def dNdM(M,window='th',z=0):
"""
The halo mass function as given equation 2 of
Tinker 2008 ApJ 679, 1218
Parameters
----------
M: float
Halo mass in units of M_sun/h
window: string, optional
Choice of window function. By default it
is a top hat profile.
z: float, optional
Redshift at which the mass funciton is to
be computed. Default value: 0
Returns
-------
dNdM: float
dN/dM. Implicitly dependent of redshift.
This is in units of M^2/rho_m. To get the
true dN/dM, multiply by rho_m/M^2
"""
import numpy as np
from compos import const
const.initializecosmo(z=z)
rho_crit0 = 2.776992e12*const.cosmo['h']**2 #M_sun/Mpc^3
rho_m = const.cosmo['omega_0']*rho_crit0*(1+z)**3
R = (3*M/const.cosmo['h']/(4*np.pi*rho_m))**(1/3)
sigma = np.sqrt(psvariance(R,z=z)[0])
dNdM = -f_of_sigma(sigma)*R*dlogsigma_dr(R)/3
return dNdM
def psvariance(R, W='th',low = 1e-7,high=100,z=0):
"""
Variance of the linear power spectrum. Use the
power spectrum from COMPOS (Ziang Yen). Numerically
and obtains the variance.
Parameters
----------
R: float
Smoothing radius
W: string, optional
Form of the normalised window function.
'th' for top-hat profile and 'ga' for
gaussian.
low: float, optional
Lower integration limit to get the variance
high: float, optional
Upper integration limit
z: float, optional
Redshift. Defualt value is 0.
Returns
-------
variance: float
Variance of the smoothed ps.
error: float
Error incurred in variance from numerical integration
"""
import numpy as np
from scipy.integrate import quad
from compos import const, matterps
const.initializecosmo(z=z)
integrand = lambda k: (k*window_th(k,R))**2*matterps.normalizedmp(k)
integral = quad(integrand,low,high)
variance = integral[0]/(2*np.pi)**2
error = integral[1]/(2*np.pi)**2
return variance, error
# This script calculates linear matter power spectrum at
# z = 0 with a given set of cosmologycal parameters#
import numpy as np
import matplotlib.pyplot as mp
from compos import const, matterps
const.initializecosmo()
k = np.linspace(-4, np.log10(6.71600e+02), 10000)
k = 10**k * const.cosmo['h']
p = matterps.normalizedmp(k)
# p_nw = matterps.normalizedmpnw(k)
mp.loglog(k / const.cosmo['h'], p * const.cosmo['h']**3)
plottextl = mp.xlim()[0] * 2
plottextd = mp.ylim()[0] * 2
mp.text(plottextl,
plottextd,
r'$h = $' + str(const.cosmo['h']) + ', $\Omega_mh^2$ = ' +
str(const.cosmo['omega_0'] * const.cosmo['h']**2) +
', $\Omega_bh^2$ = ' +
str(const.cosmo['omega_b'] * const.cosmo['h']**2),
fontsize=15)
mp.ylabel('P(k)(h$^{-3}$Mpc$^{-3}$)')
mp.xlabel('k (h Mpc$^{-1}$)')
mp.savefig('../../results/matterps/mps.jpg')
mp.savefig('../../results/matterps/mps.pdf')
mp.show()
# This script uses pyhalofit.py to calculate nonlinear power spectra# import numpy as np import matplotlib.pyplot as mp from compos import const, pyhalofit, growthfactor, matterps # set parameters(as an example)# const.initializecosmo() x = np.linspace(-4, 1, 1000) k = 10 ** x d2 = growthfactor.growfunc_z(10) d1 = growthfactor.growfunc_z(5) pyhalofit.supparams(growthf=d2) np2 = pyhalofit.nlpowerspec(k, 10) pyhalofit.supparams(growthf=d1) np1 = pyhalofit.nlpowerspec(k, 5) pyhalofit.supparams() np0 = pyhalofit.nlpowerspec(k, 0) t = np.zeros((2, np.size(k))) p2 = matterps.normalizedmp(k, 10) p1 = matterps.normalizedmp(k, 5) p0 = matterps.normalizedmp(k, 0) mp.loglog(k/const.cosmo['h'], np0, label='nonlinear, z=0') mp.loglog(k/const.cosmo['h'], p0, label='linear, z=0') mp.loglog(k/const.cosmo['h'], np1, label='nonlinear,z=5')
# This code calls camb to generate a matter power spectrum
# at a given set of cosmological parameters and interpolate it at a given k#
# This script calculates linear matter power spectrum at
# z = 0 with a given set of cosmologycal parameters#
import numpy as np
import os
import matplotlib.pyplot as mp
from compos import const, camb_interp
f = os.getcwd()
const.initializecosmo(kmax=20, callcamb=1)
os.chdir(f)
k = np.linspace(-3, 1, 10000)
k = 10**k * const.cosmo['h']
p = camb_interp.normCAMB_Pk(k)
mp.loglog(k / const.cosmo['h'], p * const.cosmo['h']**3)
plottextl = mp.xlim()[0] * 2
plottextd = mp.ylim()[0] * 2
mp.text(plottextl,
plottextd,
r'$h = $' + str(const.cosmo['h']) + ', $\Omega_mh^2$ = ' +
str(const.cosmo['omega_0'] * const.cosmo['h']**2) +
', $\Omega_bh^2$ = ' +
str(const.cosmo['omega_b'] * const.cosmo['h']**2),
fontsize=15)
import numpy as np
import matplotlib.pyplot as mp
import os
from compos import const, camb_interp, pyhalofit_camb
f = os.getcwd()
const.initializecosmo(callcamb=1)
pyhalofit_camb.supparams()
x = np.linspace(-4, np.log(2), 1000)
k = 10 ** x
p = pyhalofit_camb.nlpowerspec(k)
t = np.zeros((2, np.size(k)))
t[0] = k
t[1] = p
t = np.transpose(t)
p2 = camb_interp.CAMB_Pk(k)
os.chdir(f)
np.savetxt('../../results/pyhalofit/halofit_camb.txt', t)
mp.loglog(k, p, label='nonlinear')
mp.loglog(k, p2, label='linear')
mp.text(0.001, 0.1, '$h = 0.7, \Omega_mh^2$ = ' +
str(const.cosmo['omega_0']*const.cosmo['h']**2) +
',$ \Omega_qh^2 = $'+str(const.cosmo['omega_q'] *
const.cosmo['h']**2)+',', fontsize=15)
mp.legend()
mp.xlabel('k (h Mpc$^{-1}$)')
mp.ylabel('P(k) (h$^{-3}$ Mpc$^{-3}$)')
mp.savefig('../../results/pyhalofit/pyhalofit_camb.pdf')
# This code calls camb to generate a matter power spectrum
# at a given set of cosmological parameters and interpolate it at a given k#
# This script calculates linear matter power spectrum at
# z = 0 with a given set of cosmologycal parameters#
import numpy as np
import os
import matplotlib.pyplot as mp
from compos import const, camb_interp
f = os.getcwd()
const.initializecosmo(kmax=20, callcamb=1)
os.chdir(f)
k = np.linspace(-3, 1, 10000)
k = 10 ** k * const.cosmo['h']
p = camb_interp.normCAMB_Pk(k)
mp.loglog(k / const.cosmo['h'], p * const.cosmo['h'] ** 3)
plottextl = mp.xlim()[0] * 2
plottextd = mp.ylim()[0] * 2
mp.text(plottextl, plottextd, r'$h = $' + str(const.cosmo['h']) +
', $\Omega_mh^2$ = ' + str(const.cosmo['omega_0'] *
const.cosmo['h'] ** 2) +
', $\Omega_bh^2$ = ' + str(const.cosmo['omega_b'] *
const.cosmo['h'] ** 2), fontsize=15)
mp.ylabel('P(k)(h$^{-3}$Mpc$^{-3}$)')
mp.xlabel('k (h Mpc$^{-1}$)')
# This script gives examples of growth factor with respect to
# a with different set of (w_0, w_1)
import numpy as np
import matplotlib.pyplot as mp
import time
from compos import const, growthfactor
t0 = time.time()
const.initializecosmo(.3, 0, 0.67, 2.7255/2.7, omq=0.7, sigma8=0.8288)
a = np.linspace(0.0001, 1, 500)
# growthfactor.generateDE(-1, 0)
g1 = np.zeros(np.size(a))
for i in range(0, np.size(g1)):
g1[i] = growthfactor.growfunc_a(a[i])
const.initializecosmo(0.3, 0, 0.67, 2.7255/2.7, omq=0.7, sigma8=0.8288,
w_0=-0.8, w_1=0, n_s=0.96)
# growthfactor.generateDE(-0.8, 0)
g2 = np.zeros(np.size(a))
for i in range(0, np.size(g1)):
g2[i] = growthfactor.growfunc_a(a[i])
const.initializecosmo(0.3, 0, 0.67, 2.7255/2.7, omq=0.7, sigma8=0.8288,
w_0=-0.8, w_1=-0.6, n_s=0.96)