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abhodfits.py
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abhodfits.py
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"""
Module to perform power-law fits to wp(rp)
"""
import numpy as np
import emcee
import matplotlib.pyplot as plt
from scipy.special import gamma as gammafn
from halotools.empirical_models import PrebuiltHodModelFactory
from halotools.empirical_models import HodModelFactory
from halotools.empirical_models import AssembiasZheng07Cens
from halotools.empirical_models import TrivialPhaseSpace
from halotools.empirical_models import AssembiasZheng07Sats
from halotools.empirical_models import NFWPhaseSpace
from halotools.mock_observables import return_xyz_formatted_array
from halotools.mock_observables import wp
from halotools.sim_manager import CachedHaloCatalog
# fast correlation function calculation
from Corrfunc import _countpairs
# default settings of all parameters
from abhodfit_defaults import *
# A class to hold the attributes of a power-law model for wp(rp)
class ABHodFitModel():
"""
HOD with assembly bias Fit model class for wp(rp)
"""
###################################################################
# Initialize an instance of the ABHodFitModel
def __init__(self,**kwargs):
"""
Initialize a ABHodFitModel.
"""
# first, set up appropriate priors on parameters
if ('priors' in kwargs.keys()):
self.set_prior(kwargs['priors'])
else:
self.set_prior(default_priors)
# set up keys for the parameter names for plotting
self.param_names=['alpha','logM1','siglogM','logM0','logMmin','Acens','Asats']
self.latex_param_names=[r'$\alpha$',r'$\log(M_1)$',
r'$\sigma_{\log M}$',r'$\log(M_0)$',r'$\log(M_{\rm min})$',
r'$\mathcal{A}_{\rm cens}$',r'$\mathcal{A}_{\rm sats}']
# set up size parameters for any MCMC
self.set_nwalkers(ndim=default_ndim,nwalkers=default_nwalkers)
# if data is specified, load it into memory
if 'rpcut' in kwargs.keys():
self.rpcut=kwargs['rpcut']
else:
self.rpcut=default_rpcut
if ('datafile' in kwargs.keys() ):
self.read_datafile(datafile=kwargs['datafile'])
else:
self.read_datafile(datafile=default_wp_datafile)
if ('covarfile' in kwargs.keys() ):
self.read_covarfile(covarfile=kwargs['covarfile'])
else:
self.read_covarfile(covarfile=default_wp_covarfile)
# if binfile is specified, load it into memory
# these are Manodeep-style bins
if ('binfile' in kwargs.keys()):
self.binfile=kwargs['binfile']
else:
self.binfile=default_binfile
# set up a default HOD Model
if ('cen_occ_model' in kwargs.keys()):
cen_occ_model=kwargs['cen_occ_model']
else:
cen_occ_model=AssembiasZheng07Cens(prim_haloprop_key='halo_mvir',
sec_haloprop_key='halo_nfw_conc')
if ('cen_prof_model' in kwargs.keys()):
cen_prof_model=kwargs['cen_prof_model']
else:
cen_prof_model=TrivialPhaseSpace()
if ('sat_occ_model' in kwargs.keys() ):
sat_occ_model=kwargs['sat_occ_model']
else:
sat_occ_model=AssembiasZheng07Sats(prim_haloprop_key='halo_mvir',
sec_haloprop_key='halo_nfw_conc')
if ('sat_prof_model' in kwargs.keys() ):
sat_prof_model=kwargs['sat_prof_model']
else:
sat_prof_model=NFWPhaseSpace()
# Default HOD Model is Zheng07 with Heaviside Assembly Bias
self.hod_model=HodModelFactory(centrals_occupation=cen_occ_model,
centrals_profile=cen_prof_model,
satellites_occupation=sat_occ_model,
satellites_profile=sat_prof_model)
# set pi_max for wp(rp) calculations
self.pi_max=default_pi_max
if ('simname' in kwargs.keys() ):
simname=kwargs['simname']
else:
simname=default_simname
if ('halo_finder' in kwargs.keys() ):
halo_finder=kwargs['halo_finder']
else:
halo_finder=default_halofinder
if ('redshift' in kwargs.keys() ):
redshift=kwargs['redshift']
else:
redshift=default_simredshift
if ('version_name' in kwargs.keys() ):
version_name=kwargs['version_name']
else:
version_name=default_version_name
# set default simulation halocatalog to work with
self.halocatalog=CachedHaloCatalog(simname=simname,
halo_finder=halo_finder,
redshift=redshift,
version_name=version_name)
return None
##############################################################################
##############################################################################
# Set MCMC dimension and number of walkers
def set_nwalkers(self,**kwargs):
"""
Sets the number of MCMC dimensions and sets the number of walkers.
Parameters
----------
Takes keyword arguments ndim and nwalkers.
"""
if ('ndim' in kwargs.keys()):
self.ndim=kwargs['ndim']
if ('nwalkers' in kwargs.keys()):
self.nwalkers=kwargs['nwalkers']
return None
# Routine to set priors on model parameters
def set_prior(self,prior_array):
"""
Sets the model priors.
Parameters
-----------
Takes keyword arguments r0min, r0max, gammamin, gammamax
"""
self.priors={} # priors are stored in a dictionary
if 'alpha' in prior_array.keys():
self.priors['alpha']=prior_array['alpha']
if 'logM1' in prior_array.keys():
self.priors['logM1']=prior_array['logM1']
if 'sigma_logM' in prior_array.keys():
self.priors['sigma_logM']=prior_array['sigma_logM']
if 'logM0' in prior_array.keys():
self.priors['logM0']=prior_array['logM0']
if 'logMmin' in prior_array.keys():
self.priors['logMmin']=prior_array['logMmin']
if 'mean_occupation_centrals_assembias_param1' in prior_array.keys():
self.priors['mean_occupation_centrals_assembias_param1']=prior_array['mean_occupation_centrals_assembias_param1']
if 'mean_occupation_satellites_assembias_param1' in prior_array.keys():
self.priors['mean_occupation_satellites_assembias_param1']=prior_array['mean_occupation_satellites_assembias_param1']
return None
# Read in the data
def read_datafile(self,**kwargs):
"""
Read in the data. This can assume the input_data_file attribute or it
can accept a new data file as a keyword argument, datafile.
"""
if ('datafile' in kwargs.keys()):
self.datafile=kwargs['datafile']
col1,col2,col3=np.loadtxt(self.datafile,unpack=True)
self.Number_gals=col1[0]
self.ngal=col2[0]
self.ngalerr=col3[0]
self.rp=col1[1:]
self.wp=col2[1:]
self.wperr=col3[1:]
# Use data only out to the bin at rp=rpcut
ikeep=np.where(self.rp<=self.rpcut)
self.rp=self.rp[ikeep]
self.wp=self.wp[ikeep]
self.wpT=self.wp.T
self.wperr=self.wperr[ikeep]
# set the number of bins
self.nrpbins=self.rp.size
return None
# Read in the data covariances
def read_covarfile(self,**kwargs):
"""
Read in the data covariances
"""
if ('covarfile' in kwargs.keys() ):
self.covarfile=kwargs['covarfile']
else:
self.covarfile=default_wp_covarfile
self.covar=np.loadtxt(self.covarfile,unpack=True)
self.cov_inv=np.linalg.inv(self.covar)
# A routine to give wp(rp) computed via a halo model.
def wp_hod(self,hod_parameters):
"""
An HOD model for wp(rp) computed by direct simulation
population.
hod_parameters[0] : alpha
hod_parameters[1] : logM1
hod_parameters[2] : sigma_logM
hod_parameters[3] : logM0
hod_parameters[4] : logMmin
hod_parameters[5] : Acen
hod_parameters[6] : Asat
"""
# The first step is to set the param_dict of the hod_model.
self.hod_model.param_dict['alpha']=hod_parameters[0]
self.hod_model.param_dict['logM1']=hod_parameters[1]
self.hod_model.param_dict['sigma_logM']=hod_parameters[2]
self.hod_model.param_dict['logM0']=hod_parameters[3]
self.hod_model.param_dict['logMmin']=hod_parameters[4]
self.hod_model.param_dict['mean_occupation_centrals_assembias_param1']=hod_parameters[5]
self.hod_model.param_dict['mean_occupation_satellites_assembias_param1']=hod_parameters[6]
# Populate a mock galaxy catalog
#self.hod_model.populate_mock()
try:
self.hod_model.mock.populate()
except:
self.hod_model.populate_mock(self.halocatalog)
# Instruct wp(rp) routine to compute autocorrelation
autocorr=1
# Number of threads
nthreads=4
# use the z-direction as line-of-sight and add RSD
z_distorted = self.hod_model.mock.galaxy_table['z']+self.hod_model.mock.galaxy_table['vz']/100.0
# enforce periodicity of the box
self.hod_model.mock.galaxy_table['zdist']=z_distorted % self.hod_model.mock.Lbox[0]
# Return projected correlation function computed using
# Manodeep Simha's optimized C code.
cpout = np.array( _countpairs.countpairs_wp(self.hod_model.mock.Lbox[0],
self.pi_max,
nthreads,
self.binfile,
self.hod_model.mock.galaxy_table['x'].astype('float32'),
self.hod_model.mock.galaxy_table['y'].astype('float32'),
self.hod_model.mock.galaxy_table['zdist'].astype('float32') ) )
return np.array(cpout[0])[:,3]
# A routine to compute wp(rp) in a power-law model xi = (r/r0)^-gamma.
def wp_powerlaw_model(self,rsep,r0,gamma):
"""
Power law model for wp(rp) assuming that xi = (r/r0)^-gamma.
"""
if rsep.any < 0.0:
return np.inf
return rsep*(rsep/r0)**(-gamma)*gammafn(0.5)*gammafn((gamma-1.0)/2.0)/gammafn(gamma/2.0)
# A routine to compute the likelihood of a power-law wp(rp) given data.
def lnlike(self,theta):
"""
Log likelihood of a power-law model.
Parameters
------------
theta : (alpha,logM1,sigma_logM,logM0,logMmin)
rp : numpy array containing separations
wp : numpy array containing projected correlation functions
wperr : numpy array containing errors on measured wp
"""
# log likelihood from clustering
wpmodel=self.wp_hod(theta)
#print 'wpmodel shape = ',np.shape(wpmodel)
#print 'wperr shape = ',np.shape(self.wperr)
#print 'wp shape = ',np.shape(self.wp)
#print 'rp shape = ',np.shape(self.rp)
wp_dev=(wpmodel-self.wp)
wplike=-0.5*np.dot(np.dot(wp_dev,self.cov_inv),wp_dev)
# log likelihood from number density
number_gals=len(self.hod_model.mock.galaxy_table)
ngal=number_gals/(self.hod_model.mock.Lbox[0]**3)
ng_theory_error=ngal/np.sqrt(number_gals)
nglike=-0.5*((ngal-self.ngal)**2/(self.ngalerr**2+ng_theory_error**2))
return wplike+nglike
# A prior function on the two parameters in the list theta
def lnprior(self,theta):
"""
Prior function
Parameters
----------
theta : [alpha,logM1,sigma_logM,logM0,logMmin,Acen,Asat]
Priors are so-called hard priors specified in self.priors.
"""
alpha,logM1,sigma_logM,logM0,logMmin,Acen,Asat=theta
if alpha < self.priors['alpha'][0]:
return -np.inf
if alpha > self.priors['alpha'][1]:
return -np.inf
if logM1 < self.priors['logM1'][0]:
return -np.inf
if logM1 > self.priors['logM1'][1]:
return -np.inf
if sigma_logM < self.priors['sigma_logM'][0]:
return -np.inf
if sigma_logM > self.priors['sigma_logM'][1]:
return -np.inf
if logM0 < self.priors['logM0'][0]:
return -np.inf
if logM0 > self.priors['logM0'][1]:
return -np.inf
if logMmin < self.priors['logMmin'][0]:
return -np.inf
if logMmin > self.priors['logMmin'][1]:
return -np.inf
if Acen < self.priors['mean_occupation_centrals_assembias_param1'][0]:
return -np.inf
if Acen > self.priors['mean_occupation_centrals_assembias_param1'][1]:
return -np.inf
if Asat < self.priors['mean_occupation_satellites_assembias_param1'][0]:
return -np.inf
if Asat > self.priors['mean_occupation_satellites_assembias_param1'][1]:
return -np.inf
return 0.0
# The probability function including priors and likelihood
def lnprob(self,theta):
"""
Probability function to sample in an MCMC.
"""
lp=self.lnprior(theta)
if not np.isfinite(lp):
return -np.inf
return lp + self.lnlike(theta)
# Set the starting position of an MCMC.
def set_start_position(self,theta_start=default_start):
"""
Set the starting position for the MCMC.
"""
self.position=np.zeros([self.nwalkers,self.ndim])
for iparam in range(self.ndim):
self.position[:,iparam]=theta_start[iparam] + 0.05*np.random.randn(self.nwalkers)
return None
# Fit the data with the hod model model
def mcmcfit(self,theta_start,**kwargs):
"""
Peform an MCMC fit to the wp data using the power-law model.
"""
if ( 'samples' in kwargs.keys() ):
self.nsamples=kwargs['samples']
else:
self.nsamples=100
if ('nwalkers' in kwargs.keys()):
self.set_nwalkers(nwalkers=kwargs['nwalkers'])
self.wpsampler=emcee.EnsembleSampler(self.nwalkers,self.ndim,self.lnprob)
self.set_start_position(theta_start)
if ( 'burnin' in kwargs.keys() ):
self.nburnin=kwargs['burnin']
self.position,self.prob,self.state=self.wpsampler.run_mcmc(self.position,self.nburnin)
self.wpsampler.reset()
else:
self.nburnin=0
self.wpsampler.run_mcmc(self.position,self.nsamples)
self.mcmcsamples=self.wpsampler.chain[:,:,:].reshape((-1,self.ndim))
self.lnprobability=self.wpsampler.lnprobability.reshape(-1,1)
self.compute_parameter_constraints()
return None
# given a set of MCMC samples in self.mcmcsamples, compute the 1-D parameter constraints.
def compute_parameter_constraints(self):
"""
Computes the 1D marginalized parameter constraints from
self.mcmcsamples.
"""
self.alpha_mcmc,self.logM1_mcmc,self.sigma_logM_mcmc,self.logM0_mcmc,self.logMmin_mcmc,self.Acen_mcmc,self.Asat_mcmc=map(
lambda v: (v[1],v[2]-v[1],v[1]-v[0]),zip(*np.percentile(self.mcmcsamples,[16,50,84],axis=0)))
self.alpha_1side,self.logM1_1side,self.sigma_logM_1side,self.logM0_1side,self.logMmin_1side,self.Acen_1side,self.Asat_1side=map(
lambda v: (v[0],v[1],v[2],v[3],v[4],v[5],v[6],v[7]),zip(*np.percentile(self.mcmcsamples,[1,5,10,16,84,90,95,99],axis=0)))
return None
# save chains to file
def save_chains(self,**kwargs):
"""
Save the chain to an ascii file.
"""
if ( 'filename' in kwargs.keys()):
fname=kwargs['filename']
else:
fname=self.datafile
if fname.endswith('.dat'):
fname=fname[:-4]
fname=fname+'_abfit.chain'
out_data=np.hstack( (self.mcmcsamples,self.lnprobability) )
np.savetxt(fname,out_data,delimiter=' ')
return None
# load a chain from an existing chain file
def load_chains(self,chainfile_names):
"""
Load a pre-existing chain into memory from a file.
"""
for chainfile in chainfile_names:
read_data=np.loadtxt(chainfile,unpack=True).T
samples=read_data[:,0:self.ndim]
lnprob=read_data[:,self.ndim]
samples=samples.reshape(-1,self.ndim)
lnprob=lnprob.reshape(-1,1)
if (hasattr(self,'mcmcsamples')):
self.mcmcsamples=np.concatenate((self.mcmcsamples,samples),axis=0)
self.lnprobability=np.concatenate((self.lnprobability,lnprob),axis=0)
else:
self.mcmcsamples=samples
self.lnprobability=lnprob
# self.mcmcsamples=self.mcmcsamples.reshape(-1,self.ndim)
# self.lnprobability=self.lnprobability.reshape(-1,1)
return None
# plot the data
def plot_data(self):
"""
plot the data only
"""
fig1=plt.figure()
plt.loglog(self.rp,self.wp,'sk')
plt.errorbar(self.rp,self.wp,yerr=self.wperr,fmt='sk',ecolor='k')
plt.xlabel(r'$r_{\rm p}$')
plt.ylabel(r'$w_{\rm p}(r_{\rm p})$')
fig1.savefig('wpdata.png')
return None
# plot the mcmc run
def plot_parameter_run(self):
"""
plot the mcmc samples.
"""
for idim in range(self.ndim):
fig=plt.figure()
plt.plot(range(len(self.mcmcsamples[:,idim])),self.mcmcsamples[:,idim],'k')
plt.xlabel('sample number')
plt.ylabel(self.latex_param_names[idim])
filename=self.datafile
if filename.endswith('.dat'):
filename=filename[:-4]
plabel=self.param_names[idim].strip('$')
plabel=plabel.strip('\\')
filename=filename+'_'+plabel+'_'+'chain.png'
fig.savefig(filename)
del fig
# plot fitting results
def plot_chain_samples(self,**kwargs):
"""
Plots samples from the mcmc chain alongside the data.
"""
lnp_max=np.max(self.lnprobability)
if ('deltachi2' in kwargs.keys()):
lnp_threshold=lnp_max-kwargs['deltachi2']/2.0
else:
lnp_threshold=lnp_max-0.5
if ('samples' in kwargs.keys()):
numsamples=kwargs['samples']
else:
numsamples=50
fig=plt.figure()
#print ' + Beginning sample selection.'
igood=np.where((self.lnprobability.reshape(-1)>lnp_threshold))
#print 'numsamples = ',numsamples
#print 'Length(igood) = ',len(igood[0])
#print 'Shape(igood) = ',np.shape(igood)
# reduce the number of samples if there are very few
if len(igood[0]) < 1:
print ' > Too few samples that satisfy criterion, n = ',len(igood[0])
return None
elif len(igood[0]) < numsamples:
numsamples=len(igood[0])-1
good_models=self.mcmcsamples[igood]
#print 'igood is ',igood
#print 'good_models = ',good_models
#print 'numsamples = ',numsamples
irandoms=np.random.randint(len(good_models),size=numsamples)
#print 'len(irandoms) = ',len(irandoms)
#print 'irandoms = ',irandoms
for parameters in good_models[irandoms,:]:
#print 'Within for loop'
#print 'Parameters are',parameters
plt.loglog(self.rp,self.wp_hod(parameters),color='k',alpha=0.07)
plt.xlim(0.92*np.min(self.rp),1.05*np.max(self.rp))
plt.xticks(size=15)
plt.yticks(size=15)
plt.xlabel(r'$r_{\rm p}$ [$h^{-1}$Mpc]',fontsize=20)
plt.ylabel(r'$w_{\rm p}(r_{\rm p})$ [$h^{-1}$Mpc]',fontsize=20)
#plt.loglog(self.rp,self.wp,'sk')
plt.errorbar(self.rp,self.wp,yerr=self.wperr,fmt='s',color='firebrick',ecolor='firebrick')
filename=self.datafile
if filename.endswith('.dat'):
filename=filename[:-4]
filename=filename+'_chainsamples.pdf'
fig.savefig(filename,format='pdf',bbox_inches='tight')