def build_MCMC_cov_nbar_xi_gmf(Mr=21, b_normal=0.25):
''' Build covariance matrix used in MCMC for the full nbar, xi, gmf data vector
using realisations of galaxy mocks for "data" HOD parameters in the
halos from the other subvolumes (subvolume 1 to subvolume 125) of
the simulation. Covariance matrices for different sets of observables
can be extracted from the full covariance matrix by slicing through
the indices.
'''
nbars = []
xir = []
gmfs = []
thr = -1. * np.float(Mr)
model = PrebuiltHodModelFactory('zheng07', threshold=thr)
halocat = CachedHaloCatalog(simname='multidark',
redshift=0,
halo_finder='rockstar')
###model.new_haloprop_func_dict = {'sim_subvol': util.mk_id_column}
#some settings for tpcf calculations
rbins = xi_binedges()
rmax = rbins.max()
approx_cell1_size = [rmax, rmax, rmax]
approx_cellran_size = [rmax, rmax, rmax]
#load randoms and RRs
randoms = data_random(box='md_sub')
RR = data_RR(box='md_sub')
NR = len(randoms)
for i in xrange(1, 125):
print 'mock#', i
# populate the mock subvolume
###mocksubvol = lambda x: util.mask_func(x, i)
###model.populate_mock(halocat,
### masking_function=mocksubvol,
### enforce_PBC=False)
model.populate_mock(halocat)
# returning the positions of galaxies in the entire volume
pos = three_dim_pos_bundle(model.mock.galaxy_table, 'x', 'y', 'z')
# masking out the galaxies outside the subvolume i
pos = util.mask_galaxy_table(pos, i)
# calculate nbar
print "shape of pos", pos.shape
nbars.append(len(pos) / 200**3.)
# translate the positions of randoms to the new subbox
xi0, yi0, zi0 = util.random_shifter(i)
temp_randoms = randoms.copy()
temp_randoms[:, 0] += xi0
temp_randoms[:, 1] += yi0
temp_randoms[:, 2] += zi0
#calculate xi(r)
xi = tpcf(pos,
rbins,
pos,
randoms=temp_randoms,
period=None,
max_sample_size=int(3e5),
estimator='Natural',
approx_cell1_size=approx_cell1_size,
approx_cellran_size=approx_cellran_size,
RR_precomputed=RR,
NR_precomputed=NR)
xir.append(xi)
# calculate gmf
nbar = len(pos) / 200**3.
b = b_normal * (nbar)**(-1. / 3)
groups = pyfof.friends_of_friends(pos, b)
w = np.array([len(x) for x in groups])
gbins = gmf_bins()
gmf = np.histogram(w, gbins)[0] / 200.**3.
gmfs.append(gmf)
# save nbar variance
nbar_var = np.var(nbars, axis=0, ddof=1)
nbar_file = ''.join([util.obvs_dir(), 'nbar_var.Mr', str(Mr), '.dat'])
np.savetxt(nbar_file, [nbar_var])
# write full covariance matrix of various combinations of the data
# and invert for the likelihood evaluations
# --- covariance for all three ---
fulldatarr = np.hstack(
(np.array(nbars).reshape(len(nbars),
1), np.array(xir), np.array(gmfs)))
fullcov = np.cov(fulldatarr.T)
fullcorr = np.corrcoef(fulldatarr.T)
# and save the covariance matrix
nopoisson_file = ''.join([
util.obvs_dir(), 'MCMC.nbar_xi_gmf_cov', '.no_poisson', '.Mr',
str(Mr), '.bnorm',
str(round(b_normal, 2)), '.dat'
])
np.savetxt(nopoisson_file, fullcov)
return None
def build_nbar_xi_gmf(Mr=21, b_normal=0.25):
''' Build data vector [nbar, xi, gmf] and save to file
This data vector is built from the zeroth slice of the multidark
The other slices will be used for building the covariance matrix.
Parameters
----------
Mr : (int)
Absolute magnitude cut off M_r. Default M_r = -21.
b_normal : (float)
FoF Linking length
'''
thr = -1. * np.float(Mr)
model = PrebuiltHodModelFactory('zheng07', threshold=thr)
halocat = CachedHaloCatalog(simname='multidark',
redshift=0,
halo_finder='rockstar')
####model.new_haloprop_func_dict = {'sim_subvol': util.mk_id_column}
####datsubvol = lambda x: util.mask_func(x, 0)
####model.populate_mock(halocat, masking_function=datsubvol, enforce_PBC=False)
model.populate_mock(halocat)
#all the things necessary for tpcf calculation
pos = three_dim_pos_bundle(model.mock.galaxy_table, 'x', 'y', 'z')
#masking the galaxies outside the subvolume 0
pos = util.mask_galaxy_table(pos, 0)
rbins = xi_binedges()
rmax = rbins.max()
approx_cell1_size = [rmax, rmax, rmax]
approx_cellran_size = [rmax, rmax, rmax]
#compute number density
nbar = len(pos) / 200**3.
# load MD subvolume randoms and RRs
randoms = data_random(box='md_sub')
RR = data_RR(box='md_sub')
NR = len(randoms)
#compue tpcf with Natural estimator
data_xir = tpcf(pos,
rbins,
pos,
randoms=randoms,
period=None,
max_sample_size=int(2e5),
estimator='Natural',
approx_cell1_size=approx_cell1_size,
approx_cellran_size=approx_cellran_size,
RR_precomputed=RR,
NR_precomputed=NR)
fullvec = np.append(nbar, data_xir)
#compute gmf
b = b_normal * (nbar)**(-1. / 3)
groups = pyfof.friends_of_friends(pos, b)
w = np.array([len(x) for x in groups])
gbins = gmf_bins()
gmf = np.histogram(w, gbins)[0] / (200.**3.)
fullvec = np.append(fullvec, gmf)
output_file = data_file(Mr=Mr, b_normal=b_normal)
np.savetxt(output_file, fullvec)
return None
def _sum_stat(self, theta, prior_range=None, observables=['nbar', 'gmf']):
'''
Given theta, sum_stat calculates the observables from our forward model
Parameters
----------
theta : (self explanatory)
prior_range : If specified, checks to make sure that theta is within the prior range.
'''
self.model.param_dict['logM0'] = theta[0]
self.model.param_dict['sigma_logM'] = np.exp(theta[1])
self.model.param_dict['logMmin'] = theta[2]
self.model.param_dict['alpha'] = theta[3]
self.model.param_dict['logM1'] = theta[4]
rbins = xi_binedges()
rmax = rbins.max()
period = None
approx_cell1_size = [rmax, rmax, rmax]
approx_cellran_size = [rmax, rmax, rmax]
if prior_range is None:
rint = np.random.randint(1, 125)
####simsubvol = lambda x: util.mask_func(x, rint)
####self.model.populate_mock(self.halocat,
#### masking_function=simsubvol,
#### enforce_PBC=False)
self.model.populate_mock(self.halocat)
pos = three_dim_pos_bundle(self.model.mock.galaxy_table, 'x', 'y',
'z')
pos = util.mask_galaxy_table(pos, rint)
xi, yi, zi = util.random_shifter(rint)
temp_randoms = self.randoms.copy()
temp_randoms[:, 0] += xi
temp_randoms[:, 1] += yi
temp_randoms[:, 2] += zi
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(len(pos) /
200**3.) # nbar of the galaxy catalog
elif obv == 'gmf':
#compute group richness
nbar = len(pos) / 200**3.
b = self.b_normal * (nbar)**(-1. / 3)
groups = pyfof.friends_of_friends(pos, b)
w = np.array([len(x) for x in groups])
gbins = data_gmf_bins()
gmf = np.histogram(w, gbins)[0] / (200.**3.)
obvs.append(gmf)
elif obv == 'xi':
greek_xi = tpcf(pos,
rbins,
pos,
randoms=temp_randoms,
period=period,
max_sample_size=int(1e5),
estimator='Natural',
approx_cell1_size=approx_cell1_size,
approx_cellran_size=approx_cellran_size,
RR_precomputed=self.RR,
NR_precomputed=self.NR)
obvs.append(greek_xi)
else:
raise NotImplementedError(
'Only nbar 2pcf, gmf implemented so far')
return obvs
else:
if np.all((prior_range[:, 0] < theta)
& (theta < prior_range[:, 1])):
# if all theta_i is within prior range ...
try:
rint = np.random.randint(1, 125)
simsubvol = lambda x: util.mask_func(x, rint)
self.model.populate_mock(self.halocat,
masking_function=simsubvol,
enforce_PBC=False)
pos = three_dim_pos_bundle(self.model.mock.galaxy_table,
'x', 'y', 'z')
xi, yi, zi = util.random_shifter(rint)
temp_randoms = self.randoms.copy()
temp_randoms[:, 0] += xi
temp_randoms[:, 1] += yi
temp_randoms[:, 2] += zi
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(len(pos) /
200**3.) # nbar of the galaxy catalog
elif obv == 'gmf':
nbar = len(pos) / 200**3.
b = self.b_normal * (nbar)**(-1. / 3)
groups = pyfof.friends_of_friends(pos, b)
w = np.array([len(x) for x in groups])
gbins = data_gmf_bins()
gmf = np.histogram(w, gbins)[0] / (200.**3.)
obvs.append(gmf)
elif obv == 'xi':
greek_xi = tpcf(
pos,
rbins,
pos,
randoms=temp_randoms,
period=period,
max_sample_size=int(2e5),
estimator='Natural',
approx_cell1_size=approx_cell1_size,
approx_cellran_size=approx_cellran_size,
RR_precomputed=self.RR,
NR_precomputed=self.NR)
obvs.append(greek_xi)
else:
raise NotImplementedError(
'Only nbar, tpcf, and gmf are implemented so far'
)
return obvs
except ValueError:
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(10.)
elif obv == 'gmf':
bins = data_gmf_bins()
obvs.append(np.ones_like(bins)[:-1] * 1000.)
elif obv == 'xi':
obvs.append(np.zeros(len(xi_binedges()[:-1])))
return obvs
else:
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(10.)
elif obv == 'gmf':
bins = data_gmf_bins()
obvs.append(np.ones_like(bins)[:-1] * 1000.)
elif obv == 'xi':
obvs.append(np.zeros(len(xi_binedges()[:-1])))
return obvs
def build_MCMC_cov_nbar_xi_gmf(Mr=21, b_normal=0.25):
''' Build covariance matrix used in MCMC for the full nbar, xi, gmf data vector
using realisations of galaxy mocks for "data" HOD parameters in the
halos from the other subvolumes (subvolume 1 to subvolume 125) of
the simulation. Covariance matrices for different sets of observables
can be extracted from the full covariance matrix by slicing through
the indices.
'''
nbars = []
xir = []
gmfs = []
thr = -1. * np.float(Mr)
model = PrebuiltHodModelFactory('zheng07', threshold=thr)
halocat = CachedHaloCatalog(simname = 'multidark', redshift = 0, halo_finder = 'rockstar')
###model.new_haloprop_func_dict = {'sim_subvol': util.mk_id_column}
#some settings for tpcf calculations
rbins = xi_binedges()
rmax = rbins.max()
approx_cell1_size = [rmax , rmax , rmax]
approx_cellran_size = [rmax , rmax , rmax]
#load randoms and RRs
randoms = data_random(box='md_sub')
RR = data_RR(box='md_sub')
NR = len(randoms)
for i in xrange(1,125):
print 'mock#', i
# populate the mock subvolume
###mocksubvol = lambda x: util.mask_func(x, i)
###model.populate_mock(halocat,
### masking_function=mocksubvol,
### enforce_PBC=False)
model.populate_mock(halocat)
# returning the positions of galaxies in the entire volume
pos = three_dim_pos_bundle(model.mock.galaxy_table, 'x', 'y', 'z')
# masking out the galaxies outside the subvolume i
pos = util.mask_galaxy_table(pos , i)
# calculate nbar
print "shape of pos" , pos.shape
nbars.append(len(pos) / 200**3.)
# translate the positions of randoms to the new subbox
xi0 , yi0 , zi0 = util.random_shifter(i)
temp_randoms = randoms.copy()
temp_randoms[:,0] += xi0
temp_randoms[:,1] += yi0
temp_randoms[:,2] += zi0
#calculate xi(r)
xi=tpcf(
pos, rbins, pos,
randoms=temp_randoms, period=None,
max_sample_size=int(3e5), estimator='Natural',
approx_cell1_size=approx_cell1_size,
approx_cellran_size=approx_cellran_size,
RR_precomputed = RR,
NR_precomputed = NR)
xir.append(xi)
# calculate gmf
nbar = len(pos) / 200**3.
b = b_normal * (nbar)**(-1./3)
groups = pyfof.friends_of_friends(pos , b)
w = np.array([len(x) for x in groups])
gbins = gmf_bins()
gmf = np.histogram(w , gbins)[0] / 200.**3.
gmfs.append(gmf)
# save nbar variance
nbar_var = np.var(nbars, axis=0, ddof=1)
nbar_file = ''.join([util.obvs_dir(), 'nbar_var.Mr', str(Mr), '.dat'])
np.savetxt(nbar_file, [nbar_var])
# write full covariance matrix of various combinations of the data
# and invert for the likelihood evaluations
# --- covariance for all three ---
fulldatarr = np.hstack((np.array(nbars).reshape(len(nbars), 1),
np.array(xir),
np.array(gmfs)))
fullcov = np.cov(fulldatarr.T)
fullcorr = np.corrcoef(fulldatarr.T)
# and save the covariance matrix
nopoisson_file = ''.join([util.obvs_dir(),
'MCMC.nbar_xi_gmf_cov', '.no_poisson', '.Mr', str(Mr), '.bnorm', str(round(b_normal,2)), '.dat'])
np.savetxt(nopoisson_file, fullcov)
return None
def build_nbar_xi_gmf(Mr=21, b_normal=0.25):
''' Build data vector [nbar, xi, gmf] and save to file
This data vector is built from the zeroth slice of the multidark
The other slices will be used for building the covariance matrix.
Parameters
----------
Mr : (int)
Absolute magnitude cut off M_r. Default M_r = -21.
b_normal : (float)
FoF Linking length
'''
thr = -1. * np.float(Mr)
model = PrebuiltHodModelFactory('zheng07', threshold=thr)
halocat = CachedHaloCatalog(simname = 'multidark', redshift = 0, halo_finder = 'rockstar')
####model.new_haloprop_func_dict = {'sim_subvol': util.mk_id_column}
####datsubvol = lambda x: util.mask_func(x, 0)
####model.populate_mock(halocat, masking_function=datsubvol, enforce_PBC=False)
model.populate_mock(halocat)
#all the things necessary for tpcf calculation
pos = three_dim_pos_bundle(model.mock.galaxy_table, 'x', 'y', 'z')
#masking the galaxies outside the subvolume 0
pos = util.mask_galaxy_table(pos , 0)
rbins = xi_binedges()
rmax = rbins.max()
approx_cell1_size = [rmax , rmax , rmax]
approx_cellran_size = [rmax , rmax , rmax]
#compute number density
nbar = len(pos) / 200**3.
# load MD subvolume randoms and RRs
randoms = data_random(box='md_sub')
RR = data_RR(box='md_sub')
NR = len(randoms)
#compue tpcf with Natural estimator
data_xir = tpcf(
pos, rbins, pos,
randoms=randoms, period=None,
max_sample_size=int(2e5), estimator='Natural',
approx_cell1_size=approx_cell1_size,
approx_cellran_size=approx_cellran_size,
RR_precomputed=RR,
NR_precomputed=NR)
fullvec = np.append(nbar, data_xir)
#compute gmf
b = b_normal * (nbar)**(-1./3)
groups = pyfof.friends_of_friends(pos , b)
w = np.array([len(x) for x in groups])
gbins = gmf_bins()
gmf = np.histogram(w , gbins)[0] / (200.**3.)
fullvec = np.append(fullvec, gmf)
output_file = data_file(Mr=Mr, b_normal=b_normal)
np.savetxt(output_file, fullvec)
return None
def _sum_stat(self, theta, prior_range=None, observables=['nbar', 'gmf']):
'''
Given theta, sum_stat calculates the observables from our forward model
Parameters
----------
theta : (self explanatory)
prior_range : If specified, checks to make sure that theta is within the prior range.
'''
self.model.param_dict['logM0'] = theta[0]
self.model.param_dict['sigma_logM'] = np.exp(theta[1])
self.model.param_dict['logMmin'] = theta[2]
self.model.param_dict['alpha'] = theta[3]
self.model.param_dict['logM1'] = theta[4]
rbins = xi_binedges()
rmax = rbins.max()
period = None
approx_cell1_size = [rmax , rmax , rmax]
approx_cellran_size = [rmax , rmax , rmax]
if prior_range is None:
rint = np.random.randint(1, 125)
####simsubvol = lambda x: util.mask_func(x, rint)
####self.model.populate_mock(self.halocat,
#### masking_function=simsubvol,
#### enforce_PBC=False)
self.model.populate_mock(self.halocat)
pos =three_dim_pos_bundle(self.model.mock.galaxy_table, 'x', 'y', 'z')
pos = util.mask_galaxy_table(pos , rint)
xi , yi , zi = util.random_shifter(rint)
temp_randoms = self.randoms.copy()
temp_randoms[:,0] += xi
temp_randoms[:,1] += yi
temp_randoms[:,2] += zi
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(len(pos) / 200**3.) # nbar of the galaxy catalog
elif obv == 'gmf':
#compute group richness
nbar = len(pos) / 200**3.
b = self.b_normal * (nbar)**(-1./3)
groups = pyfof.friends_of_friends(pos , b)
w = np.array([len(x) for x in groups])
gbins = data_gmf_bins()
gmf = np.histogram(w , gbins)[0] / (200.**3.)
obvs.append(gmf)
elif obv == 'xi':
greek_xi = tpcf(
pos, rbins, pos,
randoms=temp_randoms, period = period,
max_sample_size=int(1e5), estimator='Natural',
approx_cell1_size=approx_cell1_size,
approx_cellran_size=approx_cellran_size,
RR_precomputed = self.RR,
NR_precomputed = self.NR)
obvs.append(greek_xi)
else:
raise NotImplementedError('Only nbar 2pcf, gmf implemented so far')
return obvs
else:
if np.all((prior_range[:,0] < theta) & (theta < prior_range[:,1])):
# if all theta_i is within prior range ...
try:
rint = np.random.randint(1, 125)
simsubvol = lambda x: util.mask_func(x, rint)
self.model.populate_mock(self.halocat,
masking_function=simsubvol,
enforce_PBC=False)
pos =three_dim_pos_bundle(self.model.mock.galaxy_table, 'x', 'y', 'z')
#imposing mask on the galaxy table
pos = util.mask_galaxy_table(pos , rint)
xi , yi , zi = util.random_shifter(rint)
temp_randoms = self.randoms.copy()
temp_randoms[:,0] += xi
temp_randoms[:,1] += yi
temp_randoms[:,2] += zi
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(len(pos) / 200**3.) # nbar of the galaxy catalog
elif obv == 'gmf':
nbar = len(pos) / 200**3.
b = self.b_normal * (nbar)**(-1./3)
groups = pyfof.friends_of_friends(pos , b)
w = np.array([len(x) for x in groups])
gbins =data_gmf_bins()
gmf = np.histogram(w , gbins)[0] / (200.**3.)
obvs.append(gmf)
elif obv == 'xi':
greek_xi = tpcf(
pos, rbins, pos,
randoms=temp_randoms, period = period,
max_sample_size=int(1e5), estimator='Natural',
approx_cell1_size=approx_cell1_size,
approx_cellran_size=approx_cellran_size,
RR_precomputed = self.RR,
NR_precomputed = self.NR)
obvs.append(greek_xi)
else:
raise NotImplementedError('Only nbar, tpcf, and gmf are implemented so far')
return obvs
except ValueError:
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(10.)
elif obv == 'gmf':
bins = data_gmf_bins()
obvs.append(np.ones_like(bins)[:-1]*1000.)
elif obv == 'xi':
obvs.append(np.zeros(len(xi_binedges()[:-1])))
return obvs
else:
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(10.)
elif obv == 'gmf':
bins = data_gmf_bins()
obvs.append(np.ones_like(bins)[:-1]*1000.)
elif obv == 'xi':
obvs.append(np.zeros(len(xi_binedges()[:-1])))
return obvs