def euclid_nzs(num_dens):
'''
euclid num density = 30 arcmin^-2 = 108,000 deg^-2
In steradians: A steradian is (180/π)^2 square degrees, or 3282.8 deg^2
So Euclid number density
= 108,000 * 3282.8 = 354,543,086 galaxies per steradian
'''
nz = 1000
# zmin , zmax = 0., 3.
# z = np.linspace(zmin, zmax, nz)
pz = ccl.PhotoZGaussian(sigma_z0=0.05)
dNdz_true = ccl.dNdzSmail(alpha=1.3, beta=1.5, z0=0.65)
dNdz_obs = ccl.dNdz_tomog(z=z,
zmin=zmin,
zmax=zmax,
pz_func=pz,
dNdz_func=dNdz_true)
# scale to the given number density
dNdz_obs = dNdz_obs / dNdz_obs.sum() * num_dens
nzs = []
for i in range(nbins):
# calculate the number density of galaxies per steradian per bin
zmin_i, zmax_i = i * (2. / nbins), (i + 1) * (2. / nbins)
mask = (z > zmin_i) & (z < zmax_i)
nzs.append(dNdz_obs[mask].sum())
return nzs
def euclid_nzs(num_dens):
"""
Calculate the (AVERAGE?!) number density of sub-sample galaxies per redshift bin
num_dens = 354,543,086 galaxies per steradian
Euclid num density = 30 arcmin^-2 = 108,000 deg^-2 (arcmin^2 to deg^2 = 60^2)
In steradians: A steradian is (180/π)^2 square degrees, or 3282.8 deg^2
So Euclid number density
= 108,000 * 3282.8 = 354,543,086 galaxies per steradian
Returns
nzs --- list --- (AVERAGE?!) number density of galaxies in redshift bin
"""
# zmin , zmax = 0., 3.
# z = np.linspace(zmin, zmax, nz)
pz = ccl.PhotoZGaussian(sigma_z0=0.05)
dNdz_true = ccl.dNdzSmail(alpha=1.3, beta=1.5, z0=0.65)
dNdz_obs = ccl.dNdz_tomog(z=z,
zmin=zmin,
zmax=zmax,
pz_func=pz,
dNdz_func=dNdz_true)
# scale to the given number density of 30 per arcmin squared
dNdz_obs = dNdz_obs / dNdz_obs.sum() * num_dens
nzs = []
for i in range(nbins):
# calculate the number density of galaxies per steradian per bin
zmin_i, zmax_i = i * (2. / nbins), (i + 1) * (2. / nbins)
mask = (z > zmin_i) & (z < zmax_i)
nzs.append(dNdz_obs[mask].sum())
return nzs
def euclid_ccl(Omega_c, sigma8):
"""
Generate C_ell as function of ell for a given Omega_c and Sigma8
Assumes a redshift distribution given by
z^alpha * exp(z/z0)^beta
with alpha=1.3, beta = 1.5 and z0 = 0.65
Assumes photo-z error is Gaussian with a bias is 0.05(1+z)
"""
cosmo_fid = ccl.Cosmology(Omega_c=Omega_c,
Omega_b=0.045,
h=0.71,
sigma8=sigma8,
n_s=0.963)
ell = np.logspace(np.log10(100), np.log10(6000), 10)
pz = ccl.PhotoZGaussian(sigma_z0=0.05)
dNdz_true = ccl.dNdzSmail(alpha=1.3, beta=1.5, z0=0.65)
dNdzs = np.zeros((nbins, z.size))
shears = []
for i in range(nbins):
# edges of nbins equal width redshift bins, between 0 and 2
zmin, zmax = i * (2. / nbins), (i + 1) * (2. / nbins)
# generate dNdz per bin
dNdzs[i, :] = ccl.dNdz_tomog(z=z,
zmin=zmin,
zmax=zmax,
pz_func=pz,
dNdz_func=dNdz_true)
# calculate the shear per bin
gal_shapes = ccl.WeakLensingTracer(cosmo_fid, dndz=(z, dNdzs[i, :]))
shears.append(gal_shapes)
# calculate nbin*(nbin+1)/2 spectra from the shears
Cls = []
bin_indices = [
] # list of length nbin*(nbin+1)/2 containing tuples with the indices of the bins
for i in range(nbins):
for j in range(0, i + 1):
bin_indices.append((i, j))
Cls.append(ccl.angular_cl(cosmo_fid, shears[i], shears[j], ell))
return ell, np.array(Cls), dNdzs, bin_indices
def euclid_nzs(num_dens):
'''
Calculate integrated number density per bin, scale to given num_dens
Euclid num density = 30 arcmin^-2
'''
nz = 1000
zmin , zmax = 0., 3.
z = np.linspace(zmin, zmax,nz)
pz = ccl.PhotoZGaussian(sigma_z0=0.05)
dNdz_true = ccl.dNdzSmail(alpha = 1.3, beta = 1.5, z0=0.65)
dNdz_obs = ccl.dNdz_tomog(z=z, zmin=zmin, zmax=zmax, pz_func=pz, dNdz_func = dNdz_true)
# scale to the given number density
dNdz_obs = dNdz_obs*num_dens/dNdz_obs.sum()
nzs = []
for i in range(10):
zmin_i, zmax_i = i*.2 , (i+1)*.2
mask = (z>zmin_i)&(z<zmax_i)
nzs.append(dNdz_obs[mask].sum()) #*num_dens)
return nzs
def check_redshifts(cosmo):
"""
Check that redshift functions can be run and produce finite values.
"""
# Types of scale factor input (scalar, list, array)
a_scl = 0.5
a_lst = [0.2, 0.4, 0.6, 0.8, 1.]
a_arr = np.linspace(0.2, 1., 5)
# Types of redshift input
z_scl = 0.5
z_lst = [0., 0.5, 1., 1.5, 2.]
z_arr = np.array(z_lst)
# p(z) function for dNdz_tomog
def pz1(z_ph, z_s, args):
return np.exp(-(z_ph - z_s)**2. / 2.)
# Lambda function p(z) function for dNdz_tomog
pz2 = lambda z_ph, z_s, args: np.exp(-(z_ph - z_s)**2. / 2.)
# PhotoZFunction classes
PZ1 = ccl.PhotoZFunction(pz1)
PZ2 = ccl.PhotoZFunction(pz2)
PZ3 = ccl.PhotoZGaussian(sigma_z0=0.1)
# dNdz (in terms of true redshift) function for dNdz_tomog
def dndz1(z, args):
return z**1.24 * np.exp(-(z / 0.51)**1.01)
# dNdzFunction classes
dNdZ1 = ccl.dNdzFunction(dndz1)
dNdZ2 = ccl.dNdzSmail(alpha=1.24, beta=1.01, z0=0.51)
# Check that dNdz_tomog is finite with the various combinations
# of PhotoZ and dNdz functions
zmin = 0.
zmax = 1.
assert_(all_finite(ccl.dNdz_tomog(z_scl, zmin, zmax, PZ1, dNdZ1)))
assert_(all_finite(ccl.dNdz_tomog(z_lst, zmin, zmax, PZ1, dNdZ1)))
assert_(all_finite(ccl.dNdz_tomog(z_arr, zmin, zmax, PZ1, dNdZ1)))
assert_(all_finite(ccl.dNdz_tomog(z_scl, zmin, zmax, PZ2, dNdZ1)))
assert_(all_finite(ccl.dNdz_tomog(z_lst, zmin, zmax, PZ2, dNdZ1)))
assert_(all_finite(ccl.dNdz_tomog(z_arr, zmin, zmax, PZ2, dNdZ1)))
assert_(all_finite(ccl.dNdz_tomog(z_scl, zmin, zmax, PZ3, dNdZ1)))
assert_(all_finite(ccl.dNdz_tomog(z_lst, zmin, zmax, PZ3, dNdZ1)))
assert_(all_finite(ccl.dNdz_tomog(z_arr, zmin, zmax, PZ3, dNdZ1)))
assert_(all_finite(ccl.dNdz_tomog(z_scl, zmin, zmax, PZ1, dNdZ2)))
assert_(all_finite(ccl.dNdz_tomog(z_lst, zmin, zmax, PZ1, dNdZ2)))
assert_(all_finite(ccl.dNdz_tomog(z_arr, zmin, zmax, PZ1, dNdZ2)))
assert_(all_finite(ccl.dNdz_tomog(z_scl, zmin, zmax, PZ2, dNdZ2)))
assert_(all_finite(ccl.dNdz_tomog(z_lst, zmin, zmax, PZ2, dNdZ2)))
assert_(all_finite(ccl.dNdz_tomog(z_arr, zmin, zmax, PZ2, dNdZ2)))
assert_(all_finite(ccl.dNdz_tomog(z_scl, zmin, zmax, PZ3, dNdZ2)))
assert_(all_finite(ccl.dNdz_tomog(z_lst, zmin, zmax, PZ3, dNdZ2)))
assert_(all_finite(ccl.dNdz_tomog(z_arr, zmin, zmax, PZ3, dNdZ2)))
# Wrong function type
assert_raises(TypeError, ccl.dNdz_tomog, z_scl, zmin, zmax, pz1, z_arr)
assert_raises(TypeError, ccl.dNdz_tomog, z_scl, zmin, zmax, z_arr, dNdZ1)
assert_raises(TypeError, ccl.dNdz_tomog, z_scl, zmin, zmax, None, None)
Cls.append(ccl.angular_cl(cosmo_fid, shears[i], shears[j], ells))
return np.array(Cls), dNdzs
nz = 1000 #redshift resolution
zmin = 0.
zmax = 2.
z = np.linspace(zmin, zmax, nz)
# number of tomographic bins
nbins = 1
# number of cross/auto angular power spectra
ncombinations = int(nbins * (nbins + 1) / 2)
# 100 log equal spaced ell samples
ells = np.logspace(np.log10(100), np.log10(1000), 100)
"""
Assume a redshift distribution given by
z^alpha * exp(z/z0)^beta
with alpha=1.3, beta = 1.5 and z0 = 0.65
"""
dNdz_true = ccl.dNdzSmail(alpha=1.3, beta=1.5, z0=0.65)
# Assumes photo-z error is Gaussian with a bias is 0.05(1+z)
pz = ccl.PhotoZGaussian(sigma_z0=0.05)
Omega_c = 0.21
print(f'Generating power spectra with Omega_c = {Omega_c}')
Cls, dNdzs = euclid_ccl(Omega_c)
Omega_c = 0.20
print(f'Generating power spectra with Omega_c = {Omega_c}')
Cls, dNdzs = euclid_ccl(Omega_c)
def test_redshift_numerical():
"""
Compare the redshift functions to a high precision integral.
"""
# Redshift input
z_lst = [0., 0.5, 1., 1.5, 2.]
# p(z) function for dNdz_tomog
def pz1(z_ph, z_s, args):
return np.exp(- (z_ph - z_s)**2. / 2.)
# Lambda function p(z) function for dNdz_tomog
pz2 = lambda z_ph, z_s, args: np.exp(-(z_ph - z_s)**2. / 2.)
# Set up a function equivalent to the PhotoZGaussian
def pz3(z_ph, z_s, sigz):
sig = sigz*(1.+ z_s)
return (np.exp(- (z_ph - z_s)**2. / 2. / sig**2) / np.sqrt(2.
*np.pi) / sig)
# PhotoZFunction classes
PZ1 = ccl.PhotoZFunction(pz1)
PZ2 = ccl.PhotoZFunction(pz2)
PZ3 = ccl.PhotoZGaussian(sigma_z0=0.1)
# dNdz (in terms of true redshift) function for dNdz_tomog
def dndz1(z, args):
return z**1.24 * np.exp(- (z / 0.51)**1.01)
# dNdzFunction classes
dNdZ1 = ccl.dNdzFunction(dndz1)
dNdZ2 = ccl.dNdzSmail(alpha = 1.24, beta = 1.01, z0 = 0.51)
# Do the integral in question directly in numpy at high precision
zmin = 0.
zmax = 1.
zp = np.linspace(zmin, zmax, 10000)
zs = np.linspace(0., 5., 10000) # Assume any dNdz does not extend
# above z=5
denom_zp_1 =np.asarray([np.trapz(pz1(zp, z, []), zp) for z in zs])
denom_zp_2 =np.asarray([np.trapz(pz2(zp, z, []), zp) for z in zs])
denom_zp_3 =np.asarray([np.trapz(pz3(zp, z, 0.1), zp) for z in zs])
np_dndz_1 = ([ dndz1(z, []) * np.trapz(pz1(zp, z, []), zp) /
np.trapz(dndz1(zs, []) * denom_zp_1, zs) for z in
z_lst])
np_dndz_2 = ([ dndz1(z, []) * np.trapz(pz2(zp, z, []), zp) /
np.trapz(dndz1(zs, []) * denom_zp_2, zs) for z in
z_lst])
np_dndz_3 = ([ dndz1(z, []) * np.trapz(pz3(zp, z, 0.1), zp) /
np.trapz(dndz1(zs, []) * denom_zp_3, zs) for z in
z_lst])
# Check that for the analytic case introduced above, we get the
# correct value.
for i in range(0, len(z_lst)):
assert_allclose(ccl.dNdz_tomog(z_lst[i], zmin, zmax, PZ1,
dNdZ1), np_dndz_1[i], rtol=TOLERANCE)
assert_allclose(ccl.dNdz_tomog(z_lst[i], zmin, zmax, PZ1,
dNdZ2), np_dndz_1[i], rtol=TOLERANCE)
assert_allclose(ccl.dNdz_tomog(z_lst[i], zmin, zmax, PZ2,
dNdZ1), np_dndz_2[i], rtol=TOLERANCE)
assert_allclose(ccl.dNdz_tomog(z_lst[i], zmin, zmax, PZ2,
dNdZ2), np_dndz_2[i], rtol=TOLERANCE)
assert_allclose(ccl.dNdz_tomog(z_lst[i], zmin, zmax, PZ3,
dNdZ1), np_dndz_3[i], rtol=TOLERANCE)
assert_allclose(ccl.dNdz_tomog(z_lst[i], zmin, zmax, PZ3,
dNdZ2), np_dndz_3[i], rtol=TOLERANCE)