def clkk_gen(Omega_m, A_se9, zs=1.0):
A_s = A_se9 * 1e-9
omch2 = (OmegaM - OmegaB) * h**2
LambdaCDM = Class()
LambdaCDM.set({
'omega_b': ombh2,
'omega_cdm': omch2,
'h': h,
'A_s': A_s,
'n_s': n_s
})
LambdaCDM.set({
'output': 'mPk,sCl',
'P_k_max_1/Mpc': 10.0,
'l_switch_limber': 100,
'selection': 'dirac',
'selection_mean': zs,
'l_max_lss': lmax,
'non linear': 'halofit'
})
# run class
LambdaCDM.compute()
si8 = LambdaCDM.sigma8()
cls = LambdaCDM.density_cl(lmax)
ell = cls['ell'][2:]
clphiphi = cls['ll'][0][2:]
clkk = 1.0 / 4 * (ell + 2.0) * (ell + 1.0) * (ell) * (ell - 1.0) * clphiphi
return si8, ell, clkk
def class_pk(self, z, cosmo_params=None, pk_params=None, return_s8=False):
if cosmo_params is None:
cosmo_params = self.cosmo_params
if pk_params is None:
pk_params = self.pk_params
cosmoC = Class()
h = cosmo_params['h']
class_params = {
'h': h,
'omega_b': cosmo_params['Omb'] * h**2,
'omega_cdm': (cosmo_params['Om'] - cosmo_params['Omb']) * h**2,
'A_s': cosmo_params['Ase9'] * 1.e-9,
'n_s': cosmo_params['ns'],
'output': 'mPk',
'z_max_pk': 100, #max(z)*2, #to avoid class error.
#Allegedly a compiler error, whatever that means
'P_k_max_1/Mpc': pk_params['kmax'] * h * 1.1,
}
if pk_params['non_linear'] == 1:
class_params['non linear'] = 'halofit'
class_params['N_ur'] = 3.04 #ultra relativistic species... neutrinos
if cosmo_params['mnu'] != 0:
class_params['N_ur'] -= 1 #one massive neutrino
class_params['m_ncdm'] = cosmo_params['mnu']
class_params['N_ncdm'] = 3.04 - class_params['N_ur']
if cosmo_params['w'] != -1 or cosmo_params['wa'] != 0:
class_params['Omega_fld'] = cosmo_params['Oml']
class_params['w0_fld'] = cosmo_params['w']
class_params['wa_fld'] = cosmo_params['wa']
for ke in class_accuracy_settings.keys():
class_params[ke] = class_accuracy_settings[ke]
cosmoC = Class()
cosmoC.set(class_params)
try:
cosmoC.compute()
except Exception as err:
print(class_params, err)
raise Exception('Class crashed')
k = self.kh * h
pkC = np.array([[cosmoC.pk(ki, zj) for ki in k] for zj in z])
pkC *= h**3
s8 = cosmoC.sigma8()
cosmoC.struct_cleanup()
if return_s8:
return pkC, self.kh, s8
else:
return pkC, self.kh
def class_pk(self, z, cosmo_params=None, pk_params=None, return_s8=False):
#output is in same unit as CAMB
if not cosmo_params:
cosmo_params = self.cosmo_params
if not pk_params:
pk_params = self.pk_params
kh = np.logspace(np.log10(pk_params['kmin']),
np.log10(pk_params['kmax']), pk_params['nk'])
cosmoC = Class()
h = cosmo_params['h']
class_params = {
'h': h,
'omega_b': cosmo_params['Omb'] * h**2,
'omega_cdm': (cosmo_params['Om'] - cosmo_params['Omb']) * h**2,
'A_s': cosmo_params['As'],
'n_s': cosmo_params['ns'],
'output': 'mPk',
'z_max_pk': max(z) + 0.1,
'P_k_max_1/Mpc': pk_params['kmax'] * h,
}
if pk_params['non_linear'] == 1:
class_params['non linear'] = 'halofit'
class_params['N_ur'] = 3.04 #ultra relativistic species... neutrinos
if cosmo_params['mnu'] != 0:
class_params['N_ur'] -= 1 #one massive neutrino
class_params['m_ncdm'] = cosmo_params['mnu']
class_params['N_ncdm'] = 3.04 - class_params['N_ur']
if cosmo_params['w'] != -1:
class_params['Omega_fld'] = cosmo_params['Oml']
class_params['w0_fld'] = cosmo_params['w']
class_params['wa_fld'] = cosmo_params['wa']
for ke in class_accuracy_settings.keys():
class_params[ke] = class_accuracy_settings[ke]
cosmoC = Class()
cosmoC.set(class_params)
cosmoC.compute()
k = kh * h #output is in same unit as CAMB
pkC = np.array([[cosmoC.pk(ki, zj) for ki in k] for zj in z])
pkC *= h**3
s8 = cosmoC.sigma8()
cosmoC.struct_cleanup()
if return_s8:
return pkC, kh, s8
else:
return pkC, kh
def compute_Sigma8(self):
# compute the values of sigma_8
# given that we have already assigned
# the cosmologies
# this part does not depend on the systematics
cosmo = Class()
cosmo.set(self.cosmoParams)
if self.settings.include_neutrino:
cosmo.set(self.other_settings)
cosmo.set(self.neutrino_settings)
cosmo.set(self.class_argumets)
try:
cosmo.compute()
except CosmoComputationError as failure_message:
print(failure_message)
self.sigma_8 = np.nan
except CosmoSevereError as critical_message:
print(critical_message)
self.sigma_8 = np.nan
sigma_8 = cosmo.sigma8()
cosmo.struct_cleanup()
cosmo.empty()
del cosmo
return sigma_8
def setup_class(self):
obh2, och2, w, ns, ln10As, H0, Neff = self.parameters
h = H0/100.
Omega_b = obh2/h**2
Omega_c = och2/h**2
Omega_m = Omega_b+Omega_c
params = {'output': 'mPk',
'h': h,
'ln10^{10}A_s': ln10As,
#'sigma8':sigma8,
'n_s': ns,
'w0_fld': w, 'wa_fld': 0.0, 'Omega_b': Omega_b,
'Omega_cdm': Omega_c, 'Omega_Lambda': 1.- Omega_m,
'N_eff': Neff,
'P_k_max_1/Mpc':10., 'z_max_pk':5.,'non linear':'halofit'}
cosmo = Class()
cosmo.set(params)
print("CLASS is computing")
cosmo.compute()
print("\tCLASS done")
self.class_cosmo_object = cosmo
self.sigma8 = cosmo.sigma8()
return
b4ar = [
256.82199304134315, 78.62142674299282, 374.08451421691973,
-146.54664459312085
]
norm = 1.
# b1 = 1.909433
# b2 = -2.357092
# bG2 = 3.818261e-01
# css0 = -2.911944e+01
# css2 = -1.235181e+01
# Pshot = 2.032084e+03
# bGamma3 = 0.
# b4 = 1.924983e+02
print('S8=', cosmo.sigma8() * (cosmo.Omega_m() / 0.3)**0.5)
kmsMpc = 3.33564095198145e-6
rd = cosmo.rs_drag()
print('rd=', rd)
for j in range(len(chunk)):
z = zs[j]
b1 = b1ar[j]
b2 = b2ar[j]
bG2 = bG2ar[j]
css0 = css0ar[j]
css2 = css2ar[j]
Pshot = Pshotar[j]
bGamma3 = bGamma3ar[j]
b4 = b4ar[j]
def fitEE(self):
# function to cimpute the band powers
cosmo = Class()
cosmo.set(self.cosmoParams)
if self.settings.include_neutrino:
cosmo.set(self.other_settings)
cosmo.set(self.neutrino_settings)
cosmo.set(self.class_argumets)
try:
cosmo.compute()
except CosmoComputationError as failure_message:
print(failure_message)
self.sigma_8 = np.nan
cosmo.struct_cleanup()
cosmo.empty()
return np.array([np.nan] * self.nzcorrs * self.bo_EE), np.array(
[np.nan] * self.nzcorrs * self.bo_EE), np.array(
[np.nan] * self.nzcorrs * self.bo_EE)
except CosmoSevereError as critical_message:
print(critical_message)
self.sigma_8 = np.nan
cosmo.struct_cleanup()
cosmo.empty()
return np.array([np.nan] * self.nzcorrs * self.bo_EE), np.array(
[np.nan] * self.nzcorrs * self.bo_EE), np.array(
[np.nan] * self.nzcorrs * self.bo_EE)
# retrieve Omega_m and h from cosmo (CLASS)
self.Omega_m = cosmo.Omega_m()
self.small_h = cosmo.h()
self.rho_crit = self.get_critical_density()
# derive the linear growth factor D(z)
linear_growth_rate = np.zeros_like(self.redshifts)
# print self.redshifts
for index_z, z in enumerate(self.redshifts):
try:
# for CLASS ver >= 2.6:
linear_growth_rate[
index_z] = cosmo.scale_independent_growth_factor(z)
except BaseException:
# my own function from private CLASS modification:
linear_growth_rate[index_z] = cosmo.growth_factor_at_z(z)
# normalize to unity at z=0:
try:
# for CLASS ver >= 2.6:
linear_growth_rate /= cosmo.scale_independent_growth_factor(0.)
except BaseException:
# my own function from private CLASS modification:
linear_growth_rate /= cosmo.growth_factor_at_z(0.)
# get distances from cosmo-module:
r, dzdr = cosmo.z_of_r(self.redshifts)
self.sigma_8 = cosmo.sigma8()
# Get power spectrum P(k=l/r,z(r)) from cosmological module
# this doesn't really have to go into the loop over fields!
pk = np.zeros((self.settings.nellsmax, self.settings.nzmax), 'float64')
k_max_in_inv_Mpc = self.settings.k_max_h_by_Mpc * self.small_h
# note that this is being computed at only nellsmax
# followed by an interplation
record = np.zeros((self.settings.nellsmax, self.settings.nzmax))
record_k = np.zeros((self.settings.nellsmax, self.settings.nzmax))
for index_ells in range(self.settings.nellsmax):
for index_z in range(1, self.settings.nzmax):
k_in_inv_Mpc = (self.ells[index_ells] + 0.5) / r[index_z]
z = self.redshifts[index_z]
record[index_ells, index_z] = self.baryon_feedback_bias_sqr(
k_in_inv_Mpc / self.small_h,
self.redshifts[index_z],
A_bary=self.systematics['A_bary'])
record_k[index_ells, index_z] = k_in_inv_Mpc
self.record_bf = record[:, 1:].flatten()
self.record_k = record_k[:, 1:].flatten()
self.k_max_in_inv_Mpc = k_max_in_inv_Mpc
for index_ells in range(self.settings.nellsmax):
for index_z in range(1, self.settings.nzmax):
# standard Limber approximation:
# k = ells[index_ells] / r[index_z]
# extended Limber approximation (cf. LoVerde & Afshordi 2008):
k_in_inv_Mpc = (self.ells[index_ells] + 0.5) / r[index_z]
if k_in_inv_Mpc > k_max_in_inv_Mpc:
pk_dm = 0.
else:
pk_dm = cosmo.pk(k_in_inv_Mpc, self.redshifts[index_z])
# pk[index_ells,index_z] = cosmo.pk(ells[index_ells]/r[index_z], self.redshifts[index_z])
if self.settings.baryon_feedback:
pk[index_ells,
index_z] = pk_dm * self.baryon_feedback_bias_sqr(
k_in_inv_Mpc / self.small_h,
self.redshifts[index_z],
A_bary=self.systematics['A_bary'])
else:
pk[index_ells, index_z] = pk_dm
# for KiDS-450 constant biases in photo-z are not sufficient:
if self.settings.bootstrap_photoz_errors:
# draw a random bootstrap n(z); borders are inclusive!
random_index_bootstrap = np.random.randint(
int(self.settings.index_bootstrap_low),
int(self.settings.index_bootstrap_high) + 1)
# print 'Bootstrap index:', random_index_bootstrap
pz = np.zeros((self.settings.nzmax, self.nzbins), 'float64')
pz_norm = np.zeros(self.nzbins, 'float64')
for zbin in range(self.nzbins):
redshift_bin = self.redshift_bins[zbin]
# ATTENTION: hard-coded subfolder!
# index can be recycled since bootstraps for tomographic bins
# are independent!
fname = os.path.join(
self.settings.data_directory,
'{:}/bootstraps/{:}/n_z_avg_bootstrap{:}.hist'.format(
self.settings.photoz_method, redshift_bin,
random_index_bootstrap))
z_hist, n_z_hist = np.loadtxt(fname, unpack=True)
shift_to_midpoint = np.diff(z_hist)[0] / 2.
spline_pz = itp.splrep(z_hist + shift_to_midpoint, n_z_hist)
mask_min = self.redshifts >= z_hist.min() + shift_to_midpoint
mask_max = self.redshifts <= z_hist.max() + shift_to_midpoint
mask = mask_min & mask_max
# points outside the z-range of the histograms are set to 0!
pz[mask, zbin] = itp.splev(self.redshifts[mask], spline_pz)
dz = self.redshifts[1:] - self.redshifts[:-1]
pz_norm[zbin] = np.sum(0.5 * (pz[1:, zbin] + pz[:-1, zbin]) *
dz)
pr = pz * (dzdr[:, np.newaxis] / pz_norm)
else:
pr = self.pz * (dzdr[:, np.newaxis] / self.pz_norm)
# pr[pr < 0] = 0
g = np.zeros((self.settings.nzmax, self.nzbins), 'float64')
for zbin in range(self.nzbins):
# assumes that z[0] = 0
for nr in range(1, self.settings.nzmax - 1):
# for nr in range(self.nzmax - 1):
fun = pr[nr:, zbin] * (r[nr:] - r[nr]) / r[nr:]
g[nr, zbin] = np.sum(0.5 * (fun[1:] + fun[:-1]) *
(r[nr + 1:] - r[nr:-1]))
g[nr, zbin] *= 2. * r[nr] * (1. + self.redshifts[nr])
# Start loop over l for computation of C_l^shear
Cl_GG_integrand = np.zeros(
(self.settings.nzmax, self.nzbins, self.nzbins), 'float64')
Cl_GG = np.zeros((self.settings.nellsmax, self.nzbins, self.nzbins),
'float64')
Cl_II_integrand = np.zeros_like(Cl_GG_integrand)
Cl_II = np.zeros_like(Cl_GG)
Cl_GI_integrand = np.zeros_like(Cl_GG_integrand)
Cl_GI = np.zeros_like(Cl_GG)
dr = r[1:] - r[:-1]
for index_ell in range(self.settings.nellsmax):
# find Cl_integrand = (g(r) / r)**2 * P(l/r,z(r))
for zbin1 in range(self.nzbins):
for zbin2 in range(zbin1 + 1): # self.nzbins):
Cl_GG_integrand[1:, zbin1, zbin2] = g[1:, zbin1] * \
g[1:, zbin2] / r[1:]**2 * pk[index_ell, 1:]
factor_IA = self.get_factor_IA(
self.redshifts[1:], linear_growth_rate[1:],
self.systematics['A_IA']) # / self.dzdr[1:]
# print F_of_x
# print self.eta_r[1:, zbin1].shape
Cl_II_integrand[1:, zbin1, zbin2] = pr[1:, zbin1] * \
pr[1:, zbin2] * factor_IA**2 / r[1:]**2 * pk[index_ell, 1:]
pref = g[1:, zbin1] * pr[1:, zbin2] + g[1:, zbin2] * pr[
1:, zbin1]
Cl_GI_integrand[1:, zbin1,
zbin2] = pref * factor_IA / r[1:]**2 * pk[
index_ell, 1:]
# Integrate over r to get C_l^shear_ij = P_ij(l)
# C_l^shear_ii = 9/4 Omega0_m^2 H_0^4 \sum_0^rmax dr (g_i(r) g_j(r)
# /r**2) P(k=l/r,z(r))
for zbin1 in range(self.nzbins):
for zbin2 in range(zbin1 + 1): # self.nzbins):
Cl_GG[index_ell, zbin1, zbin2] = np.sum(
0.5 * (Cl_GG_integrand[1:, zbin1, zbin2] +
Cl_GG_integrand[:-1, zbin1, zbin2]) * dr)
# here we divide by 16, because we get a 2^2 from g(z)!
Cl_GG[index_ell, zbin1, zbin2] *= 9. / 16. * \
self.Omega_m**2 # in units of Mpc**4
# dimensionless
Cl_GG[index_ell, zbin1,
zbin2] *= (self.small_h / 2997.9)**4
Cl_II[index_ell, zbin1, zbin2] = np.sum(
0.5 * (Cl_II_integrand[1:, zbin1, zbin2] +
Cl_II_integrand[:-1, zbin1, zbin2]) * dr)
Cl_GI[index_ell, zbin1, zbin2] = np.sum(
0.5 * (Cl_GI_integrand[1:, zbin1, zbin2] +
Cl_GI_integrand[:-1, zbin1, zbin2]) * dr)
# here we divide by 4, because we get a 2 from g(r)!
Cl_GI[index_ell, zbin1, zbin2] *= 3. / 4. * self.Omega_m
Cl_GI[index_ell, zbin1,
zbin2] *= (self.small_h / 2997.9)**2
# ordering of redshift bins is correct in definition of theory below!
theory_EE_GG = np.zeros((self.nzcorrs, self.bo_EE), 'float64')
theory_EE_II = np.zeros((self.nzcorrs, self.bo_EE), 'float64')
theory_EE_GI = np.zeros((self.nzcorrs, self.bo_EE), 'float64')
index_corr = 0
# A_noise_corr = np.zeros(self.nzcorrs)
for zbin1 in range(self.nzbins):
for zbin2 in range(zbin1 + 1): # self.nzbins):
# correlation = 'z{:}z{:}'.format(zbin1 + 1, zbin2 + 1)
# print(zbin1, zbin2)
Cl_sample_GG = Cl_GG[:, zbin1, zbin2]
spline_Cl_GG = itp.splrep(self.ells, Cl_sample_GG)
D_l_EE_GG = self.ell_norm * \
itp.splev(self.ells_sum, spline_Cl_GG)
theory_EE_GG[index_corr, :] = self.get_theory(
self.ells_sum,
D_l_EE_GG,
self.band_window_matrix,
index_corr,
band_type_is_EE=True)
Cl_sample_GI = Cl_GI[:, zbin1, zbin2]
spline_Cl_GI = itp.splrep(self.ells, Cl_sample_GI)
D_l_EE_GI = self.ell_norm * \
itp.splev(self.ells_sum, spline_Cl_GI)
theory_EE_GI[index_corr, :] = self.get_theory(
self.ells_sum,
D_l_EE_GI,
self.band_window_matrix,
index_corr,
band_type_is_EE=True)
Cl_sample_II = Cl_II[:, zbin1, zbin2]
spline_Cl_II = itp.splrep(self.ells, Cl_sample_II)
D_l_EE_II = self.ell_norm * \
itp.splev(self.ells_sum, spline_Cl_II)
theory_EE_II[index_corr, :] = self.get_theory(
self.ells_sum,
D_l_EE_II,
self.band_window_matrix,
index_corr,
band_type_is_EE=True)
index_corr += 1
cosmo.struct_cleanup()
cosmo.empty()
return theory_EE_GG.flatten(), theory_EE_GI.flatten(
), theory_EE_II.flatten()
Plin = calc(params, z, reset=True)
ax.loglog(k, Plin, c=colors[i], label=r"$z=%.1f$" % z)
ax.legend(frameon=False)
#Now the cosmo models
cmap = vapeplot.cmap('vaporwave')
colors = [cmap(ci) for ci in np.linspace(0, 1, 3)]
z = 0
ax = axes[0]
Plin = calc(params, 0, reset=False)
ax.loglog(k,
Plin,
c=colors[0],
label=r'$\Omega_m = %.2f,\ \sigma_8=%.2f$' %
(0.3, cosmo.sigma8()))
Om = 0.35
params['Omega_cdm'] = Om - 0.05
cosmo.set(params)
cosmo.compute()
Plin = calc(params, 0, reset=False)
ax.loglog(k,
Plin,
c=colors[1],
label=r'$\Omega_m = %.2f,\ \sigma_8=%.2f$' %
(Om, cosmo.sigma8()))
Om = 0.3
params['Omega_cdm'] = Om - 0.05
params['sigma8'] = 0.98
def lookup_Pk(cosmology='planck',nonlinear=0):
"""
it saves the lookup table of the (non) linear power spectrum generate from CLASS.
If nonlinear is False (default) it generates the linear power spectrum.
You can choose between
- planck
- wmap
- ML
Choose also whether you want a nonlinear power spectrum, default is linear (nonlinear=0)
"""
# k in h/Mpc
k = N.logspace(-4., 3., 3*1024)
if nonlinear==1:
hf = 'halofit'
saveto = 'data_itam/'+cosmology+'_pk.txt'
else:
hf = ''
saveto = 'data_itam/'+cosmology+'_pk_linear.txt'
if cosmology == 'planck':
class_params = {
'non linear': hf,
'output': ['mPk','vTk'],
'P_k_max_1/Mpc': 1000.,
'z_pk': 0.,
'A_s': 2.3e-9,
'n_s': 0.96,
'h': 0.7,
'omega_b': 0.0225,
'Omega_cdm': 0.25,
}
sig8_0 = 0.8
elif cosmology == 'wmap':
class_params = {
'non linear': hf,
'output': ['mPk','vTk'],
'P_k_max_1/Mpc': 1000.,
'z_pk': 0.,
'A_s': 2.3e-9,
'n_s': 0.967,
'h': 0.704,
'omega_b': 0.02253,
'Omega_cdm': 0.226,
}
sig8_0 = 0.81
elif cosmology == 'ML':
class_params = {
'non linear': hf,
'output': ['mPk','vTk'],
'P_k_max_1/Mpc': 1000.,
'z_pk': 0.,
'A_s': 2.3e-9,
'n_s': 1.,
'h': 0.73,
'omega_b': 0.045*0.73**2,
'Omega_cdm': 0.25-0.045,
}
sig8_0 = 0.9
else:
raise ValueError("the cosmology you chose does not exist")
cosmoClass_nl = Class()
cosmoClass_nl.set(class_params)
cosmoClass_nl.compute()
# rescale the normalization of matter power spectrum to have sig8=0.8 today
sig8 = cosmoClass_nl.sigma8()
A_s = cosmoClass_nl.pars['A_s']
cosmoClass_nl.struct_cleanup() # does not clean the input class_params, cosmo.empty() does that
cosmoClass_nl.set(A_s=A_s*(sig8_0*1./sig8)**2)
cosmoClass_nl.compute()
h = cosmoClass_nl.pars['h']
pk_nl = N.asarray([ cosmoClass_nl.pk(x*h, 0.,)*h**3 for x in k ])
kpk = N.vstack((k,pk_nl))
N.savetxt(saveto,kpk)
print('saving', saveto )
return
def make_LSS_data(z, cosmo_dict, outfile=None):
"""
Args:
z (float): redshift
cosmo_dict (dictionary): the CLASS cosmology
outfile (string): file to save to
"""
if outfile is None:
outfile = "LSS_dict"
LSS_dict = {}
h = cosmo_dict["h"]
Omega_b = cosmo_dict["Omega_b"]
Omega_m = cosmo_dict["Omega_cdm"] + cosmo_dict["Omega_b"]
n_s = cosmo_dict["n_s"]
cosmo = Class()
cosmo.set(cosmo_dict)
cosmo.compute()
sigma8 = cosmo.sigma8()
print("sigma8 is:", sigma8)
k = np.logspace(-5, 3, base=10, num=4000) #1/Mpc; comoving
kh = k / h #h/Mpc; comoving
r = np.logspace(-2, 3, num=1000) #Mpc/h comoving
M = np.logspace(12, 16.3, 1000) #Msun/h
z = np.asarray(z)
for zi in z:
P_nl = np.array([cosmo.pk(ki, zi) for ki in k]) * h**3
P_lin = np.array([cosmo.pk_lin(ki, zi) for ki in k]) * h**3
xi_nl = ct.xi.xi_mm_at_r(r, kh, P_nl)
xi_lin = ct.xi.xi_mm_at_r(r, kh, P_lin)
c = np.array([
conc.concentration_at_M(Mi,
kh,
P_lin,
n_s,
Omega_b,
Omega_m,
h,
Mass_type="mean") for Mi in M
])
bias = ct.bias.bias_at_M(M, kh, P_lin, Omega_m)
args_at_z = {
"k": kh,
"P_lin": P_lin,
"P_nl": P_nl,
"r": r,
"xi_lin": xi_lin,
"xi_nl": xi_nl,
"M": M,
"concentration": c,
"bias": bias,
"h": h,
"Omega_m": Omega_m,
"n_s": n_s,
"sigma8": sigma8,
"Omega_b": Omega_b
}
LSS_dict["args_at_{z:.3f}".format(z=zi)] = args_at_z
#np.save(outfile, LSS_dict)
pickle.dump(LSS_dict, open(outfile + ".p", "wb"))
print("Saved {0}".format(outfile))
return
class ModelPk(object):
""" """
logger = logging.getLogger(__name__)
def __init__(self, **param_dict):
""" """
self.params = params.copy()
self.class_params = class_params.copy()
self.set(**param_dict) #other params for CLASS
self._cosmo = None
self._redshift_func = None
self._logpk_func = None
if self.params['mpk'] is not None:
self.load_pk_from_file(self.params['mpk'])
def load_pk_from_file(self, path):
""" """
self.logger.info(f"Loading matter power spectrum from file {path}")
k, pk = np.loadtxt(path, unpack=True)
self.logger.info(f"min k: {k.min()}, max k: {k.max()}, steps {len(k)}")
pk *= self.params['bias']**2
lk = np.log(k)
lpk = np.log(pk)
self._logpk_func = interpolate.interp1d(lk,
lpk,
bounds_error=False,
fill_value=(0, 0))
def set(self, **param_dict):
""" """
for key, value in param_dict.items():
if key == 'non_linear':
key = 'non linear'
self.logger.debug("Set %s=%s", key, value)
found = False
if key in self.class_params:
self.class_params[key] = value
found = True
if key in self.params:
self.params[key] = value
found = True
if not found:
continue
@property
def cosmo(self):
""" """
if not self._cosmo:
self._cosmo = Class()
self._cosmo.set(self.class_params)
self.logger.info("Initializing Class")
self._cosmo.compute()
if self.params['fix_sigma8']:
sig8 = self._cosmo.sigma8()
A_s = self._cosmo.pars['A_s']
self._cosmo.struct_cleanup()
# renormalize to fix sig8
self.A_s = A_s * (self.params['sigma8'] * 1. / sig8)**2
self._cosmo.set(A_s=self.A_s)
self._cosmo.compute()
sig8 = self._cosmo.sigma8()
self.params['sigma8'] = sig8
self.params['A_s'] = self._cosmo.pars['A_s']
self.params[
'sigma8z'] = sig8 * self._cosmo.scale_independent_growth_factor(
self.class_params['z_pk'])
self.params['f'] = self._cosmo.scale_independent_growth_factor_f(
self.class_params['z_pk'])
self.logger.info(f" z: {self.class_params['z_pk']}")
self.logger.info(f" sigma_8: {self.params['sigma8']}")
self.logger.info(f" sigma_8(z): {self.params['sigma8z']}")
self.logger.info(f" f(z): {self.params['f']}")
self.logger.info(
f"f sigma8(z): {self.params['f']*self.params['sigma8z']}")
return self._cosmo
def class_pk(self, k):
""" """
self.logger.info("Computing power spectrum with Class")
z = np.array([self.class_params['z_pk']]).astype('d')
shape = k.shape
k = k.flatten()
nk = len(k)
k = np.reshape(k, (nk, 1, 1))
pk = self.cosmo.get_pk(k * self.class_params['h'], z, nk, 1,
1).reshape((nk, ))
k = k.reshape((nk, ))
# set h units
pk *= self.class_params['h']**3
pk *= self.params['bias']**2
pk = pk.reshape(shape)
return pk
def get_pk(self, k):
ii = k > 0
out = np.zeros(k.shape, dtype='d')
out[ii] = np.exp(self.logpk_func(np.log(k[ii])))
return out
@property
def logpk_func(self):
if self._logpk_func is None:
k = np.logspace(self.params['log_kmin'], self.params['log_kmax'],
self.params['log_ksteps'])
pk = self.class_pk(k)
lk = np.log(k)
lpk = np.log(pk)
print("logk min", lk.min())
self._logpk_func = interpolate.interp1d(lk,
lpk,
bounds_error=False,
fill_value=(0, 0))
return self._logpk_func
def comoving_distance(self, z):
""" """
return (1 +
z) * self.cosmo.angular_distance(z) * self.class_params['h']
def redshift_at_comoving_distance(self, r):
""" """
try:
z = 10**self.redshift_func(r) - 1
except ValueError:
self.logger.error(f"r min {r.min()} max {r.max()}",
file=sys.stderr)
raise
return z
@property
def redshift_func(self):
""" """
if self._redshift_func is None:
zz = np.logspace(self.params['logzmin'], self.params['logzmax'],
self.params['logzsteps']) - 1
r = np.zeros(len(zz))
for i, z in enumerate(zz):
r[i] = self.comoving_distance(z)
self._redshift_func = interpolate.interp1d(r, np.log10(1 + zz))
return self._redshift_func
class Peturbations:
def __init__(self):
self.cosmo = Class()
def cosmo_GR(self, zlist):
"""
Compute cosmology for General Relativity
with Planck15 parameters.
"""
zstr = ','.join(map(str, zlist + zlist[-1] + 2))
lcdmpars = {
'output': 'mPk, tCl, pCl, lCl',
'lensing': 'yes',
'P_k_max_h/Mpc': 20,
'z_pk': zstr,
'background_verbose': 1, #Info
'tau_reio': 0.07,
'omega_cdm': 0.11987,
'A_s': 2.204e-9,
'h': 0.6715918, #computed from 100*theta_s=1.042143
'N_ur': 3.046 - 1.,
'N_ncdm': 1.,
'm_ncdm': 0.06,
'omega_b': 0.022252,
'n_s': 0.96475,
}
self.cosmo.set(lcdmpars)
self.cosmo.compute()
def cosmo_MG(self, zlist, alpha_b, alpha_m, a_trans, r):
"""
Compute cosmology for Modified gravity with a
LCDM background expansion (with Planck15
parameters) and 'hill_scale' parameterization
for the property functions.
"""
zstr = ','.join(map(str, zlist + zlist[-1] + 2))
mgpars = {
'output': 'mPk, tCl, pCl, lCl',
'lensing': 'yes',
'P_k_max_h/Mpc': 20,
'z_pk': zstr,
'background_verbose': 1, #Info
'tau_reio': 0.07,
'omega_cdm': 0.11987,
'A_s': 2.204e-9,
'h': 0.6715918, #computed from 100*theta_s=1.042143
'N_ur': 3.046 - 1.,
'N_ncdm': 1.,
'm_ncdm': 0.06,
'omega_b': 0.022252,
'n_s': 0.96475,
'Omega_Lambda': 0,
'Omega_fld': 0,
'Omega_smg': -1,
'expansion_model': 'lcdm',
'gravity_model': 'hill_scale',
}
# Planck Mass
Mstarsq = 1.
# Property Functions
alpha_t = 0.
alpha_k = 0.001
mgpars['parameters_smg'] = "{}, {}, {}, {}, {}, {}, {}".format(
Mstarsq, alpha_k, alpha_b, alpha_m, alpha_t, a_trans, r)
self.cosmo.set(mgpars)
self.cosmo.compute()
def D(self, z):
"""
Linear growth function
D(z) = ( P(k_ls, z) / P(k_ls, 0) )^(1 / 2)
where k_ls is a large-scale mode.
"""
k = 0.01 #Our choice of large-scale mode
mPk = self.cosmo.pk(k, z)
mPk_norm = self.cosmo.pk(k, 0) #Normalize at z=0
D = np.sqrt(mPk / mPk_norm)
return D
def f(self, z):
"""
Linear growth rate f(z) where
f(a) = d log D / d log a
where a = 1 / (1 + z) is the scale factor.
"""
a = 1. / (1. + z)
da = 0.01 #*a
gp, g, gm = [self.D(1. / ia - 1.) for ia in [a + da, a, a - da]]
f = a * (gp - gm) / (2 * g * da)
return f
def sigma8(self, z):
"""
sigma8(z) = sigma8*D(z)
"""
s8 = self.cosmo.sigma8() * self.D(z)
return s8
def fsigma8(self, z):
"""
Growth rate of structure
fsigma8(z) = f(z) * sigma8(z)
"""
fs8 = self.f(z) * self.sigma8(z)
return fs8
def fsigma8_GR(self, zlist):
"""
Get fsigma8 for General Relativity
"""
self.cosmo_GR(zlist)
fs8_GR = np.array([self.fsigma8(z) for z in zlist])
return fs8_GR
def fsigma8_MG(self, zlist, alpha_b, alpha_m, a_trans, r):
"""
Get fsigma8 for Modified Gravity with a LCDM background
expansion and hill_scale parameterization for the property
functions.
"""
self.cosmo_MG(zlist, alpha_b, alpha_m, a_trans, r)
fs8_MG = np.array([self.fsigma8(z) for z in zlist])
return fs8_MG
def fsigma8_MG_fit(self, zlist, alpha_b, a_trans, r):
"""
Get fsigma8 for Modified Gravity with a LCDM background
expansion and hill_scale parameterization for the property
functions.
"""
alpha_m = 0.1
#a_trans = 1./(1.+7.)
#r = 4.
self.cosmo_MG(zlist, alpha_b, alpha_m, a_trans, r)
fs8_MG = np.array([self.fsigma8(z) for z in zlist])
return fs8_MG
def sigma8_GR(self, zlist):
"""
Get fsigma8 for General Relativity
"""
self.cosmo_GR(zlist)
s8_GR = np.array([self.sigma8(z) for z in zlist])
return s8_GR
def sigma8_MG(self, zlist, alpha_b, alpha_m, a_trans, r):
"""
Get sigma8 for Modified Gravity with a LCDM background
expansion and hill_scale parameterization for the property
functions.
"""
self.cosmo_MG(zlist, alpha_b, alpha_m, a_trans, r)
s8_MG = np.array([self.sigma8(z) for z in zlist])
return s8_MG
def Cl_TT_GR(self, zlist, llist):
"""
Get C_ell^TT for General Relativity
"""
self.cosmo_GR(zlist)
lmax = llist[-1]
Cl_TT_GR = self.cosmo.lensed_cl(lmax)['tt'][2:]
Cl_TT_GR = (1. / (2. * np.pi)) * (llist * (llist + 1.)) * Cl_TT_GR
return Cl_TT_GR
def Cl_TT_MG(self, zlist, llist, alpha_b, alpha_m, a_trans, r):
"""
Get C_ell^TT for Modified Gravity with a LCDM background
expansion and hill_scale parameterization for the property
functions.
"""
self.cosmo_MG(zlist, alpha_b, alpha_m, a_trans, r)
lmax = llist[-1]
Cl_TT_MG = self.cosmo.lensed_cl(lmax)['tt'][2:]
Cl_TT_MG = (1. / (2. * np.pi)) * (llist * (llist + 1.)) * Cl_TT_MG
return Cl_TT_MG
def Cl_kappa_kappa_GR(self, zlist, llist):
"""
Get C_ell^kappakappa for General Relativity
"""
self.cosmo_GR(zlist)
lmax = llist[-1]
Cl_phi_phi_GR = self.cosmo.lensed_cl(lmax)['pp'][2:]
Cl_kap_kap_GR = (1. / 4.) * ((llist *
(llist + 1.))**2.) * Cl_phi_phi_GR
return Cl_kap_kap_GR
def Cl_kappa_kappa_MG(self, zlist, llist, alpha_b, alpha_m, a_trans, r):
"""
Get C_ell^kappakappa for Modified Gravity with a LCDM background
expansion and hill_scale parameterization for the property
functions.
"""
self.cosmo_MG(zlist, alpha_b, alpha_m, a_trans, r)
lmax = llist[-1]
Cl_phi_phi_MG = self.cosmo.lensed_cl(lmax)['pp'][2:]
Cl_kap_kap_MG = (1. / 4.) * ((llist *
(llist + 1.))**2.) * Cl_phi_phi_MG
return Cl_kap_kap_MG
params = {
'output': 'mPk',
"h":h,
"A_s":1.9735e-9, #Yields sigma8 = 0.8
"n_s":0.96,
"Omega_b":Ob,
"Omega_cdm":Ocdm,
'YHe':0.24755048455476272,#By hand, default value
'P_k_max_h/Mpc':3000.,
'z_max_pk':1.0,
'non linear':'halofit'}
cosmo = Class()
cosmo.set(params)
cosmo.compute()
print "sigma8 is:", cosmo.sigma8()
k = np.logspace(-5, 3, base=10, num=4000) #1/Mpc, apparently
np.savetxt("k.txt", k/h) #h/Mpc now
"""for i in range(len(meanz)):
for j in range(len(meanz[i])):
z = meanz[i,j]
Pmm = np.array([cosmo.pk(ki, z) for ki in k])
Plin = np.array([cosmo.pk_lin(ki, z) for ki in k])
np.savetxt("pnl_z%d_l%d.txt"%(i,j), Pmm*h**3) #Mpc^3/h^3
np.savetxt("plin_z%d_l%d.txt"%(i,j), Plin*h**3) #Mpc^3/h^3
print "Done with z%d"%i
"""
for z in [0.577]:
Pmm = np.array([cosmo.pk(ki, z) for ki in k])
Plin = np.array([cosmo.pk_lin(ki, z) for ki in k])
