def trial_check(d):
a = np.linspace(-1, 1, n_points)
b = np.linspace(1e-5, 1e-1, n_points)
r = np.linspace(0, 1, n_points)
e = np.linspace(1e-4, 1e-2, n_points)
A, B, R, S, E = np.meshgrid(a, b, r, r, e)
array = np.array([])
for i in d:
integrand = sp.integrate.trapz(sp.integrate.trapz(sp.integrate.trapz(
sp.integrate.trapz(sp.integrate.trapz(
(i * A + E) /
(B**2 + i**2 / uf.chi(R)**2 + E**2 -
2 * B * np.sqrt(i**2 / uf.chi(R)**2 + E**2) * A) * R * S,
a,
axis=0),
b,
axis=0),
r,
axis=0),
r,
axis=0),
e,
axis=0)
array = np.append(array, integrand)
return array
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 F_three_ints(ell, z):
Kp = np.geomspace(1.e-10, 10., n_points)
Mu = np.linspace(-0.9999, 0.9999, n_points)
Phi = np.geomspace(1.e-4, 2 * np.pi, n_points)
mu, phi, kp = np.meshgrid(Mu, Phi, Kp)
C_l = np.zeros((len(z), len(ell)))
theta_kp_arr = np.array([])
theta_K_arr = np.array([])
for j in range(len(z)):
for i in range(len(ell)):
k = ell[i] / uf.chi(z[j])
K = np.sqrt(k**2 + kp**2 - 2 * k * kp * mu * np.cos(phi))
theta_kp = np.sqrt(1 - mu**2)
theta_kp_arr = np.append(theta_kp_arr, theta_kp)
theta_K = -np.sqrt(1 - mu**2) * kp / K
theta_K_arr = np.append(theta_K_arr, theta_K)
I = theta_kp / kp**2 + theta_K * theta_kp / K / kp
z_part = (1 + z[j])**2 * np.exp(-2 * tau_inst(z[j])) * f(
z[j])**2 * D(z[j])**4 / chi(z[j])**2 * H(z[j])
integral = z_part * sp.integrate.trapz(sp.integrate.trapz(
sp.integrate.trapz(
kp**2 * I * Mps_interpf(kp) * Mps_interpf(K), Mu, axis=0),
Phi,
axis=0),
Kp,
axis=0)
C_l[j, i] = integral
return C_l, theta_kp_arr, theta_K_arr
def C_l_castro_integrand(ell, z):
Kp = np.geomspace(k_min, k_max, n_points)
Y1 = Kp * uf.chi(z) / ell
Mu = np.linspace(-1, 1, n_points)
mu, y1 = np.meshgrid(Mu, Y1)
H = uf.H
chi = uf.chi
tau = uf.tau_inst
#chi_Z=chi(Z)
f = uf.f
D = uf.D_1
const = 1e12 * T_rad**2 * x**2 / cc.c_light_Mpc_s * (sigma_T * rho_g0 /
(mu_e * m_p))**2
#kp_norm=np.linalg.norm(Kp)
#k_norm=np.linalg.norm(ell/chi_Z)
C_l = np.array([])
for i in z:
k = ell / chi(i)
constants = 1 / (2 * np.pi)**(3 / 2) * 2 * np.pi / 2
#mu=np.dot(k,Kp)/(k_norm*kp_norm)
#I=k*(k-2*kp*j)*(1-j**2)/(k**2+kp**2-2*k*kp*j)
integral = [
constants * sp.integrate.trapz(sp.integrate.trapz(
f(i)**2 * Mps_interpf(k * y1) *
Mps_interpf(k * np.sqrt(1 + y1**2 - 2 * y1 * mu)) * k *
(1 - 2 * y1 * mu)**2 * (1 - mu**2) /
(1 + y1**2 - 2 * y1 * mu)**2 * const *
(1 + i)**2 * H(i) * D(i)**4 * np.exp(-2 * tau(i)) / chi(i)**2,
Y1,
axis=0),
Mu,
axis=0)
]
C_l = np.append(C_l, integral)
return C_l
def C_l_mu_single_ell(ell):
Kp = np.geomspace(1e-4, 100, n_points)
Mu = np.linspace(-0.9999, 0.9999, n_points)
Z = np.geomspace(1e-4, z_r, n_points)
mu, kp, z = np.meshgrid(Mu, Kp, Z)
H_z = uf.H(Z)
chi_z = uf.chi(Z)
#chi_Z=chi(Z)
tau_z = uf.tau_inst(Z)
f_z = uf.f(Z)
D_z = uf.D_1(Z)
const = 1e12 * T_rad**2 * x**2 / cc.c_light_Mpc_s * (
sigma_T * rho_g0 / (mu_e * m_p))**2 / 8 / np.pi**2
#kp_norm=np.linalg.norm(Kp)
#k_norm=np.linalg.norm(ell/chi_Z)
k = ell / chi_z
K = np.sqrt(k**2 + kp**2 - 2 * k * kp * mu)
integral = sp.integrate.trapz(sp.integrate.trapz(
sp.integrate.trapz(Mps_interpf(kp) * np.exp(-2 * tau_z) * f_z**2 *
D_z**4 * H_z * (1 - mu**2) * (1 + z)**2 / chi_z**2,
Mu,
axis=0),
Kp,
axis=0),
Z,
axis=0)
return integral
def C_l_integrand(ell, z):
Kp = np.geomspace(1e-4, k_max, n_points)
Mu = np.linspace(-0.9999, 0.9999, n_points)
mu, kp = np.meshgrid(Mu, Kp)
H_z = uf.H(z)
chi_z = uf.chi(z)
#chi_Z=chi(Z)
tau_z = uf.tau_inst(z)
f_z = uf.f(z)
D_z = uf.D_1(z)
const = 1e12 * T_rad**2 * x**2 / cc.c_light_Mpc_s * (
sigma_T * rho_g0 / (mu_e * m_p))**2 / 8 / np.pi**2
#kp_norm=np.linalg.norm(Kp)
#k_norm=np.linalg.norm(ell/chi_Z)
C_l = np.array([])
for i in ell:
k = i / chi_z
K = np.sqrt(np.abs(k**2 + kp**2 - 2 * k * kp * mu))
integral = [
const * sp.integrate.trapz(sp.integrate.trapz(
k * (k - 2 * kp * mu) *
(1 - mu**2) / K**2 * Mps_interpf(kp) * Mps_interpf(K) *
(1 + z)**2 * np.exp(-2 * tau_z) * f_z**2 * D_z**4 / chi_z**2 *
H_z,
Mu,
axis=0),
Kp,
axis=0)
]
C_l = np.append(C_l, integral)
return C_l
def power_spec(ell):
kpar = np.geomspace(1e-4, 1e-1, 1000)
array = np.array([])
z = 1
for i in ell:
k = np.sqrt(kpar**2 + i**2 / uf.chi(z)**2)
integrand = Mps_interpf(k)
integral = sp.integrate.trapz(integrand, kpar, axis=0)
array = np.append(array, integral)
return array
def Delta_b_noredshift_single(ell, z):
kp_norm = np.linalg.norm(kp)
k = ell / uf.chi(z)
k_norm = np.linalg.norm(k)
mu = np.dot(k, kp) / (k_norm * kp_norm)
I = k * (k - 2 * kp * mu) * (1 - mu**2) / (k**2 + kp**2 - 2 * k * kp * mu)
constants = 1 / ((2 * np.pi**2) * (2 * np.pi)**3)
delta_sq = constants * Mps_interpf(kp) * Mps_interpf(np.abs(ell - kp)) * I
Integral = sp.integrate.trapz(delta_sq, kp)
return Integral
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 Mps_k(ell):
#Cl=np.array([])
Mps=np.array([])
kpar=(2/uf.r(1))
for i in ell:
k=np.sqrt(kpar**2+(i/uf.chi(1))**2)
Mps_one_ell=uf.Mps_interpf(k)
#Mps_div_ell=Mps*kpar**4*(T_mean(1)*(kpar**2/k**2))**2/(chi(1)**2*r(1))
#Cl=np.append(Cl,Mps_div_ell)
Mps=np.append(Mps,Mps_one_ell)
return Mps
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 C_l_mu_integral_threeints(ell, z_min):
Kp = np.geomspace(1.e-10, 10., n_points)
Mu = np.linspace(-0.9999, 0.9999, n_points)
Phi = np.geomspace(1.e-4, 2 * np.pi, n_points)
Z = np.geomspace(z_min, z_r, n_points)
mu, phi, kp, z = np.meshgrid(Mu, Phi, Kp, Z)
H_z = uf.H(z)
chi_z = uf.chi(z)
#chi_Z=chi(Z)
tau_z = uf.tau_inst(z)
f_z = uf.f(z)
D_z = uf.D_1(z)
const = 1e12 * T_rad**2 * x**2 / cc.c_light_Mpc_s * (
sigma_T * rho_g0 / (mu_e * m_p))**2 / 16 / np.pi**3
#kp_norm=np.linalg.norm(Kp)
#k_norm=np.linalg.norm(ell/chi_Z)
theta_kp_arr = np.array([])
theta_K_arr = np.array([])
I_arr = np.array([])
C_l = np.array([])
for i in ell:
k = i / chi_z
K = np.sqrt(k**2 + kp**2 - 2 * k * kp * mu * np.cos(phi))
theta_kp = np.sqrt(1 - mu**2)
theta_K = -np.sqrt(1 - mu**2) * kp / K
theta_kp_arr = np.append(theta_kp_arr, theta_kp)
theta_K_arr = np.append(theta_K_arr, theta_K)
I = theta_kp**2 / kp**2 + theta_K * theta_kp / K / kp
I_arr = np.append(I_arr, I)
#I=k*(k-2*kp*mu)*(1-mu**2)/K**2
integral = [
const * sp.integrate.trapz(sp.integrate.trapz(sp.integrate.trapz(
sp.integrate.trapz(
kp**2 * I * Mps_interpf(kp) * Mps_interpf(K) * (1 + z)**2 *
np.exp(-2 * tau_z) * f_z**2 * D_z**4 / chi_z**2 * H_z,
Mu,
axis=0),
Phi,
axis=0),
Kp,
axis=0),
Z,
axis=0)
]
C_l = np.append(C_l, integral)
return C_l, theta_kp_arr, theta_K_arr, I_arr
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 C_l(ell):
C_l=np.array([])
zz=z[:,np.newaxis]
kk=kp[np.newaxis,:]
kk_norm=np.linalg.norm(kk)
for i in ell:
#mu=kk/i
#mu=(i**2+kk**2-(np.abs(i-kk))**2)/(2*i*kk)
#print (mu)
#I=i**2/(kk**2*(i**2+kk**2))
k_norm=np.linalg.norm(i/chi(zz))
mu=np.dot(i/chi(zz),kk)/(k_norm*kk_norm)
#print (mu)
I=i/chi(zz)*(i/chi(zz)-2*kk*mu)*(1-mu**2)/((i/chi(zz))**2+kk**2-2*i/chi(zz)*kk*mu)
constants=(i/chi(zz))**3/((2*np.pi**2)*(2*np.pi)**3)
delta_sq=constants*Mps_interpf(kk)*Mps_interpf(np.abs(i/chi(zz)-kk))*I
const=8*np.pi**2*T_rad**2*x**2/cc.c_light_Mpc_s*(sigma_T*rho_g0/(mu_e*m_p))**2
integrand=[const*(1+zz)**2*uf.f(zz)**2*delta_sq*uf.chi(zz)*uf.H(zz)*np.exp(-2*tau(zz))]
C_l=np.append(C_l,sp.integrate.trapz(sp.integrate.trapz(integrand,zz,axis=0),kp,axis=0))
return C_l
def C_l_castro_triplemesh(ell, z_min):
Z = np.geomspace(z_min, z_r, n_points)
kp = np.geomspace(k_min, k_max, n_points)
Y1 = kp * uf.chi(Z) / ell
Mu = np.linspace(-1, 1, n_points)
mu, y1, z = np.meshgrid(Mu, Y1, Z)
H = uf.H
chi = uf.chi
#chi_Z=chi(Z)
tau = uf.tau_inst
f = uf.f
D = uf.D_1
const = 1e12 * T_rad**2 * x**2 / cc.c_light_Mpc_s * (sigma_T * rho_g0 /
(mu_e * m_p))**2
#kp_norm=np.linalg.norm(Kp)
#k_norm=np.linalg.norm(ell/chi_Z)
constants = 1 / (2 * np.pi)**(3 / 2) * 2 * np.pi / 2
C_l = np.array([])
for i in ell:
print(i)
#mu=np.dot(k,Kp)/(k_norm*kp_norm)
#I=k*(k-2*kp*j)*(1-j**2)/(k**2+kp**2-2*k*kp*j)
integral = [
constants *
sp.integrate.trapz(sp.integrate.trapz(sp.integrate.trapz(
f(z)**2 * Mps_interpf(i * y1 / chi(z)) *
Mps_interpf(i / chi(z) * np.sqrt(1 + y1**2 - 2 * y1 * mu)) *
i / chi(z) * (1 - 2 * y1 * mu) * (1 - mu**2) /
(1 + y1**2 - 2 * y1 * mu) * const *
(1 + z)**2 * H(z) * D(z)**4 * np.exp(-2 * tau(z)) / chi(z)**2,
Y1,
axis=0),
Mu,
axis=0),
Z,
axis=0)
]
C_l = np.append(C_l, integral)
return C_l
def C_l_mu_integral_squeezed(ell, z_min):
Kp = np.geomspace(1.e-10, .1, n_points)
Mu = np.linspace(-0.9999, 0.9999, n_points)
Z = np.geomspace(z_min, z_r, n_points)
mu, kp, z = np.meshgrid(Mu, Kp, Z)
H_z = uf.H(z)
chi_z = uf.chi(z)
#chi_Z=chi(Z)
tau_z = uf.tau_inst(z)
f_z = uf.f(z)
D_z = uf.D_1(z)
const = 1e12 * T_rad**2 * x**2 / cc.c_light_Mpc_s * (
sigma_T * rho_g0 / (mu_e * m_p))**2 / 8 / np.pi**2
#kp_norm=np.linalg.norm(Kp)
#k_norm=np.linalg.norm(ell/chi_Z)
C_l = np.array([])
for i in ell:
k = i / chi_z
#K=np.sqrt(k**2+kp**2-2*k*kp*mu) #original K
K = np.sqrt(k**2 + kp**2 - 2 * k * kp *
(np.sqrt(1 - mu**2))) #changed K, correct one
#I=(1-mu**2) #in squeezed with original
#I=k*(k-2*kp*mu)*(1-mu**2)/K**2 #original I, without squeezed
#I=k*(k-2*kp*np.sqrt(1-mu**2))*(mu**2)/K**2 #I, without squeezed, changed, correct one
I = mu**2 #I, with squeezed, changed, correct one
integral = [
const * sp.integrate.trapz(sp.integrate.trapz(sp.integrate.trapz(
I * Mps_interpf(kp) * Mps_interpf(k) * (1 + z)**2 *
np.exp(-2 * tau_z) * f_z**2 * D_z**4 / chi_z**2 * H_z,
Mu,
axis=0),
Kp,
axis=0),
Z,
axis=0)
]
C_l = np.append(C_l, integral)
return C_l
def k(i,y,z):
k=np.sqrt(uf.kpar(y,z)**2+(i/uf.chi(z))**2)
return k
from decimal import Decimal cosmo=uf.cosmo Mps_interpf=uf.Mps_interpf n_points=uf.n_points z_r=10. x_e=1. G=cc.G_const_Mpc_Msun_s/cc.M_sun_g #rho_c=3*H0**2/(8.*np.pi*G) rho_c=den.cosmo_densities(**cosmo)[0]*cc.M_sun_g #in units of g/Mpc^3 sigma_T=cc.sigma_T_Mpc tau_r=0.055 T_rad=2.73 #In Kelvin chi_r = uf.chi(z_r) chi_m = uf.chi(1100) chi_min=0.0001 k_min=1e-3 k_max=0.1 chi_array=np.linspace(chi_min,chi_m,n_points) #tau_r=0.046*omega_b_0*h*x_e[np.sqrt(omega_M_0(1+z_r)**3+(1-omega_M_0))-1] #get matter power spec data mu_e=1.44 m_p=cc.m_p_g #in grams rho_g0=cosmo['omega_b_0']*rho_c #plt.loglog(uf.kabs,Mps_interpf(uf.kabs)) #plt.show() zed=uf.zed z=uf.z
if n_u(i/(2.*np.pi))==0:
n_u1=1/1e100
else:
n_u1=n_u(i/(2.*np.pi))
n=np.append(n,n_u1)
Nbs= 1024.*(1024.-1.)
#norm=Nbs/sp.integrate.trapz(n*2*np.pi*(l/(2.*np.pi)), l/(2.*np.pi))
C=n#*noprint (nu_min)
A_bull= ((Tsys**2)*(lam**4)*Sarea) / (nu21*npol*Ttot*(Aeff**2)*Fov_deg*Nbeam)
Warren=Tsys**2*lam**2/Aeff*4.*np.pi/(nu21*npol*Nbeam*Ttot)
#return (Warren/C)*1e12
return (A_bull/C)*1e12
ell_large=np.geomspace(1.e-10,1.e6,10000)
kperp_min_orig,kperp_max_orig=uf.ell_lims(z,6.,6*1024)/uf.chi(z)
kperp_min,kperp_max=kperp_min_orig,kperp_max_orig
#print (kperp_min,kperp_max)
kpar_min=uf.kpar_min(z,delta_z)
#print (kpar_min)
kperp_arr=np.geomspace(kperp_min,kperp_max,n)
kpar_arr=np.geomspace(kpar_min,5.,n)
ell_min,ell_max=uf.chi(z)*kperp_min,uf.chi(z)*kperp_max
ell=np.geomspace(ell_min,ell_max,n)
ell=np.geomspace(1.,1.e4,n)
kperp_arr=ell/chi(1.26)
kpar_arr=np.geomspace(1.e-4,.15,n)
y=kpar_arr*r(1.26)
def P_delta_N_v(z, kperp, kpar, Noise):
k = np.sqrt(kperp**2 + kpar**2)
Nv_func_of_k = Noise(uf.chi(z) * kperp) / k**4 * kpar**2
return Nv_func_of_k * Mps_interpf(k)
def P_v_N_delta(z, kperp, kpar, Noise):
k = np.sqrt(kperp**2 + kpar**2)
Pv_func_of_k = Mps_interpf(k) / k**4 * kpar**2
return Pv_func_of_k * Noise(uf.chi(z) * kperp)
Ttot)
#return (Warren/C)*1e12
return (A_bull / C) * 1e12
ell_large = np.geomspace(1.e-10, 1.e5, 10000)
kperp_min_orig, kperp_max_orig = uf.kperp_lims(z, 6., 6. * 1024.)
kperp_min, kperp_max = kperp_min_orig, kperp_max_orig
#print (kperp_min,kperp_max)
kpar_min = uf.kpar_min(z, delta_z)
#print (kpar_min)
kperp_arr = np.geomspace(kperp_min, kperp_max, n)
kpar_arr = np.geomspace(kpar_min, 5., n)
ell_min, ell_max = uf.chi(z) * kperp_min, uf.chi(z) * kperp_max
ell = np.geomspace(ell_min, ell_max, n)
ell = np.geomspace(1., 1.e4, n)
#np.savetxt('Hirax_noise_z_1_Ddish_6_Dsep_7_geom.out',(ell_large,HiraxNoise(ell_large,6.,7.,1.)))
#ell_new,Hirax_noise_z_1=np.genfromtxt('/home/zahra/python_scripts/kSZ_21cm_signal/Hirax_noise_z_1_Ddish_6_Dsep_7.out')
Hirax_noise_z_1pt26_deltaz_pt2 = interp1d(ell_large,
HiraxNoise(ell_large, 6., 7., 1.26,
0.2),
bounds_error=False)
Hirax_noise_z_1pt26_deltaz_pt05 = interp1d(ell_large,
HiraxNoise(ell_large, 6., 7., 1.26,
0.05),
bounds_error=False)
Hirax_noise_z_1pt26_deltaz_pt0015 = interp1d(ell_large,
HiraxNoise(
x_e = 1. G = cc.G_const_Mpc_Msun_s / cc.M_sun_g #rho_c=3*H0**2/(8.*np.pi*G) rho_c = den.cosmo_densities(**cosmo)[0] * cc.M_sun_g #in units of g/Mpc^3 sigma_T = cc.sigma_T_Mpc tau_r = 0.055 T_rad = 2.725 #In Kelvin chi_m = uf.chi(1100) chi_min = 0.0001 k_min = 1e-4 k_max = 4.5e-2 chi_array = np.linspace(chi_min, chi_m, n_points) #tau_r=0.046*omega_b_0*h*x_e[np.sqrt(omega_M_0(1+z_r)**3+(1-omega_M_0))-1] #get matter power spec data mu_e = 1.44
plt.show()
'''
def cumulative_SNR(SNR_2D_binned):
sum_each_kperp=np.array([])
SNR_y,SNR_x=SNR_2D_binned.shape
for i in range(SNR_x):
sum_one_kperp=np.sum(SNR_2D_binned[:,i])
sum_each_kperp=np.append(sum_each_kperp,sum_one_kperp)
return sum_each_kperp
S_area=15000
SNR=Bispec_SNR
kperp_arr,kpar_arr,SNR_arr=SNR_binned(z,delta_z,Noise,SNR,S_area,Dsep=7.)
ell=kperp_arr*uf.chi(z)
#print (np.cumsum(cum_SNR(SNR_arr)))
pylab.pcolormesh(kperp_arr,kpar_arr,SNR_arr) ; cbar=plt.colorbar()
cbar.ax.tick_params(labelsize=12)
plt.tick_params(axis='both', which='major', labelsize=12)
pylab.xlim([np.min(kperp_arr),np.max(kperp_arr)]) ; pylab.ylim([np.min(kpar_arr),np.max(kpar_arr)])
plt.xlabel(r'$k_\perp$',fontsize=12); plt.ylabel(r'$k_\parallel$',fontsize=12); plt.title('Pixel SN for bispectrum', x=1.13, y=1.05)
pylab.show()
plt.plot(kperp_arr,np.cumsum(cumulative_SNR(SNR_arr)))
plt.ylabel('Cumulative S/N')
plt.xlabel(r'$k_\perp$')
plt.show()
