)
D_z = uf.D_1(z)
H_zi = uf.H(z_i)
tau_z = uf.tau_inst(z)
kpar = y / uf.r(z)
const = 1.e6 / (
4. * np.pi**2
) * T_rad * T_mean_zi**2 / cc.c_light_Mpc_s * f_zi * D_zi**2 * H_zi / (
chi_zi**2 * r_zi) / (1. + z_i) * x * (sigma_T * rho_g0 / (mu_e * m_p))
#Cl=np.array([])
kp_perp = kp * np.sqrt(1 - u**2)
kp_par = kp * u
k_perp = ell / chi_zi
k = np.sqrt(k_perp**2 + kpar**2)
rsd = 1. + f_zi * kpar**2 / k**2
zeta = (kpar / k * u + k_perp / k * np.sqrt(1 - u**2))
k_dot_kp = k_perp * kp_perp + kpar * kp_par * zeta
K = np.sqrt(k**2 + kp**2 - 2 * k_dot_kp)
#theta_kp=kpar*zeta/k+k_perp*np.sqrt(np.abs(1-zeta**2))/k
theta_K = kpar / K / k**2 * (
k**2 - k_dot_kp) - kp * k_perp * np.sqrt(1 - zeta**2) / k / K
#print (theta_K.min(),theta_K.max())
theta_kp = u
#theta_K=np.where(theta_K > 0, theta_K, 0)
I = theta_kp * (theta_kp / kp**2 + theta_K / K / kp)
z_integral = sp.integrate.trapz(f_z * D_z**2 * (1 + z) * np.exp(-tau_z), z)
integrand_1 = z_integral * Mps_interpf(kp) * Mps_interpf(
K) * rsd**2 * theta_kp**2
#+theta_K/K/kp)#-mu*kp*np.gradient(Mps_interpf(k),axis=0))
integrand_2 = z_integral * Mps_interpf(kp) * Mps_interpf(
k) * rsd**2 * kp**2 * theta_kp * theta_K / kp / K
integral_sing_1 = const * sp.integrate.trapz(
sp.integrate.trapz(integrand_1, U, axis=0), Kp, axis=0)
integral_sing_2 = const * sp.integrate.trapz(
sp.integrate.trapz(integrand_2, U, axis=0), Kp, axis=0)
#Cl=np.append(Cl,integral)
return integral_sing_1 + integral_sing_2
def Cl_21(ell,y,z):
#Cl=[]
Cl=np.array([])
for i in ell:
kpar=y/uf.r(z)
k=np.sqrt(kpar**2+(i/uf.chi(z))**2)
mu_k_sq=kpar**2/k**2
a=uf.b_HI+uf.f(z)*mu_k_sq
Cl_one=(uf.T_mean(z)*a*uf.D_1(z))**2*uf.Mps_interpf(k)/(uf.chi(z)**2*uf.r(z))
Cl=np.append(Cl,Cl_one)
return Cl
def Cl_21_func_of_y(ell, z, y):
z1 = 1.
kpar = y / r(z1)
chi_1 = uf.chi(z1)
f_1 = uf.f(z1)
D_1 = uf.D_1(z1)
k = np.sqrt(kpar**2 + (ell / chi_1)**2)
mu_k_sq = kpar**2 / k**2
a = uf.b_HI + f_1 * mu_k_sq
Cl = (uf.T_mean(z1) * a * D_1)**2 * uf.Mps_interpf(k) / chi_1**2 / r(z1)
return Cl
def crosscorr_squeezed_integral_y(ell, z_i, delta_z):
n = n_points #number of points over which to integrate
#y=np.geomspace(1.,3000.,n)
#Kpar=y/uf.r(z)
Kpar = np.geomspace(1.e-6, .15, n)
U = np.linspace(-.9999, .9999, n)
Kp = np.geomspace(1.e-6, .1, n)
Z_min = z_i - delta_z
Z_max = z_i + delta_z
z = np.geomspace(Z_min, Z_max, n)
u, kp, kpar = np.meshgrid(U, Kp, Kpar)
T_mean_zi = uf.T_mean(z_i)
chi_zi = chi(z_i)
chi_z = chi(z)
f_zi = uf.f(z_i)
f_z = uf.f(z)
D_zi = uf.D_1(z_i)
r_zi = uf.r(z_i)
D_z = uf.D_1(z)
H_zi = uf.H(z_i)
tau_z = uf.tau_inst(z)
const = 1.e6 / (
8. * np.pi**3
) * T_rad * T_mean_zi**2 / cc.c_light_Mpc_s * f_zi * D_zi**2 * H_zi / (
chi_zi**2) / (1. + z_i) * x * (sigma_T * rho_g0 / (mu_e * m_p))
#Cl=np.array([])
kp_perp = kp * np.sqrt(1 - u**2)
kp_par = kp * u
k_perp = ell / chi_zi
k = np.sqrt(k_perp**2 + kpar**2)
rsd = 1. + f_zi * kpar**2 / k**2
zeta = (kpar / k * u + k_perp / k * np.sqrt(1 - u**2))
k_dot_kp = k_perp * kp_perp + kpar * kp_par * zeta
K = np.sqrt(k**2 + kp**2 - 2 * k_dot_kp)
#theta_kp=kpar*zeta/k+k_perp*np.sqrt(np.abs(1-zeta**2))/k
theta_K = kpar / K / k**2 * (
k**2 - k_dot_kp) - kp * k_perp * np.sqrt(1 - zeta**2) / k / K
theta_kp = u
#theta_K=np.where(theta_K > 0, theta_K, 0)
I = theta_kp * (theta_kp / kp**2 + theta_K / K / kp)
z_dep_integ = sp.integrate.trapz(f_z * D_z**2 * (1 + z) * np.exp(-tau_z),
z)
integrand = Mps_interpf(kp) * Mps_interpf(
k
) * rsd**2 * kp**2 * I #+theta_K/K/kp)#-mu*kp*np.gradient(Mps_interpf(k),axis=0))
integral_sing = const * z_dep_integ * sp.integrate.trapz(
sp.integrate.trapz(
sp.integrate.trapz(integrand, U, axis=0), Kp, axis=0),
Kpar,
axis=0)
#Cl=np.append(Cl,integral)
return integral_sing
def Integrand_doppler_21cm(ell, y):
z1 = 1.
z2 = z1
r_1 = r(z1)
chi_1 = chi(z1)
f_1 = f(z1)
D1 = D(z1)
tau_1 = tau(z1)
H_1 = H(z1)
H_2 = H(z2)
f_2 = f(z2)
D2 = D(z2)
chi_2 = chi(z2)
tau_2 = tau(z2)
kpar = y / r_1
k = np.sqrt(kpar**2 + ell**2 / chi_1**2)
const = uf.T_mean(z1) * uf.T_mean(z2) / cc.c_light_Mpc_s**2
mu_k = kpar / k
rsd = 1 + f_1 * mu_k**2
integrand = D1 * D2 * H_1 * H_2 * f_1 * f_2 * Mps_interpf(k) * np.cos(
kpar * (chi_1 - chi_2)) * rsd**2 / (1 + z1) / (
1 + z2) * mu_k**2 / k**2 / chi_1**2 / r_1
return const * integrand
def Cl_21_lksz(ell,y,z):
#Cl=[]
Cl=np.array([])
for i in ell:
a=uf.b_HI+uf.f(z)*mu_k(i,y,z)**2
#print (a)
delta_tcm=(uf.T_mean(z)*a*uf.D_1(z))/(uf.chi(z)**2*uf.r(z))
#print (delta_tcm)
delta_lksz=const*u(z_r)*np.abs(np.cos(uf.kpar(y,z_r)*chi_r))/k(i,y,z_r)**2*lksz.Mps_interpf(k(i,y,z_r))
#print (delta_lksz)
Cl_one=delta_tcm*delta_lksz
Cl=np.append(Cl,Cl_one)
return Cl
def Cl_21(ell, z1):
y = np.linspace(1, 3000, n_points)
kpar = np.geomspace(1e-10, 1e-2, n_points)
kpar = y / r(z1)
Cl = np.array([])
for i in ell:
#integral=sp.integrate.quadrature(lambda kpar:Cl_21_func_of_y(z1,kpar,i),1e-4,1e-1)[0]
chi_1 = uf.chi(z1)
f_1 = uf.f(z1)
D_1 = uf.D_1(z1)
k = np.sqrt(kpar**2 + (i / chi_1)**2)
mu_k_sq = kpar**2 / k**2
a = uf.b_HI + f_1 * mu_k_sq
integral = sp.integrate.trapz((uf.T_mean(z1) * a * D_1)**2 *
uf.Mps_interpf(k) / chi_1**2 / r(z1),
y,
axis=0)
Cl = np.append(Cl, integral)
return Cl
def crosscorr_squeezedlim(ell,
y): #with the assumption that zi=z so no cos factor
z_i = 1.
delta_z = 0.3
n = 100
Mu = np.linspace(-0.9999, 0.9999, n)
Kp = np.linspace(1.e-4, 10., n)
mu, kp = np.meshgrid(Mu, Kp)
z = z_i
T_mean_zi = uf.T_mean(z_i)
chi_zi = chi(z_i)
chi_z = chi(z)
f_zi = uf.f(z_i)
f_z = uf.f(z)
D_zi = uf.D_1(z_i)
r_zi = uf.r(z_i)
D_z = uf.D_1(z)
H_zi = uf.H(z_i)
tau_z = uf.tau_inst(z)
const = 1.e6 / (
2. * np.pi
)**2 * T_rad * T_mean_zi / cc.c_light_Mpc_s * f_zi * D_zi**2 * H_zi / (
chi_zi**2 * r_zi) / (1. + z_i) * x * (
sigma_T * rho_g0 /
(mu_e * m_p)) * delta_z * f_z * D_z**2 * (1 + z) * np.exp(-tau_z)
#Cl=np.array([])
kpar = y / r_zi
k_perp = ell / chi_zi
k = np.sqrt(k_perp**2 + kpar**2)
rsd = 1. + f_zi * kpar**2 / k**2
theta_kp = kpar * mu / k + k_perp * np.sqrt(1. - mu**2) / k
integrand = Mps_interpf(kp) * rsd * theta_kp**2 * (
Mps_interpf(k)) #-mu*kp*np.gradient(Mps_interpf(k),axis=0))
integral_sing = const * sp.integrate.trapz(
sp.integrate.trapz(integrand, Mu, axis=0), Kp, axis=0)
#Cl=np.append(Cl,integral)
return integral_sing