def __init__(
self,
dc=1.686e0,
h0=0.702e0,
om=0.274e0,
ode=0.725e0,
w0=-1.0e0,
ob=0.0458,
o_r=8.6e-5,
o_k=0.0e0,
f_nl=0.0e0,
tau_r=0.087,
z_r=10.4,
ns=0.96,
hmf_type="tinker",
):
"""
Constructor.
Default initialisation with WMAP7+BAO+H0 parameters,
Tinker mass function and fitted P(k).
"""
print "Cosmology"
self.delta_c = dc
self.h_0 = h0
self.O_m0 = om
self.O_de0 = ode
self.w_0 = w0
self.O_b0 = ob
self.O_r0 = o_r
self.O_k0 = o_k
self.fnl = f_nl
self.tau_rec = tau_r
self.z_rec = z_r
self.eta_r = self.eta(self.z_rec)
self.H_0 = h0 * 100.0e0
self.n_s = ns
self.mf = hmf.Hmf(mf_type=hmf_type)
import inspect
print inspect.getframeinfo(inspect.currentframe().f_back)[3]
# print inspect.stack()
self.pk = PowSpec(self)
class Cosmology:
def __init__(
self,
dc=1.686e0,
h0=0.702e0,
om=0.274e0,
ode=0.725e0,
w0=-1.0e0,
ob=0.0458,
o_r=8.6e-5,
o_k=0.0e0,
f_nl=0.0e0,
tau_r=0.087,
z_r=10.4,
ns=0.96,
hmf_type="tinker",
):
"""
Constructor.
Default initialisation with WMAP7+BAO+H0 parameters,
Tinker mass function and fitted P(k).
"""
print "Cosmology"
self.delta_c = dc
self.h_0 = h0
self.O_m0 = om
self.O_de0 = ode
self.w_0 = w0
self.O_b0 = ob
self.O_r0 = o_r
self.O_k0 = o_k
self.fnl = f_nl
self.tau_rec = tau_r
self.z_rec = z_r
self.eta_r = self.eta(self.z_rec)
self.H_0 = h0 * 100.0e0
self.n_s = ns
self.mf = hmf.Hmf(mf_type=hmf_type)
import inspect
print inspect.getframeinfo(inspect.currentframe().f_back)[3]
# print inspect.stack()
self.pk = PowSpec(self)
def display(self):
"""
Displays what you're working with.
"""
print ("YOU ARE USING THE FOLLOWING COSMOLOGY:")
print ("{h_0, O_m, O_de, w_0, O_b, O_r, O_k} = ")
print (
"{{{}, {}, {}, {}, {}, {}, {}}}".format(
self.h_0, self.O_m0, self.O_de0, self.w_0, self.O_b0, self.O_r0, self.O_k0
)
)
print ("WITH MASS FUNCTION:")
self.mf.display()
print ("WITH POWER SPECTRUM:")
self.pk.display()
def set_hmf(self, set_mf):
"""
Set method for the HMF within the Cosmology
"""
self.mf = set_mf
def set_powspec(self, set_pk):
"""
Set method for power spectrum within the Cosmology
"""
self.pk = set_pk
def rho_c(self):
"""
Critical density
"""
return rhofactor * ((3.0e0 * 100.0e0 * 100.0e0) / (8.0e0 * pi * G * Hfactor * Hfactor))
def rho_m(self, z):
"""
Average density of Universe at redshift z
"""
return rhofactor * self.O_m(z) * ((3.0e0 * 100.0e0 * 100.0e0) / (8.0e0 * pi * G * Hfactor * Hfactor))
def O_m(self, z):
"""
Omega matter.
"""
return self.O_m0 * pow(1.0e0 + z, 3.0e0) / (self.O_m0 * pow(1.0e0 + z, 3.0e0) + 1.0e0 - self.O_m0)
def h(self, z):
"""
Hubble function ***little*** h(z).
"""
a = 1.0e0 / (1.0e0 + z)
h_square = (
self.O_r0 / pow(a, 4.0e0)
+ self.O_m0 / pow(a, 3.0e0)
+ self.O_k0 / pow(a, 2.0e0)
+ self.O_de0 / pow(a, 3.0e0 * (1.0e0 + self.w_0))
)
return sqrt(h_square)
def _integ_one_on_h_scalar(self, z_min, z_max):
"""Scalar calculation of 1/h between z_min and z_max
"""
integfunc = lambda x: 1.0e0 / self.h(x)
return integrate.quad(integfunc, z_min, z_max)[0]
_integ_one_on_h_vector = np.vectorize(_integ_one_on_h_scalar)
def H(self, z):
"""
Hubble function ***upper*** H(z).
"""
return self.H_0 * self.h(z)
def dvdz(self, z):
"""
Comoving volume element at redshift z.
"""
return 4.0e0 * 2998e0 * (1 + z) * (1 + z) * pi * pow(self.D_a(z), 2.0e0) / self.h(z)
def V_between(self, z_min, z_max):
"""
Volume between two redshifts.
"""
points = 200
int_arr = np.zeros(points)
z_arr = np.linspace(z_min, z_max, points)
for i in np.arange(points):
int_arr[i] = self.dvdz(z_arr[i])
return integrate.trapz(int_arr, z_arr)
def D_a(self, z):
"""
Angular diameter distance to redshift z.
"""
if np.isscalar(z):
integ = self._integ_one_on_h_scalar(0.0e0, z)
else:
integ = self._integ_one_on_h_vector(self, 0.0e0, z)
return 2998.0e0 * integ / (1.0e0 + z)
def D_l(self, z):
"""
Luminosity distance to redshift z.
"""
return D_a(z) * (1.0e0 + z) ** 2.0e0
def D_c(self, z):
"""
Comoving radial distance to redshift z.
"""
return D_a(z) * (1.0e0 + z) / (100.0e0 * self.h0)
def dist_mod(self, z):
"""
Distance modulus.
5 * log(D_l(z)) + 25
"""
return 5.0e0 * np.log10(self.D_l(z)) + 25.0e0
def eta(self, z):
"""
Size of particle horizon at redshift z
"""
if z == np.inf:
retVar = 0.0e0
else:
if np.isscalar(z):
retVar = self._integ_one_on_h_scalar(z, np.inf) / (100.0e0 * self.h_0)
else:
retVar = self._integ_one_on_h_vector(self, z, np.inf) / (100.0e0 * self.h_0)
return retVar
def _integ_lookback_scalar(self, z):
"""Scalar calculation of lookback time to redshift z
"""
integfunc = lambda x: 1.0e0 / (self.h(x) * (1.0e0 + x))
return integrate.quad(integfunc, 0.0e0, z)[0] / (100.0e0 * self.h_0)
_integ_lookback_vector = np.vectorize(_integ_lookback_scalar)
def t_lookback(self, z):
"""Lookback time to redshift z
"""
if np.isscalar(z):
t_lb = self._integ_lookback_scalar(z)
else:
t_lb = self._integ_lookback_vector(self, z)
return t_lb
def _integ_growth_scalar(self, z):
"""Scalar calculation of linear growth function
"""
integfunc = lambda x: 1.0e0 / pow(self.h((1.0e0 / x) - 1.0e0) * x, 3.0e0)
return (5.0e0 / 2.0e0) * self.O_m0 * self.h(z) * integrate.quad(integfunc, 0.0e0, 1.0e0 / (1.0e0 + z))[0]
_integ_growth_vector = np.vectorize(_integ_growth_scalar)
def growth(self, z):
"""Linear growth function.
"""
if np.isscalar(z):
Dplus = self._integ_growth_scalar(z)
else:
Dplus = self._integ_growth_vector(self, z)
return Dplus
def dndlnm(self, lnm, z):
"""
Comoving number density of dark matter haloes in logarithmic m.
"""
s = self.pk.sigma(lnm)
dlnsdlnm = self.pk.dlnsigmadlnm(lnm)
D_z = self.growth(z)
D_0 = self.growth(0.0e0)
return (
self.mf.f_sigma(s * D_z / D_0, z)
* fabs(log(D_z / D_0) + dlnsdlnm)
* self.rho_m(z)
/ (exp(lnm))
* self.mf.r_ng(s * D_z / D_0, self.delta_c, self.fnl)
)
def computeNinBin(self, z_min, z_max, lnm_min, lnm_max):
"""
Total number of dark matter haloes expected within a given mass,
redshift bin.
"""
return integrate.dblquad(self.dNdlnmdz, z_min, z_max, lambda lnm: lnm_min, lambda lnm: lnm_max)[0]
def computeLittleNinZBin(self, lnm_min, lnm_max, z):
"""
Total number of haloes within a given mass bin at fixed redshift.
"""
return integrate.quad(self.dndlnm, lnm_min, lnm_max, args=(z))[0]
def dNdlnmdz(self, lnm, z):
"""
Total number of dark matter haloes at a given redshift.
Product of dndlnm * dVdz
"""
return self.dndlnm(lnm, z) * self.dvdz(z)
def dNdlnm0dz(self, lnm, z):
"""
Total number of dark matter haloes,
of equivalent mass at redshift zero, at a given redshift.
Product of dndlnm * dVdz
"""
return self.dndlnm(lnm, 0.0e0) * self.dvdz(z)
