def __init__(self,M,N=1e4,MMinInfall=1e-5,MMaxInfall=1e-1,Rmax=2,C=None,include_disruption=True,weighted_sample=True): ''' initialize the sampling parameters. M: host mass in 1e10Msun/h N: number of subhaloes to generate MMinInfall: minimum infall mass, in unit of host mass MMaxInfall: maximum infall mass, in unit of host mass Rmax: maximum radius to sample, in unit of host virial radius C: host concentration. If None, it will be determined by the mean mass-concentration relation. include_disruption: whether to include disrupted subhaloes in the sample. weighted_sample: whether to sample the mass in a weighted way, so that different mass ranges are sampled equally well. this is useful if you have a large dynamic range in mass, e.g., from 10^-6 to 10^12 Msun. ''' self.M=M self.Host=NFWHalo(M,C) #self.Host.density=my_density_func #to use custom density, overwrite Host.density() function. self.C=self.Host.C self.HOD=ModelParameter(self.M) self.Rmax=Rmax self.Msample=self.Host.mass(Rmax*self.Host.Rv) #mass inside Rmax self.mAccMin=MMinInfall*M self.mAccMax=MMaxInfall*M self.n=N #sample size self.nPred=self.HOD.A*self.Msample*(self.mAccMin**-self.HOD.alpha-self.mAccMax**-self.HOD.alpha)/self.HOD.alpha #expected number of subhaloes per host. self.include_disruption=include_disruption if include_disruption: self.nSurvive=int(N*self.HOD.fs) self.nDisrupt=N-self.nSurvive else: self.nPred*=self.HOD.fs #only survived subhaloes are generated. self.nSurvive=N self.nDisrupt=int(N/self.HOD.fs*(1-self.HOD.fs)) self.weighted_sample=weighted_sample
class SubhaloSample:
''' a sample of subhaloes '''
def __init__(self,M,N=1e4,MMinInfall=1e-5,MMaxInfall=1e-1,Rmax=2,C=None,include_disruption=True,weighted_sample=True):
''' initialize the sampling parameters.
M: host mass in 1e10Msun/h
N: number of subhaloes to generate
MMinInfall: minimum infall mass, in unit of host mass
MMaxInfall: maximum infall mass, in unit of host mass
Rmax: maximum radius to sample, in unit of host virial radius
C: host concentration. If None, it will be determined by the mean mass-concentration relation.
include_disruption: whether to include disrupted subhaloes in the sample.
weighted_sample: whether to sample the mass in a weighted way, so that different mass ranges are sampled equally well. this is useful if you have a large dynamic range in mass, e.g., from 10^-6 to 10^12 Msun.
'''
self.M=M
self.Host=NFWHalo(M,C)
#self.Host.density=my_density_func #to use custom density, overwrite Host.density() function.
self.C=self.Host.C
self.HOD=ModelParameter(self.M)
self.Rmax=Rmax
self.Msample=self.Host.mass(Rmax*self.Host.Rv) #mass inside Rmax
self.mAccMin=MMinInfall*M
self.mAccMax=MMaxInfall*M
self.n=N #sample size
self.nPred=self.HOD.A*self.Msample*(self.mAccMin**-self.HOD.alpha-self.mAccMax**-self.HOD.alpha)/self.HOD.alpha #expected number of subhaloes per host.
self.include_disruption=include_disruption
if include_disruption:
self.nSurvive=int(N*self.HOD.fs)
self.nDisrupt=N-self.nSurvive
else:
self.nPred*=self.HOD.fs #only survived subhaloes are generated.
self.nSurvive=N
self.nDisrupt=int(N/self.HOD.fs*(1-self.HOD.fs))
self.weighted_sample=weighted_sample
def _lnPDF(self, x):
''' R in units of Rv'''
lnmu,lnR=x
lnmubar=np.log(self.HOD.mustar)+self.HOD.beta*lnR
dlnmu=lnmu-lnmubar
if lnmu>0: #mu<1
return -np.inf
if dlnmu>np.log(4.2): #mu<mumax=4.2*mubar
return -np.inf
if lnR>np.log(self.Rmax):
return -np.inf
lnPDFmu=-0.5*(dlnmu/self.HOD.sigma_mu)**2
lnPDFR=3.*lnR+np.log(self.Host.density(np.exp(lnR)*self.Host.Rv)) #dM/dlnR=rho*R^3.
return lnPDFmu+lnPDFR
def assign_mu_R(self, nwalkers=8, nburn=200, plot_chain=True):
'''run emcee to sample mu and R '''
nsteps=int(self.n/nwalkers+1+nburn) #one more step to make up for potential round-off in N/nwalkers
print 'running %d steps'%nsteps
ndim=2
x00=np.array([-0.5,-0.5])
x0=np.kron(np.ones([nwalkers,1]),x00)#repmat to nwalkers rows
x0+=(np.random.rand(ndim*nwalkers).reshape(nwalkers,ndim)-0.5)*0.1 #random offset, [-0.5,0.5]*0.1
sampler=emcee.EnsembleSampler(nwalkers,ndim,self._lnPDF)
sampler.run_mcmc(x0,nsteps)
if plot_chain:
plt.figure()
labels=[r"$\ln \mu$",r"$\ln R/R_{200}$"]
for i in range(ndim):
plt.subplot(ndim,1,i+1)
for j in range(nwalkers):
plt.plot(range(nsteps),sampler.chain[j,:,i],'.')
plt.ylabel(labels[i])
plt.plot([nburn,nburn],plt.ylim(),'k--')
plt.xlabel('Step')
plt.subplot(211)
plt.title('%d walkers, %d burn-in steps assumed'%(nwalkers,nburn), fontsize=10)
#==========extract mu and R===========
sample=sampler.chain[:,nburn:,:]
flatchain=sample.reshape([-1,ndim])[-self.n:] #take the last N entries
flatchain=np.exp(flatchain) #from log() to linear
self.mu,self.R=flatchain.T
#==========disruptions===============
if self.include_disruption:
self.mu[self.nSurvive:]=0. #trailing masses set to 0.
def project_radius(self):
phi=np.arccos(np.random.rand(self.n)*2-1.) #random angle around the z-axis
self.Rp=self.R*np.sin(phi) #projected radius
def assign_mass(self):
'''sample m and mAcc'''
if self.weighted_sample:
lnmmin,lnmmax=np.log(self.mAccMin), np.log(self.mAccMax)
lnmAcc=np.random.rand(self.n)*(lnmmax-lnmmin)+lnmmin #uniform distribution between lnmmin and lnmmax
self.mAcc=np.exp(lnmAcc)
self.weight=self.mAcc**-self.HOD.alpha
self.weight=self.weight/self.weight.sum()*self.nPred #w/sum(w)*Npred, equals to dN/dlnm*[delta(lnm)/N] as N->inf
#self.weight=self.HOD.fs*self.HOD.A*Host.Msample*mAcc**-self.HOD.alpha*(lnmmax-lnmmin)/self.n #the weight is dN/dlnm*[delta(lnm)/N]
print np.sum(self.weight), self.nPred
else:
mmax,mmin=self.mAccMin**(-self.HOD.alpha),self.mAccMax**(-self.HOD.alpha)
mAcc=np.random.rand(self.n)*(mmax-mmin)+mmin #uniform in m**-alpha which is proportional to N
self.mAcc=mAcc**-(1./self.HOD.alpha)
self.weight=1.*self.nPred/self.n*np.ones(self.n)
self.m=self.mAcc*self.mu
def populate(self, plot_chain=True):
'''populate the sample with m,mAcc,R and weight'''
self.assign_mu_R(plot_chain=plot_chain)
self.assign_mass()
def assign_stellarmass(self):
'''generate stellar mass from infall mass, according to an abundance matching model'''
logMstar=np.log10(InfallMass2StellarMass(self.mAcc))
sigmaLogMstar=0.192
deltaLogMstar=np.random.normal(0, sigmaLogMstar, self.n)
self.mStar=10**(logMstar+deltaLogMstar)
def assign_annihilation_emission(self, concentration_model='Ludlow'):
'''generate annihilation luminosity
concentration_model: 'MaccioW1', Maccio08 relation with WMAP 1 cosmology
'Ludlow', Ludlow14 relation with WMAP 1 cosmology'''
#first generate concentration from infall mass, according to a mass-concetration relation
logC=np.log10(mean_concentration(self.mAcc[:self.nSurvive],concentration_model)) #mean
sigmaLogC=0.13
deltaLogC=np.random.normal(0, sigmaLogC, self.nSurvive) #scatter
cAcc=10**(logC+deltaLogC)
SatHalo=[NFWHalo(self.mAcc[i], cAcc[i]) for i in range(self.nSurvive)]
rt=np.array([SatHalo[i].radius(self.m[i]) for i in range(self.nSurvive)]) #truncation radius
self.L=np.zeros_like(self.m)
self.L[:self.nSurvive]=np.array([SatHalo[i].luminosity(rt[i]) for i in range(self.nSurvive)]) #truncated luminosity
def save(self, outfile, save_all=False):
''' save the sample to outfile.
if save_all=True, save all the properties; otherwise only R,m,mAcc,weight will be saved.'''
if save_all:
np.savetxt(outfile, np.array([self.R,self.m,self.mAcc,self.weight,self.Rp,self.mStar,self.L]).T, header='R/R200, m/[1e10Msun/h], mAcc/[1e10Msun/h], weight, Rp/R200, mStar/[1e10Msun/h], Luminosity/[(1e10Msun/h)^2/(kpc/h)^3]')
else:
np.savetxt(outfile, np.array([self.R,self.m,self.mAcc,self.weight]).T, header='R/R200, m/[1e10Msun/h], mAcc/[1e10Msun/h], weight')