def compute_recon_power_spectrum(fishcast,z,b=-1.,b2=-1.,bs=-1.,N=None):
'''
Returns the reconstructed power spectrum, following Stephen's paper.
'''
if b == -1.: b = compute_b(fishcast,z)
if b2 == -1: b2 = 8*(b-1)/21
if bs == -1: bs = -2*(b-1)/7
noise = 1/compute_n(fishcast,z)
if fishcast.experiment.HI: noise = castorinaPn(z)
if N is None: N = 1/compute_n(fishcast,z)
f = fishcast.cosmo.scale_independent_growth_factor_f(z)
bL1 = b-1.
bL2 = b2-8*(b-1)/21
bLs = bs+2*(b-1)/7
K,MU = fishcast.k,fishcast.mu
h = fishcast.params['h']
klin = np.logspace(np.log10(min(K)),np.log10(max(K)),fishcast.Nk)
mulin = MU.reshape((fishcast.Nk,fishcast.Nmu))[0,:]
plin = np.array([fishcast.cosmo.pk_cb_lin(k*h,z)*h**3. for k in klin])
zelda = Zeldovich_Recon(klin,plin,R=15,N=2000,jn=5)
kSparse,p0ktable,p2ktable,p4ktable = zelda.make_pltable(f,ngauss=3,kmin=min(K),kmax=max(K),nk=200,method='RecSym')
bias_factors = np.array([1, bL1, bL1**2, bL2, bL1*bL2, bL2**2, bLs, bL1*bLs, bL2*bLs, bLs**2,0,0,0])
p0Sparse = np.sum(p0ktable*bias_factors, axis=1)
p2Sparse = np.sum(p2ktable*bias_factors, axis=1)
p4Sparse = np.sum(p4ktable*bias_factors, axis=1)
p0,p2,p4 = Spline(kSparse,p0Sparse)(klin),Spline(kSparse,p2Sparse)(klin),Spline(kSparse,p4Sparse)(klin)
l0,l2,l4 = legendre(0),legendre(2),legendre(4)
Pk = lambda mu: p0*l0(mu) + p2*l2(mu) + p4*l4(mu)
result = np.array([Pk(mu) for mu in mulin]).T
return result.flatten() + N
def nonnorm_Wg(z):
result = fishcast.cosmo.Hubble(z)
try:
number_density = compute_n(fishcast,z)
except:
if X == Y and X == 'k': number_density = 10
else: raise Exception('Attemped to integrate outside of \
specificed n(z) range')
if fishcast.experiment.HI: number_density = castorinaPn(z)
result *= number_density * dchidz(z) * chi(z)**2
return result
def compute_real_space_cross_power(fishcast, X, Y, z, gamma=1., b=-1.,
b2=-1,bs=-1,alpha0=-1,alphax=0,N=None):
'''
Wrapper function for CLEFT. Returns P_XY where X,Y = k or g
as a function of k.
'''
if b == -1.: b = compute_b(fishcast,z)
if b2 == -1: b2 = 8*(b-1)/21
if bs == -1: bs = -2*(b-1)/7
if alpha0 == -1: alpha0 = 1.22 + 0.24*b**2*(z-5.96)
if N == None:
N = 1/compute_n(fishcast,z)
if fishcast.experiment.HI: N = castorinaPn(z)
bk = (1+gamma)/2-1
h = fishcast.params['h']
K = fishcast.k
klin = np.array([K[i*fishcast.Nmu] for i in range(fishcast.Nk)])
plin = np.array([fishcast.cosmo.pk_cb_lin(k*h,z)*h**3. for k in klin])
########################################################################################################
if fishcast.linear:
print('IMPLEMENT STUFF HERE')
if X == Y and X == 'k':
plin = np.array([fishcast.cosmo.pk_lin(k*h,z)*h**3. for k in klin])
cleft = CLEFT(klin,plin,cutoff=2.)
cleft.make_ptable(kmin=min(klin),kmax=max(klin),nk=fishcast.Nk)
kk,pmm = cleft.combine_bias_terms_pk(0,0,0,0,0,0)
if z>10: pmm=np.array([fishcast.cosmo.pk(k*h,z)*h**3. for k in klin])
return interp1d(kk, pmm, kind='linear', bounds_error=False, fill_value=0.)
cleft = CLEFT(klin,plin,cutoff=2.)
cleft.make_ptable(kmin=min(klin),kmax=max(klin),nk=fishcast.Nk)
bL1 = b-1.
bL2 = b2 - 8*(b-1)/21
bLs = bs + 2*(b-1)/7
if X == Y and X == 'g':
kk,pgg = cleft.combine_bias_terms_pk(bL1,bL2,bLs,alpha0,0,N)
return interp1d(kk, pgg, kind='linear', bounds_error=False, fill_value=0.)
# if neither of the above cases are true, return Pkg
kk = cleft.pktable[:,0]
pkg = cleft.pktable[:,1]+0.5*(bL1+bk)*cleft.pktable[:,2]+bL1*bk*cleft.pktable[:,3]+\
0.5*bL2*cleft.pktable[:,4]+0.5*bk*bL2*cleft.pktable[:,5]+0.5*bLs*cleft.pktable[:,7]+\
0.5*bk*bLs*cleft.pktable[:,8]+alphax*kk**2*cleft.pktable[:,11]
return interp1d(kk, pkg, kind='linear', bounds_error=False, fill_value=0.)
def PNoiseShot(self, z, Tb):
"""21cm shot noise power spectrum.
Parameters
----------
z : float
Redshift.
Tb : float
Mean 21cm brightness temperature (your choice of units).
Returns
-------
pn : float or array
Shot noise power spectrum, in Mpc^3 times square of input Tb units.
"""
return Tb**2 * castorinaPn(z) / (self.C['h'])**3
def PNoiseShot(self, z, Tb):
return Tb**2 * castorinaPn(z) / (self.C['h'])**3
def Nz(z):
if X == Y and X == 'k': return 0
if not fishcast.experiment.HI: return 1/compute_n(fishcast,z) * N/N_fid
else: return castorinaPn(z) * N/N_fid
def compute_lensing_Cell(fishcast, X, Y, zmin=None, zmax=None,zmid=None,gamma=1.,
b=-1,b2=-1,bs=-1, alpha0=-1,alphax=0.,N=-1,
noise=False,Nzsteps=100,Nzeff='auto',maxDz=0.2):
'''
Calculates C^XY_l using the Limber approximation where X,Y = 'k' or 'g'.
Returns an array of length len(fishcast.ell). If X=Y=k, use CLASS with
HaloFit to calculate the lensing convergence.
---------------------------------------------------------------------
noise: if True returns the projected shot noise.
(replaces P -> 1/n)
Nzsteps: number of integration points
---------------------------------------------------------------------
'''
if X == Y and X == 'k' and zmin is None and zmax is None:
lmin,lmax = int(min(fishcast.ell)),int(max(fishcast.ell))
Cphiphi = fishcast.cosmo.raw_cl(lmax)['pp'][lmin:]
return 0.25*fishcast.ell**2*(fishcast.ell+1)**2*Cphiphi*((1+gamma)/2)**2
if zmin is None or zmax is None: raise Exception('Must specify zmin and zmax')
if zmid is None: zmid = (zmin+zmax)/2
b_fid = compute_b(fishcast,zmid)
b2_fid = 8*(b_fid-1)/21
bs_fid = -2*(b_fid-1)/7
alpha0_fid = 1.22 + 0.24*b_fid**2*(zmid-5.96)
N_fid = 1/compute_n(fishcast,zmid)
if fishcast.experiment.HI: N_fid = castorinaPn(zmid)
if b == -1: b = b_fid
if b2 == -1: b2 = b2_fid
if bs == -1: bs = bs_fid
if alpha0 == -1: alpha0 = alpha0_fid
if N == -1: N = N_fid
z_star = 1098
chi = lambda z: (1.+z)*fishcast.cosmo.angular_distance(z)*fishcast.params['h']
def dchidz(z):
if z <= 0.02: return (chi(z+0.01)-chi(z))/0.01
return (-chi(z+0.02)+8*chi(z+0.01)-8*chi(z-0.01)+chi(z-0.02))/0.12
chi_star = chi(z_star)
# CMB lensing convergence kernel
W_k = lambda z: 1.5*(fishcast.params['omega_cdm']+fishcast.params['omega_b'])/\
fishcast.params['h']**2*(1/2997.92458)**2*(1+z)*chi(z)*\
(chi_star-chi(z))/chi_star
# Galaxy kernel (arbitrary normalization)
def nonnorm_Wg(z):
result = fishcast.cosmo.Hubble(z)
try:
number_density = compute_n(fishcast,z)
except:
if X == Y and X == 'k': number_density = 10
else: raise Exception('Attemped to integrate outside of \
specificed n(z) range')
if fishcast.experiment.HI: number_density = castorinaPn(z)
result *= number_density * dchidz(z) * chi(z)**2
return result
zs = np.linspace(zmin,zmax,Nzsteps)
chis = np.array([chi(z) for z in zs])
Wg = np.array([nonnorm_Wg(z) for z in zs])
Wg /= simps(Wg,x=chis)
Wk = np.array([W_k(z) for z in zs])
if X == Y and X == 'k': kern = Wk**2/chis**2
elif X == Y and X == 'g': kern = Wg**2/chis**2
else: kern = Wg*Wk/chis**2
if Nzeff == 'auto': Nzeff = ceil((zmax-zmin)/maxDz)
if Nzeff > Nzsteps: Nzeff = Nzsteps
mask = [(zs < np.linspace(zmin,zmax,Nzeff+1)[1:][i])*\
(zs >= np.linspace(zmin,zmax,Nzeff+1)[:-1][i]) for i in range(Nzeff)]
mask[-1][-1] = True
zeff = np.array([simps(kern*zs*m,x=chis)/simps(kern*m,x=chis) for m in mask])
bz = lambda z: compute_b(fishcast,z) * b/b_fid
b2z = lambda z: 8*(compute_b(fishcast,z)-1)/21 * b2/b2_fid
bsz = lambda z: -2*(compute_b(fishcast,z)-1)/7 * bs/bs_fid
alpha0z = lambda z: (1.22 + 0.24*compute_b(fishcast,z)**2*(z-5.96)) * alpha0/alpha0_fid
def Nz(z):
if X == Y and X == 'k': return 0
if not fishcast.experiment.HI: return 1/compute_n(fishcast,z) * N/N_fid
else: return castorinaPn(z) * N/N_fid
# calculate P_XY
if not noise: P = [compute_real_space_cross_power(
fishcast, X, Y, zz, gamma=gamma, b=bz(zz),
b2=b2z(zz),bs=bsz(zz),alpha0=alpha0z(zz),alphax=alphax,N=Nz(zz)) for zz in zeff]
if noise: P = [fishcast.get_f_at_fixed_mu(np.ones(fishcast.Nk*fishcast.Nmu)/\
compute_n(fishcast, zz),0) for zz in zeff]
P = np.array(P)
def result(ell):
kval = (ell+0.5)/chis
integrands = np.array([kern*P[i](kval) for i in range(Nzeff)])*mask
integrand = np.sum(integrands,axis=0)
return simps(integrand,x=chis)
return np.array([result(l) for l in fishcast.ell])
def compute_tracer_power_spectrum(fishcast, z, b=-1., b2=-1, bs=-1,
alpha0=-1, alpha2=0, alpha4=0.,alpha6=0.,
N=None,N2=-1,N4=0.,f=-1., A_lin=-1.,
omega_lin=-1., phi_lin=-1.,kIR=0.2,
moments=False,bL1=None,bL2=None,bLs=None,
one_loop=True):
'''
Computes the nonlinear redshift-space power spectrum P(k,mu) [Mpc/h]^3
of the matter tracer. Returns an array of length Nk*Nmu.
'''
exp = fishcast.experiment
if fishcast.recon:
return compute_recon_power_spectrum(fishcast,z,b=b,b2=b2,bs=bs,N=N)
if b == -1.: b = compute_b(fishcast,z)
if b2 == -1 and exp.b2 is not None: b2 = exp.b2(z)
elif b2 == -1: b2 = 8*(b-1)/21
if bs == -1: bs = -2*(b-1)/7
if f == -1.: f = fishcast.cosmo.scale_independent_growth_factor_f(z)
if A_lin == -1.: A_lin = fishcast.A_lin
if omega_lin == -1.: omega_lin = fishcast.omega_lin
if phi_lin == -1.: phi_lin = fishcast.phi_lin
if alpha0 == -1: alpha0 = 1.22 + 0.24*b**2*(z-5.96)
if N is None: N = 1/compute_n(fishcast,z)
#
noise = 1/compute_n(fishcast,z)
if exp.HI: noise = castorinaPn(z) # only keep the shot noise piece
sigv = exp.sigv
Hz = fishcast.Hz_fid(z)
if N2 == -1: N2 = -noise*((1+z)*sigv/fishcast.Hz_fid(z))**2
K = fishcast.k
MU = fishcast.mu
h = fishcast.params['h']
klin = np.array([K[i*fishcast.Nmu] for i in range(fishcast.Nk)])
plin = np.array([fishcast.cosmo.pk_cb_lin(k*h,z)*h**3. for k in klin])
plin *= (1. + A_lin * np.sin(omega_lin * klin + phi_lin))
if fishcast.smooth: plin = get_smoothed_p(fishcast,z)
if fishcast.linear2:
pmatter = np.repeat(plin,fishcast.Nmu)
result = pmatter * (b+f*MU**2.)**2.
result /= 1 - N2*(K*MU)**2/noise
result += N
return result
if fishcast.linear:
# If not using velocileptors, use linear theory
# and approximate RSD with Kaiser.
pmatter = np.repeat(plin,fishcast.Nmu)
result = pmatter * (b+f*MU**2.)**2.
result += N+N2*(K*MU)**2+N4*(K*MU)**4
result += pmatter*K**2*(alpha0+alpha2*MU**2+alpha4*MU**4)
return result
if bL1 is None: bL1 = b-1.
if bL2 is None: bL2 = b2 - 8*(b-1)/21
if bLs is None: bLs = bs + 2*(b-1)/7
biases = [bL1,bL2,bLs,0.]
cterms = [alpha0,alpha2,alpha4,alpha6]
stoch = [0,N2,N4]
pars = biases + cterms + stoch
lpt = LPT_RSD(klin,plin,kIR=kIR,one_loop=one_loop,cutoff=2)
lpt.make_pltable(f,kmin=min(klin),kmax=max(klin),nk=len(klin))
k,p0,p2,p4 = lpt.combine_bias_terms_pkell(pars)
if moments: return k,p0,p2,p4
p0 = np.repeat(p0,fishcast.Nmu)
p2 = np.repeat(p2,fishcast.Nmu)
p4 = np.repeat(p4,fishcast.Nmu)
pkmu = p0+0.5*(3*MU**2-1)*p2+0.125*(35*MU**4-30*MU**2+3)*p4 + N
del lpt
return pkmu
for name, zs in [("zlow", zlow)]: #,("zhigh",zhigh)]:
f = open("background_%s.dat" % (name), 'w')
f.write(
"# z distance(z)[Mpc] growth(z)[normalised at z=0] f(z)=dlng/dlna Tspin(z) [mK] b(z) N(z) [Mpc^3] \n"
)
for z in zs:
print z
afact = 1. / (1 + z)
dist = ccl.luminosity_distance(cosmo, afact) # this is what class has
gf = ccl.growth_factor(cosmo, afact)
gr = ccl.growth_rate(cosmo, afact)
print z, gr
if z < 10:
Ts = Tspin(z, OmegaH, OmegaC)
bias = castorinaBias(z)
Pn = castorinaPn(z) / h**3 # converting from Mpc/h^3 to Mpc^3
else:
Ts = pritchardTSpin(z)
bias = 1.0
Pn = 0.0
f.write("%3.2f %g %g %g %g %g %g \n" %
(z, dist, gf, gr, Ts, bias, Pn))
f.close()
# next write power spectrum
f = open("pk0.dat", "w")
f.write("# k [1/Mpc] Pk [Mpc^3] \n")
for k in np.logspace(-3, 1, 200):
print k
f.write("%g %g\n" % (k, ccl.linear_matter_power(cosmo, k, 1.0)))
f.close()
def HI_shot(z):
'''
PUMA shot noise Mpc^3/h^3 from Emanuele Castorina.
'''
return castorinaPn(z)