def desi_elg(zee, force=False):
zee = np.asarray(zee)
aa = 1. / (1. + zee)
if force:
return 0.84 / growth_factor(aa)
if np.any(zee > 1.8):
raise ValueError(
'\n\nCalling b(z) outside range of ELGs (z < 1.8).\n\n')
return 0.84 / growth_factor(aa)
def desi_qso(zee, force=False):
zee = np.asarray(zee)
aa = 1. / (1. + zee)
if force:
return 1.20 / growth_factor(aa)
if np.any(zee > 5.0):
raise ValueError(
'\n\nCalling b(z) outside range of QSOs (z < 5.0).\n\n')
return 1.20 / growth_factor(aa)
def desi_lrg(zee, force=False):
zee = np.asarray(zee)
aa = 1. / (1. + zee)
if force:
return 1.70 / growth_factor(aa)
if np.any(zee > 1.3):
raise ValueError(
'\n\nCalling b(z) outside range of LRGs (z < 1.3).\n\n')
return 1.70 / growth_factor(aa)
def desi_bgs(zee, force=False):
zee = np.asarray(zee)
aa = 1. / (1. + zee)
if force:
return 1.34 / growth_factor(aa)
if np.any(zee > 0.5):
raise ValueError(
'\n\nCalling b(z) outside range of BGS (z < 0.5).\n\n')
return 1.34 / growth_factor(aa)
def tinker_sigma(Pk_interps, Ms, z):
## Beware variable definitions wrt massfn.py, which is based upon https://arxiv.org/pdf/1005.2239.pdf
result = []
## Lift Martin's linear z=0 P(k).
data = np.loadtxt('../dat/pklin_1.0000.txt')
PMW = interp1d(data[:, 0],
data[:, 1],
kind='linear',
copy=True,
bounds_error=False,
fill_value=0.0,
assume_sorted=False)
for M in Ms:
## Implicitly a fn. of z by rho_b, Pmm and the growth factor.
ks = np.arange(1.e-3, 1.e1, 1.e-3)
Rms = (3. * M / 4 / np.pi / rho_b)**(1. / 3.)
## Ps = Pmm(Pk_interps, ks, 0.0, type='linear')
Ps = PMW(ks)
Ws = W(ks * Rms)
## Defined by linear or non-linear.
integrand = ks * ks * Ps * Ws
sig = simps(integrand, dx=ks[1] - ks[0])
sig *= growth_factor(z)
result.append(sig)
return np.array(result)
def Pmm(Pk_interps, k, z, type='nlinear'):
## Required to take an array of k values, and float argument for z.
a = 1. / (1. + z)
if (type == 'lpt') & (z >= 1.) & (z <= 3.5):
## print("\n\nAssuming LPT parameters of Modi++ for Pmm prediction within (1. < z < 3.5)")
bestfitz = rround(z)
alpha = modi_hbias[bestfitz]['amm']
Ploop = Pk_interps['PA'](k) + Pk_interps['PW'](k)
result = (1 - alpha * k * k / 2.) * Pk_interps['PZ'](k) + Ploop
## result[kmax > 3.0] ## Impose kmax cut on LPT predictions.
result *= growth_factor(a)**2. ## Growth factor is exact in redshift.
elif type == 'linear':
## print("\n\nAssuming CAMB linear matter power spectrum.")
result = Pk_interps['camb_lin'](z, k)
elif type == 'nlinear':
## print("\n\nAssuming CAMB non-linear matter power spectrum.")
result = Pk_interps['camb_nlin'](z, k)
else:
raise ValueError('Type %s not available for Pmm.' % type)
return result
def sigma(Pk_interps, Ms, z):
result = []
## Lift Martin's linear z=0 P(k).
data = np.loadtxt('../dat/pklin_1.0000.txt')
PMW = interp1d(data[:, 0],
data[:, 1],
kind='linear',
copy=True,
bounds_error=False,
fill_value=0.0,
assume_sorted=False)
for M in Ms:
## Implicitly a fn. of z by rho_b, Pmm and the growth factor.
ks = np.arange(1.e-3, 1.e1, 1.e-3)
Rms = (3. * M / 4 / np.pi / rho_b)**(1. / 3.)
## Ps = Pmm(Pk_interps, ks, 0.0, type='linear')
Ps = PMW(ks)
Ws = W(ks * Rms)
## Defined by linear or non-linear.
integrand = ks * ks * Ps * Ws * Ws
sig2 = simps(integrand, dx=ks[1] - ks[0])
sig2 *= growth_factor(z)**2.
sig2 /= (2. * np.pi**2.)
result.append(np.sqrt(sig2))
return np.array(result)
def Phh(Pk_interps, k, z, scross=0.0):
## Required to take an array of k values, and float argument for z.
a = 1. / (1. + z)
## Round provided z to the nearest for which a bias value is available.
bestfitz = rround(z)
if biastype == 'Modi':
if (bestfitz >= 1.) & (bestfitz <= 3.5):
alpha = biasdict[bestfitz]['ahm']
b1 = biasdict[bestfitz]['b1']
b2 = biasdict[bestfitz]['b2']
bs2 = biasdict[bestfitz]['bs']
bD2 = 0.
Ploop = Pk_interps['PA'](k) + Pk_interps['PW'](k)
## b2*b2*Pk_interps['Pd2d2'](k): incorrect normalisation, needs divided by four on input.
result = (1 - alpha * k * k / 2.) * Pk_interps['PZ'](
k) + Ploop + b1 * Pk_interps['Pd'](k) + b1**2. * Pk_interps[
'Pdd'](k) + b2 * Pk_interps['Pd2'](k)
result += b1 * b2 * Pk_interps['Pdd2'](k) + b2 * b2 * Pk_interps[
'Pd2d2'](k) + bs2 * Pk_interps['Ps2'](
k) + b1 * bs2 * Pk_interps['Pds2'](k)
result += b2 * bs2 * Pk_interps['Pd2s2'](
k) + bs2 * bs2 * Pk_interps['Ps2s2'](k) + 2 * bD2 * Pk_interps[
'PD2d'](k) + 2 * b1 * bD2 * Pk_interps['PdD2d'](k)
## result[kmax > 3.0] ## Impose kmax cut on LPT predictions.
## NOTE: Cannot simply scale by D+^2.
result *= growth_factor(
a)**2. ## Growth factor is exact in redshift.
else:
result = Pk_interps['camb_nlin'](
z,
k) ## For z < 1. and z > 3.5, replace with CAMB SPT results.
elif biastype == 'dropouts':
b1 = biasdict[bestfitz][
'b1'] ## Stored Lagrangian bias, Eulerian is (1. + b1).
result = (1. + b1) * (1. + b1) * Pk_interps['camb_nlin'](z, k)
elif biastype == 'linz':
result = (1. + z) * (1. + z) * Pk_interps['camb_nlin'](z, k)
else:
raise ValueError("Type is not available for Pmm.")
return result
def Pmh(Pk_interps, k, z, scross=0.):
## Required to take an array of k values and float argument for z.
a = 1. / (1. + z)
bestfitz = rround(z)
if biastype == 'Modi':
if (bestfitz >= 1.) & (bestfitz <= 3.5):
alpha = biasdict[bestfitz]['ahm']
b1 = biasdict[bestfitz]['b1']
b2 = biasdict[bestfitz]['b2']
bs2 = biasdict[bestfitz]['bs']
bD2 = 0.0
Ploop = Pk_interps['PA'](k) + Pk_interps['PW'](k)
## Read in
result = (1 - alpha * k * k / 2.) * Pk_interps['PZ'](k) + Ploop + (
b1 / 2.) * Pk_interps['Pdd'](k) + (b2 / 2.) * Pk_interps[
'Pd2d2'](k) + (bs2 / 2.) * Pk_interps['Ps2'](k)
result += bD2 * Pk_interps['PD2d'](k) + scross
## result[kmax > 3.0] = 0.0 ## Impose kmax cut on LPT predictions.
## NOTE: Cannot simply scale by D+^2.
result *= growth_factor(
a)**2. ## Growth factor is exact in redshift.
else:
result = Pk_interps['camb_nlin'](
z,
k) ## For z < 1. and z > 3.5, replace with CAMB SPT results.
elif biastype == 'dropouts':
b1 = biasdict[bestfitz]['b1']
result = (1. + b1) * Pk_interps['camb_nlin'](z, k)
elif biastype == 'linz':
result = (1. + z) * Pk_interps['camb_nlin'](z, k)
else:
raise ValueError("Type is not available for Pmm.")
return result
def prep_pk(z):
try:
ks, Ps = np.loadtxt('dat/pk.dat', unpack=True)
except:
## Prepare pycamb module; linear, non-linear matter P(k) and Cls.
cambx = CAMB()
Pk_interps = get_PkInterps(cambx)
## Write Linear power spectrum.
ks = np.arange(0.01, 1., 0.01)
Ps = Pk_interps['camb_lin'](0.0, ks)
np.savetxt('dat/pk.dat', np.c_[ks, Ps])
aa = 1. / (1. + z)
dd = growth_factor(aa)
return ks, dd * dd * Ps
def lenses_bz(zee):
aa = 1. / (1. + zee)
return 0.95 / growth_factor(aa)
def lrg_bz(zz):
aa = 1. / (1. + zz)
Dp = growth_factor(aa)
return 1.7 / Dp
def qso_bz(zz):
aa = 1. / (1. + zz)
Dp = growth_factor(aa)
return 1.2 / Dp
def bgs_bz(zz):
aa = 1. / (1. + zz)
Dp = growth_factor(aa)
return 1.0 / Dp
def elg_bz(zz):
aa = 1. / (1. + zz)
Dp = growth_factor(aa)
return 0.84 / Dp
def invG_bz(z): return 1. / growth_factor(z)
def bz_fitmodel(z, A, B): aa = 1. / (1. + z) DD = growth_factor(aa) return A / aa + B / aa**2.
##
pl.scatter(har[:, 0], har[:, 1], c='b', marker='^', label='24.0', s=14)
pl.scatter(har[:, 0], har[:, 2], c='orange', marker='^', label='', s=14)
pl.scatter(har[:, 0], har[:, 3], c='c', marker='^', label='', s=14)
pl.scatter(har[:, 0], har[:, 4], c='y', marker='^', label='', s=14)
##
pl.scatter(cars[:, 0], cars[:, 1], c='orange', marker='s', label='24.5', s=14)
pl.scatter(cars[:, 0], cars[:, 2], c='c', marker='s', label='25.0', s=14)
pl.scatter(cars[:-1, 0], cars[:-1, 3], c='y', marker='s', label='25.5', s=14)
pl.xlim(2.90, 5.10)
pl.ylim(1.75, 9.75)
pl.xlabel(r'$z$')
pl.ylabel(r'$b(z)$')
pl.legend(loc=2, ncol=2, handletextpad=.05, frameon=False)
plt.tight_layout()
zs = np.arange(2.5, 6.0, 0.01)
aa = 1. / (1. + zs)
gs = growth_factor(aa)
pl.plot(zs, 0.3 / (gs**1.9), 'k-')
## pl.plot(zs, 0.2 * (1. + zs) ** 2., 'r-')
pl.show()
## pl.savefig('bz.pdf')
pl.xlim(3.0, 0.0)
pl.ylim(0.0, 3.50e3)
pl.xlabel(r'$z_{\rm{max}}$')
pl.ylabel(r'$N(< z_{\rm{max}}) \ \ [\rm{gals. \ / \ deg^2}]$')
## Second b(z) axis.
ax = pl.gca()
axx = ax.twinx()
## LSST sources
## biases.append(lambda z: 1. + z)
## LSST lenses
biases.append(lambda z: 0.95 / growth_factor(1. / (1. + z)))
biases.append(mean_bias)
zmaxes.append(3.5) ## LSST bias limit
zmaxes.append(3.5) ## DESI mean bias limit
for i, (bz, zmax) in enumerate(zip(biases, zmaxes)):
axx.plot(zs[zs < zmax],
bz(zs[zs < zmax]),
c=colors[i],
alpha=0.45,
dashes=[3, 1],
label='')
axx.set_ylabel(r'$b(z)$')
