def profile_check(c):
a = [1E12, 1E13, 1E14]
for k in range(0, 3):
x0 = a[k]
cosmology.setCosmology('planck100',\
{'flat': True, 'H0': 67.3, 'Om0': 0.315, 'Ob0': 0.049, 'sigma8': 0.81, 'ns': 0.95})
p_nfw = profile_nfw.NFWProfile(M=x0, c=3.5, z=0, mdef='vir')
r = np.logspace(-4, 3.5, 1000)
rho = p_nfw.density(r)
##这里的r表示rs
#plt.loglog(r, rho)
plt.loglog(10**(-3) * r, 10**9 * rho, ls='--')
#plt.xlabel(r'$kpc/h$')
#plt.ylabel(r'$h^2M_\odot/kpc^3$')
plt.xlabel(r'$Mpc/h$')
plt.ylabel(r'$h^2M_\odot/Mpc^3$')
#plt.savefig(r'$rho-r$',dpi=600)
return
def _convert_m_vmax(self,mass,v_max,z): """ Convert from mass and v_max to profile amplitude and concentration for an NFW Args: mass (float): Mass of the NFW in units of M_sun/h v_max (float): v_max of the NFW in units of km/s z (float): The redshift of the NFW Returns, ((float,float,float,float)): A tuple containing the concentration of the NFW, the amplitude of the NFW in units of M_sun*h^2/kpc^3, and the scale radius in units of Mpc/h. """ # Create our f function def f(x): return np.log(1+x)-x/(1+x) rho_overd = mass_so.densityThreshold(z,'vir') # Create our v_max function def v_max_dif(c,mass,v_max): if c < 1: return 100 r_vir = (mass/(4*np.pi/3*rho_overd))**(1/3) # In kpc/h v_max_calc = np.sqrt(self.__class__.G_TRADITIONAL * mass / r_vir * f( self.__class__.XMAX)/f(c)*c/self.__class__.XMAX) return v_max_calc-v_max c = root_scalar(v_max_dif,args=(mass,v_max),x0=6,x1=10).root # Use colossus to convert to the amplitude and scale radius. rho, r_s = profile_nfw.NFWProfile.fundamentalParameters(M=mass,c=c,z=z, mdef='vir') v_vir = profile_nfw.NFWProfile(M=mass,c=c,z=z, mdef='vir').circularVelocity(c*r_s) # Divide the scale radius by 1000 to convert it to Mpc/h from kpc/h r_s /= 1000 r_vir = r_s * c return c, rho, r_s, v_vir, r_vir
set_model = apcy.Planck15.clone(H0=67.74, Om0=0.311)
input_cosm_model(get_model=set_model)
cosmos_param()
z0 = 0.50
v_m = 200
Mh0 = 14
c0 = 5
R_0 = np.logspace(0, 3.5, 100)
sigma_m = sigmam(R_0, Mh0, z0, c0)
sigma_c = sigmac(R_0, Mh0, z0, c0)
p_nfw = profile_nfw.NFWProfile(M=1E14, c=c0, z=z0, mdef='200m')
p_Sigma = p_nfw.surfaceDensity(R_0)
print(p_Sigma / sigma_m)
p_nfw_c = profile_nfw.NFWProfile(M=1E14, c=c0, z=z0, mdef='200c')
p_Sigma_c = p_nfw_c.surfaceDensity(R_0)
print(p_Sigma_c / sigma_c)
rho_c, rho_m = rhom_set(z0)
c_rho_c = cosmos.rho_c(z0)
c_rho_m = cosmos.rho_m(z0)
print(c_rho_c / rho_c)
print(c_rho_m / rho_m)
sigma_crit = (constants.c**2 / (4 * np.pi * constants.G) * d_s / (
d_l * d_ls)).to(u.solMass / u.kpc**2).value
ds = np.zeros((len(log_mvir), len(rp)))
kappa = np.zeros((len(log_mvir), len(rp)))
# %%
for i, mvir in enumerate(10**log_mvir):
w = dn[i] / np.sum(dn)
if w == 0:
continue
profile = profile_nfw.NFWProfile(
M=mvir, c=concentration(mvir, 'vir', z_l, model='diemer19'), z=z_l,
mdef='vir')
for j in range(len(rp)):
rp_phys = 1000 * rp[j] / (1 + z_l) # phys. in kpc/h
ds[i, j] = profile.surfaceDensity(rp_phys) / (1 + z_l)**2
kappa[i, j] = profile.surfaceDensity(rp_phys) / sigma_crit
# %%
alpha_s = 2.0
fig, (ax1, ax2) = plt.subplots(nrows=2, sharex=True)
idxp1 = np.sum(cat.Npart[:idx]) idxp2 = idxp1 + cat.Npart[idx] plt.scatter(pos[idxp1:idxp2][:, 0], pos[idxp1:idxp2][:, 1], s=0.1) plt.show() plt.scatter(pos[idxp1:idxp2][:, 0], pos[idxp1:idxp2][:, 2], s=0.1) plt.show() plt.scatter(pos[idxp1:idxp2][:, 1], pos[idxp1:idxp2][:, 2], s=0.1) plt.show() # Getting Radius r = ((pos[idxp1:idxp2] - cat.pos[idx])**2).sum(axis=1)**0.5 rhist = np.geomspace(r.min(), r.max(), 10) mhist, aux = np.histogram(r, bins=rhist) mhist = mp * mhist mhist = np.cumsum(mhist) mhist = np.append([0], mhist) profile = profile_nfw.NFWProfile(M=cat.Mass[idx], mdef='200c', z=0.0, c=4.0) fit = profile.fit(rhist * 1e3, mhist, 'M') c = concentration.concentration(cat.Mass, '200c', 0.0, model='bhattacharya13') print(c[idx], rDelta[idx] * 1e3 / fit['x'][1]) plt.plot(rhist, fit['q_fit']) plt.plot(rhist, mhist) plt.show()
for i in range(300):
print(conc.dtype, rdelta.dtype, r.dtype, theta.dtype, phi.dtype)
NFWx.random_nfw(npart, conc, rdelta, r, theta, phi)
#r = randomr(conc[0], n=npart[0])
# Getting Radius
R = r
rhist = np.linspace(R.min(), R.max())
mhist, aux = np.histogram(R, bins=rhist)
mhist = mp * mhist
mhist = np.cumsum(mhist)
mhist = np.append([0], mhist) #\+ np.sum(r<=rhist.min()) * 1e10
profile = profile_nfw.NFWProfile(M=mpart,
mdef='200c',
z=0.0,
c=conc[0])
mfid = profile.enclosedMass(rhist * 1e3)
print(profile.enclosedMass(rdelta * 1e3) / mpart)
#plt.plot(rhist, mhist)
#plt.plot(rhist, mfid)
#plt.show()
fit = profile.fit(rhist * 1e3, mhist, 'M')
prec_dict[nparti] += [conc / (rdelta * 1e3 / fit['x'][1])]
plt.plot(rhist, mhist)
plt.plot(rhist, fit['q_fit'])
plt.show()
plt.hist(np.array(prec_dict[nparti]).flatten(), bins=30)
plt.show()
def DStheo(theta, args):
"""
Computes de theoretical :math:`\Delta\Sigma_{NFW}` profile for a given mass
:math:`m_{200}`, z and cosmology.
Parameters
----------
theta: tuple
Parameters for the mcmc
args: dict
Contains the cosmology and other mean values computed from the data
Returns
-------
ds: np.array
The thoretical :math:`\Delta\Sigma_{NFW}` profile
Notes
-----
The parameters for the NFW function are the mass :math:`m_{200}` and the
concentration :math:`c_{200}`. However, in this anlysis, we use the
Duffy et al. (2008) concetration-mass relation to get the profile only
as a function of the mass. See: https://github.com/joergdietrich/NFW for
more details on the NFW function.
"""
runtype = args['runtype']
runconfig = args['runconfig']
if runtype == 'data':
if runconfig == 'Full':
m200, pcc, Am, B0, Rs = theta #M200c [Msun]
elif runconfig == 'OnlyM':
m200 = theta[0]
elif runconfig == 'FixAm':
m200, pcc, B0, Rs = theta
elif runtype == 'cal':
m200 = theta[0]
elif runtype == 'calsys':
if runconfig == 'Full':
m200, pcc, Am, B0, Rs = theta #M200c [Msun]
h = args['h']
z_mean = args['z_mean']
R = args['R'] #in physical [Mpc]
cosmo = args['cosmo'] #astropy cosmology object
cmodel = args[
'cmodel'] #diemer18 (obs.: lastest version of Colossus renamed to diemer19)
twohalo = args['twohalo']
factor2h = args['factor2h'] #boolean, if True multiply 2-halo term by h
cosmodict = args['cosmodict']
omega_m = cosmodict['om']
sigma_crit_inv = args['Sigma_crit_inv']
#Setting up the cosmology for Colossus
params = {
'flat': True,
'H0': cosmodict['h'] * 100.,
'Om0': cosmodict['om'],
'Ob0': cosmodict['ob'],
'sigma8': cosmodict['sigma8'],
'ns': cosmodict['ns']
}
cosmology.addCosmology('myCosmo', params)
cosmoc = cosmology.setCosmology('myCosmo')
cmodel = cmodel
c200c = concentration.concentration(
m200 * h, '200c', z_mean, model=cmodel,
conversion_profile='nfw') #m200c_in is [Msun/h], m200c_out is [Msun/h]
nfw = NFW(m200,
c200c,
z_mean,
cosmology=cosmo,
overdensity_type='critical') #input mass should be in [Msun]
#For DeltaSigma calculation, data and sim, the radius has to be in physical [Mpc]
if runtype == 'cal':
ds = (nfw.delta_sigma(R).value
) / 1.e12 #DeltaSigma is in units of physical [M_sun/Mpc^2]
#This two-halo part was not used in the analysis, the compuation is too slow
if twohalo:
#Adding the 2-halo term
b = bias.haloBias(m200 * h, z_mean, '200c',
model='tinker10') #mass_in is [Msun/h]
outer_term_xi = profile_outer.OuterTermCorrelationFunction(
z=z_mean, bias=b)
p_nfw = profile_nfw.NFWProfile(
M=m200 * h,
c=c200c,
z=z_mean,
mdef='200c',
outer_terms=[outer_term_xi]) #mass_in is [Msun/h]
#Radius in physical kpc/h
two_nfw0 = p_nfw.deltaSigmaOuter((R * 1e3) * h,
interpolate=True,
interpolate_surface_density=False,
min_r_interpolate=1.e-6 * h,
max_r_integrate=2.e5 * h,
max_r_interpolate=2.e5 * h)
two_nfw1 = two_nfw0 / 1.e6 #in physical [h Msun/pc^2]
if factor2h:
two_nfw = h * (two_nfw1 * h
) #something like physical [Msun/(h pc^2)]
else:
two_nfw = (
two_nfw1 * h
) #in physical [Msun/pc^2] #This should be the right one
ds_model = ds + two_nfw #NFW + 2-halo in physical [Msun/pc^2] if factor2h=False
else:
ds_model = ds
return ds_model #physical [M_sun/pc^2]
if runtype == 'data' or runtype == 'calsys':
ds = (
nfw.delta_sigma(R).value
) / 1.e12 #units of h Msun/pc^2 physical (but h=1, so actually is M_sun/pc^2)
sigma = (nfw.sigma(R).value) / 1.e12
# Computing miscetering correction from data
m200p = m200
z = np.array([z_mean])
if runtype == 'data':
cluster = ClusterEnsemble(z,
cosmology=FlatLambdaCDM(H0=100, Om0=0.3),
cm='Diemer18',
cmval=c200c)
misc_off = 0.1326 #here in [Mpc], since h=1
elif runtype == 'calsys':
cluster = ClusterEnsemble(z,
cosmology=FlatLambdaCDM(H0=h * 100,
Om0=omega_m),
cm='Diemer18',
cmval=c200c)
misc_off = 0.1326 / h #input needs to be in units of [Mpc]
if np.shape(m200p) == (1, 1):
m200p = np.reshape(m200p, (1, ))
try:
cluster.m200 = m200p #M200c [Msun]
except TypeError:
cluster.m200 = np.array([m200p])
rbins = R # in physical [Mpc]
offsets = np.ones(cluster.z.shape[0]) * misc_off
cluster.calc_nfw(rbins, offsets=offsets) #NFW with offset
dsigma_offset = cluster.deltasigma_nfw.mean(
axis=0) #physical [M_sun/pc^2], but if h=1 is [h M_sun/pc**2]
DSmisc = dsigma_offset.value #physical [Msun/pc^2]
sigma_offset = cluster.sigma_nfw.mean(
axis=0) #physical [M_sun/pc**2], but if h=1 is [h M_sun/pc**2]
Smisc = sigma_offset.value #physical [Msun/pc^2]
if runconfig == 'OnlyM':
pcc = 0.75
B0 = 0.50
Rs = 2.00
#The final model
full_Sigma = pcc * sigma + (1 - pcc) * Smisc
full_model = pcc * ds + (1 - pcc) * DSmisc
if runconfig == 'Full':
full_model *= Am #shear+photo-z bias correction
elif runconfig == 'OnlyM' or 'FixAm':
full_model = full_model
#Note: R (rbins) and Rs are in physical [Mpc], need to be comoving [Mpc/h]
boost_model = ct.boostfactors.boost_nfw_at_R(rbins * h * (1 + z_mean),
B0, Rs * h * (1 + z_mean))
full_model /= boost_model #boost-factor
full_model /= (1 - full_Sigma * sigma_crit_inv) #Reduced shear
return full_model # in physical [M_sun/pc^2]