def getObvs(observables, **data_dict):
''' Given the list of observable strings return data vector and
covariance matrices
'''
if observables == ['xi']:
fake_obs = Data.data_xi(**data_dict)
fake_obs_cov = Data.data_cov(inference='abc', **data_dict)[1:16 , 1:16]
xi_Cii = np.diag(fake_obs_cov)
Cii_list = [xi_Cii]
elif observables == ['nbar','xi']:
fake_obs = np.hstack([Data.data_nbar(**data_dict), Data.data_xi(**data_dict)])
fake_obs_cov = Data.data_cov(inference='abc', **data_dict)[:16 , :16]
Cii = np.diag(fake_obs_cov)
xi_Cii = Cii[1:]
nbar_Cii = Cii[0]
Cii_list = [nbar_Cii, xi_Cii]
elif observables == ['nbar','gmf']:
##### FIRST BIN OF GMF DROPPED ###############
# CAUTION: hardcoded
fake_obs = np.hstack([Data.data_nbar(**data_dict), Data.data_gmf(**data_dict)[1:]])
# CAUTION: Covariance matrix starts at 17 instead
fake_obs_cov = Data.data_cov(inference='abc', **data_dict)
Cii = np.diag(fake_obs_cov)
gmf_Cii = Cii[17:]
nbar_Cii = Cii[0]
Cii_list = [nbar_Cii, gmf_Cii]
return fake_obs, Cii_list
def xi(Mr=20, Nmock=500):
'''
Plot xi(r) of the fake observations
'''
prettyplot()
pretty_colors = prettycolors()
xir, cii = Data.data_xi(Mr=Mr, Nmock=Nmock)
rbin = Data.data_xi_bins(Mr=Mr)
fig = plt.figure(1)
sub = fig.add_subplot(111)
sub.plot(rbin, rbin*xir, c='k', lw=1)
sub.errorbar(rbin, rbin*xir, yerr = rbin*cii**0.5 , fmt="ok", ms=1, capsize=2, alpha=1.)
sub.set_xlim([0.1, 15])
sub.set_ylim([1, 10])
sub.set_yscale("log")
sub.set_xscale("log")
sub.set_xlabel(r'$\mathtt{r}\; (\mathtt{Mpc})$', fontsize=25)
sub.set_ylabel(r'$\mathtt{r} \xi_{\rm gg}$', fontsize=25)
fig_file = ''.join([util.fig_dir(),
'xi.Mr', str(Mr), '.Nmock', str(Nmock), '.png'])
fig.savefig(fig_file, bbox_inches='tight')
plt.close()
return None
def TrueObservables(Mr=21, b_normal=0.25):
''' Plot xi and gmf for the data
'''
# xi data
xi_data = Data.data_xi(Mr=Mr, b_normal=b_normal)
cov_data = Data.data_cov(Mr=Mr, b_normal=b_normal, inference='mcmc')
data_xi_cov = cov_data[1:16, 1:16]
xi_r_bin = Data.data_xi_bin(Mr=Mr)
# gmf data
data_gmf = Data.data_gmf(Mr=Mr, b_normal=b_normal)
cov_data = Data.data_cov(Mr=Mr, b_normal=b_normal, inference='mcmc')
data_gmf_cov = cov_data[16:, 16:]
r_binedge = Data.data_gmf_bins()
gmf_r_bin = 0.5 * (r_binedge[:-1] + r_binedge[1:])
prettyplot()
pretty_colors = prettycolors()
fig = plt.figure(figsize=(12, 6))
sub_xi = fig.add_subplot(121)
sub_gmf = fig.add_subplot(122)
#sub_xi.errorbar(xi_r_bin, xi_data, yerr = np.sqrt(np.diag(data_xi_cov)), fmt="o", color='k',
# markersize=0, lw=0, capsize=3, elinewidth=1.5)
#sub_xi.scatter(xi_r_bin, xi_data, c='k', s=10, lw=0)
sub_xi.fill_between(xi_r_bin,
xi_data - np.sqrt(np.diag(data_xi_cov)),
xi_data + np.sqrt(np.diag(data_xi_cov)),
color=pretty_colors[1])
sub_xi.set_yscale('log')
sub_xi.set_xscale('log')
sub_xi.set_xlim(0.1, 20)
sub_xi.set_xlabel(r'$\mathtt{r}\; [\mathtt{Mpc}/h]$', fontsize=25)
sub_xi.set_ylabel(r'$\xi(r)$', fontsize=25)
#sub_gmf.errorbar(gmf_r_bin, data_gmf, yerr=np.sqrt(np.diag(data_gmf_cov)),
# fmt="o", color='k',
# markersize=0, lw=0, capsize=4, elinewidth=2)
#sub_gmf.scatter(gmf_r_bin, data_gmf, s=15, lw=0, c='k', label='Mock Observation')
sub_gmf.fill_between(gmf_r_bin,
data_gmf - np.sqrt(np.diag(data_gmf_cov)),
data_gmf + np.sqrt(np.diag(data_gmf_cov)),
color=pretty_colors[1])
sub_gmf.set_xlim(1, 20)
sub_gmf.set_xlabel(r'$\mathtt{N}$ (Group Richness)', fontsize=25)
sub_gmf.yaxis.tick_right()
sub_gmf.yaxis.set_ticks_position('both')
sub_gmf.yaxis.set_label_position('right')
sub_gmf.set_ylim([10**-7, 2.0 * 10**-4])
sub_gmf.set_yscale('log')
sub_gmf.set_ylabel(r'$\zeta(\mathtt{N})$', fontsize=25)
fig.subplots_adjust(hspace=0.05)
fig_name = ''.join([ut.fig_dir(), 'paper.data_observables', '.pdf'])
fig.savefig(fig_name, bbox_inches='tight', dpi=150)
plt.close()
return None
def TrueObservables(Mr=21, b_normal=0.25):
''' Plot xi and gmf for the data
'''
# xi data
xi_data = Data.data_xi(Mr=Mr, b_normal=b_normal)
cov_data = Data.data_cov(Mr=Mr, b_normal=b_normal, inference='mcmc')
data_xi_cov = cov_data[1:16, 1:16]
xi_r_bin = Data.data_xi_bin(Mr=Mr)
# gmf data
data_gmf = Data.data_gmf(Mr=Mr, b_normal=b_normal)
cov_data = Data.data_cov(Mr=Mr, b_normal=b_normal, inference='mcmc')
data_gmf_cov = cov_data[16:, 16:]
r_binedge = Data.data_gmf_bins()
gmf_r_bin = 0.5 * (r_binedge[:-1] + r_binedge[1:])
prettyplot()
pretty_colors = prettycolors()
fig = plt.figure(figsize=(12,6))
sub_xi = fig.add_subplot(121)
sub_gmf = fig.add_subplot(122)
#sub_xi.errorbar(xi_r_bin, xi_data, yerr = np.sqrt(np.diag(data_xi_cov)), fmt="o", color='k',
# markersize=0, lw=0, capsize=3, elinewidth=1.5)
#sub_xi.scatter(xi_r_bin, xi_data, c='k', s=10, lw=0)
sub_xi.fill_between(xi_r_bin,
xi_data-np.sqrt(np.diag(data_xi_cov)), xi_data+np.sqrt(np.diag(data_xi_cov)),
color=pretty_colors[1])
sub_xi.set_yscale('log')
sub_xi.set_xscale('log')
sub_xi.set_xlim(0.1, 20)
sub_xi.set_xlabel(r'$\mathtt{r}\; [\mathtt{Mpc}/h]$', fontsize=25)
sub_xi.set_ylabel(r'$\xi(r)$', fontsize=25)
#sub_gmf.errorbar(gmf_r_bin, data_gmf, yerr=np.sqrt(np.diag(data_gmf_cov)),
# fmt="o", color='k',
# markersize=0, lw=0, capsize=4, elinewidth=2)
#sub_gmf.scatter(gmf_r_bin, data_gmf, s=15, lw=0, c='k', label='Mock Observation')
sub_gmf.fill_between(gmf_r_bin,
data_gmf-np.sqrt(np.diag(data_gmf_cov)), data_gmf+np.sqrt(np.diag(data_gmf_cov)),
color=pretty_colors[1])
sub_gmf.set_xlim(1, 20)
sub_gmf.set_xlabel(r'$\mathtt{N}$ (Group Richness)', fontsize=25)
sub_gmf.yaxis.tick_right()
sub_gmf.yaxis.set_ticks_position('both')
sub_gmf.yaxis.set_label_position('right')
sub_gmf.set_ylim([10**-7, 2.0*10**-4])
sub_gmf.set_yscale('log')
sub_gmf.set_ylabel(r'$\zeta(\mathtt{N})$', fontsize=25)
fig.subplots_adjust(hspace=0.05)
fig_name = ''.join([ut.fig_dir(),
'paper.data_observables',
'.pdf'])
fig.savefig(fig_name, bbox_inches='tight', dpi=150)
plt.close()
return None
def plot_data(Mr = 21 , output_dir = None):
'''
plot summary statistics of the data
'''
if output_dir is None:
fig_dir = util.fig_dir()
else:
fig_dir = output_dir
cov = Data.data_cov()
xi_err = np.sqrt(np.diag(cov)[1:16])
gmf_err = np.sqrt(np.diag(cov)[16:])
fig , axes = plt.subplots(1, 2, figsize=(10, 5))
fig.subplots_adjust(wspace=0.4, hspace=0.4)
ax = axes[0]
x = Data.xi_binedges()
y = Data.data_xi()
ax.errorbar(0.5*(x[:-1]+x[1:]), y, yerr=xi_err, fmt=".k", capsize=0)
ax.set_yscale('log')
ax.set_xscale('log')
ax.set_xlim(0.2, 22)
ax.set_xlabel(r'$r[\mathrm{Mpc}/h]$')
ax.set_ylabel(r'$\xi(r)$')
ax = axes[1]
x = Data.gmf_bins()
y = Data.data_gmf()
ax.errorbar(0.5*(x[:-1]+x[1:]), y, yerr=gmf_err, fmt=".k", capsize=0)
ax.set_xlim(1, 20)
ax.set_yscale('log')
ax.set_xlabel(r'Group Richness $N$')
ax.set_ylabel(r'$\zeta(N)$')
fig_file = ''.join([fig_dir, "data", '_Mr', str(Mr),'.pdf'])
plt.savefig(fig_file)
plt.close()
def plot_data(Mr=21, output_dir=None):
'''
plot summary statistics of the data
'''
if output_dir is None:
fig_dir = util.fig_dir()
else:
fig_dir = output_dir
cov = Data.data_cov()
xi_err = np.sqrt(np.diag(cov)[1:16])
gmf_err = np.sqrt(np.diag(cov)[16:])
fig, axes = plt.subplots(1, 2, figsize=(10, 5))
fig.subplots_adjust(wspace=0.4, hspace=0.4)
ax = axes[0]
x = Data.xi_binedges()
y = Data.data_xi()
ax.errorbar(0.5 * (x[:-1] + x[1:]), y, yerr=xi_err, fmt=".k", capsize=0)
ax.set_yscale('log')
ax.set_xscale('log')
ax.set_xlim(0.2, 22)
ax.set_xlabel(r'$r[\mathrm{Mpc}/h]$')
ax.set_ylabel(r'$\xi(r)$')
ax = axes[1]
x = Data.gmf_bins()
y = Data.data_gmf()
ax.errorbar(0.5 * (x[:-1] + x[1:]), y, yerr=gmf_err, fmt=".k", capsize=0)
ax.set_xlim(1, 20)
ax.set_yscale('log')
ax.set_xlabel(r'Group Richness $N$')
ax.set_ylabel(r'$\zeta(N)$')
fig_file = ''.join([fig_dir, "data", '_Mr', str(Mr), '.pdf'])
plt.savefig(fig_file)
plt.close()
def PosteriorObservable(Mr=21, b_normal=0.25, clobber=False):
''' Plot 1\sigma and 2\sigma model predictions from ABC-PMC posterior likelihood
'''
prettyplot()
pretty_colors = prettycolors()
fig = plt.figure(1, figsize=(16, 12))
gs = gridspec.GridSpec(2, 2, height_ratios=[2.5, 1], width_ratios=[1, 1])
for obvs in ['nbargmf', 'nbarxi']:
if obvs == 'nbargmf':
result_dir = ''.join([
ut.dat_dir(),
'paper/ABC',
obvs,
'/run1/',
])
theta_file = lambda tt: ''.join(
[result_dir, 'nbar_gmf_theta_t',
str(tt), '.ABCnbargmf.dat'])
tf = 8
obvs_list = ['gmf']
elif obvs == 'nbarxi':
result_dir = ''.join([ut.dat_dir(), 'paper/ABC', obvs, '/'])
theta_file = lambda tt: ''.join(
[result_dir, 'nbar_xi_theta_t',
str(tt), '.abc.dat'])
tf = 9
obvs_list = ['xi']
else:
raise ValueError
theta = np.loadtxt(theta_file(tf)) # import thetas
#theta = theta[:10]
obvs_file = ''.join(
theta_file(tf).rsplit('.dat')[:-1] + ['.', obvs_list[0], '.p'])
print obvs_file
HODsimulator = ABC_HODsim(Mr=Mr, b_normal=b_normal)
if not os.path.isfile(obvs_file) or clobber:
model_obv = []
for i in xrange(len(theta)):
print i
obv_i = HODsimulator(theta[i],
prior_range=None,
observables=obvs_list)
model_obv.append(obv_i[0])
model_obv = np.array(model_obv)
pickle.dump(model_obv, open(obvs_file, 'wb'))
else:
model_obv = pickle.load(open(obvs_file, 'rb'))
if 'xi' in obvs:
r_bin = Data.data_xi_bin(Mr=Mr)
elif 'gmf' in obvs:
r_binedge = Data.data_gmf_bins()
r_bin = 0.5 * (r_binedge[:-1] + r_binedge[1:])
a, b, c, d, e = np.percentile(model_obv, [2.5, 16, 50, 84, 97.5],
axis=0)
# plotting
if obvs == 'nbarxi':
ax = plt.subplot(gs[0])
elif obvs == 'nbargmf':
ax = plt.subplot(gs[1])
if 'xi' in obvs: # 2PCF
xi_data = Data.data_xi(Mr=Mr, b_normal=b_normal)
cov_data = Data.data_cov(Mr=Mr,
b_normal=b_normal,
inference='mcmc')
data_xi_cov = cov_data[1:16, 1:16]
ax.fill_between(r_bin,
a,
e,
color=pretty_colors[3],
alpha=0.3,
edgecolor="none")
ax.fill_between(r_bin,
b,
d,
color=pretty_colors[3],
alpha=0.5,
edgecolor="none")
ax.errorbar(r_bin,
xi_data,
yerr=np.sqrt(np.diag(data_xi_cov)),
fmt="o",
color='k',
markersize=0,
lw=0,
capsize=3,
elinewidth=1.5)
ax.scatter(r_bin, xi_data, c='k', s=10, lw=0)
ax.set_ylabel(r'$\xi_\mathtt{gg}(\mathtt{r})$', fontsize=27)
ax.set_yscale('log')
ax.set_xscale('log')
ax.set_xticklabels([])
ax.set_xlim([0.1, 20.])
ax.set_ylim([0.09, 1000.])
ax = plt.subplot(gs[2])
ax.fill_between(r_bin,
a / xi_data,
e / xi_data,
color=pretty_colors[3],
alpha=0.3,
edgecolor="none")
ax.fill_between(r_bin,
b / xi_data,
d / xi_data,
color=pretty_colors[3],
alpha=0.5,
edgecolor="none")
ax.errorbar(r_bin,
np.repeat(1., len(xi_data)),
yerr=np.sqrt(np.diag(data_xi_cov)) / xi_data,
fmt="o",
color='k',
markersize=0,
lw=0,
capsize=3,
elinewidth=1.5)
ax.plot(np.arange(0.1, 20., 0.1),
np.repeat(1., len(np.arange(0.1, 20, 0.1))),
c='k',
ls='--',
lw=2)
ax.set_xlim([0.1, 20.])
ax.set_xscale('log')
ax.set_ylim([0.5, 1.5])
ax.set_xlabel(r'$\mathtt{r}\;[\mathtt{Mpc}/h]$', fontsize=25)
ax.set_ylabel(r'$\xi_\mathtt{gg}/\xi_\mathtt{gg}^\mathtt{obvs}$',
fontsize=25)
elif 'gmf' in obvs: # GMF
data_gmf = Data.data_gmf(Mr=Mr, b_normal=b_normal)
cov_data = Data.data_cov(Mr=Mr,
b_normal=b_normal,
inference='mcmc')
data_gmf_cov = cov_data[16:, 16:]
ax.fill_between(r_bin,
a,
e,
color=pretty_colors[3],
alpha=0.3,
edgecolor="none")
ax.fill_between(r_bin,
b,
d,
color=pretty_colors[3],
alpha=0.5,
edgecolor="none",
label='ABC Posterior')
ax.errorbar(r_bin,
data_gmf,
yerr=np.sqrt(np.diag(data_gmf_cov)),
fmt="o",
color='k',
markersize=0,
lw=0,
capsize=4,
elinewidth=2)
ax.scatter(r_bin,
data_gmf,
s=15,
lw=0,
c='k',
label='Mock Observation')
ax.legend(loc='upper right',
scatterpoints=1,
prop={'size': 25},
borderpad=1.0)
ax.yaxis.tick_right()
ax.yaxis.set_ticks_position('both')
ax.yaxis.set_label_position('right')
ax.set_ylabel(r'$\zeta$ $[(\mathrm{h}/\mathtt{Mpc})^{3}]$',
fontsize=25)
ax.set_yscale('log')
ax.set_xlim([1., 20.])
ax.set_xticklabels([])
ax.set_ylim([10.**-7.2, 2 * 10**-4.])
ax = plt.subplot(gs[3])
ax.fill_between(r_bin,
a / data_gmf,
e / data_gmf,
color=pretty_colors[3],
alpha=0.3,
edgecolor="none")
ax.fill_between(r_bin,
b / data_gmf,
d / data_gmf,
color=pretty_colors[3],
alpha=0.5,
edgecolor="none")
ax.errorbar(r_bin,
np.repeat(1., len(data_gmf)),
yerr=np.sqrt(np.diag(data_gmf_cov)) / data_gmf,
fmt="o",
color='k',
markersize=0,
lw=0,
capsize=3,
elinewidth=1.5)
ax.plot(np.arange(1., 20., 1),
np.repeat(1., len(np.arange(1., 20, 1))),
c='k',
ls='--',
lw=1.75)
ax.yaxis.tick_right()
ax.yaxis.set_label_position('right')
ax.set_ylim([-0.1, 2.1])
ax.set_ylabel(r'$\zeta/\zeta^\mathtt{obvs}$', fontsize=25)
ax.set_xlim([1., 20.])
ax.set_xlabel(r'$\mathtt{N}$ [Group Richness]', fontsize=25)
fig.subplots_adjust(wspace=0.05, hspace=0.0)
fig_name = ''.join([ut.fig_dir(), 'paper', '.ABCposterior', '.pdf'])
fig.savefig(fig_name, bbox_inches='tight')
plt.close()
return None
def mcmc_mpi(Nwalkers,
Nchains,
observables=['nbar', 'xi'],
data_dict={
'Mr': 21,
'b_normal': 0.25
},
prior_name='first_try',
mcmcrun=None):
'''
Standard MCMC implementaion
Parameters
-----------
- Nwalker :
Number of walkers
- Nchains :
Number of MCMC chains
- observables :
list of observables. Options are: ['nbar','xi'],['nbar','gmf'],['xi']
- data_dict : dictionary that specifies the observation keywords
'''
#Initializing the vector of observables and inverse covariance matrix
if observables == ['xi']:
fake_obs = Data.data_xi(**data_dict)
#fake_obs_icov = Data.data_inv_cov('xi', **data_dict)
fake_obs_icov = Data.data_cov(inference='mcmc', **data_dict)[1:16,
1:16]
if observables == ['nbar', 'xi']:
fake_obs = np.hstack(
[Data.data_nbar(**data_dict),
Data.data_xi(**data_dict)])
fake_obs_icov = Data.data_cov(inference='mcmc', **data_dict)[:16, :16]
if observables == ['nbar', 'gmf']:
##### FIRST BIN OF GMF DROPPED ###############
# CAUTION: hardcoded
fake_obs = np.hstack(
[Data.data_nbar(**data_dict),
Data.data_gmf(**data_dict)[1:]])
fake_obs_icov = np.zeros((10, 10))
#print Data.data_cov(**data_dict)[17: , 17:].shape
# Covariance matrix being adjusted accordingly
fake_obs_icov[1:, 1:] = Data.data_cov(inference='mcmc',
**data_dict)[17:, 17:]
fake_obs_icov[0, 1:] = Data.data_cov(inference='mcmc',
**data_dict)[0, 17:]
fake_obs_icov[1:, 0] = Data.data_cov(inference='mcmc',
**data_dict)[17:, 0]
fake_obs_icov[0, 0] = Data.data_cov(inference='mcmc', **data_dict)[0,
0]
# True HOD parameters
data_hod_dict = Data.data_hod_param(Mr=data_dict['Mr'])
data_hod = np.array([
data_hod_dict['logM0'], # log M0
np.log(data_hod_dict['sigma_logM']), # log(sigma)
data_hod_dict['logMmin'], # log Mmin
data_hod_dict['alpha'], # alpha
data_hod_dict['logM1'] # log M1
])
Ndim = len(data_hod)
# Priors
prior_min, prior_max = PriorRange(prior_name)
prior_range = np.zeros((len(prior_min), 2))
prior_range[:, 0] = prior_min
prior_range[:, 1] = prior_max
# mcmc chain output file
chain_file = ''.join([
util.mcmc_dir(),
util.observable_id_flag(observables), '.', mcmcrun, '.mcmc_chain.dat'
])
#print chain_file
if os.path.isfile(chain_file) and continue_chain:
print 'Continuing previous MCMC chain!'
sample = np.loadtxt(chain_file)
Nchain = Niter - (len(sample) / Nwalkers
) # Number of chains left to finish
if Nchain > 0:
pass
else:
raise ValueError
print Nchain, ' iterations left to finish'
# Initializing Walkers from the end of the chain
pos0 = sample[-Nwalkers:]
else:
# new chain
f = open(chain_file, 'w')
f.close()
Nchain = Niter
# Initializing Walkers
random_guess = data_hod
pos0 = np.repeat(random_guess, Nwalkers).reshape(Ndim, Nwalkers).T + \
5.e-2 * np.random.randn(Ndim * Nwalkers).reshape(Nwalkers, Ndim)
#print pos0.shape
# Initializing MPIPool
pool = MPIPool()
if not pool.is_master():
pool.wait()
sys.exit(0)
# Initializing the emcee sampler
hod_kwargs = {
'prior_range': prior_range,
'data': fake_obs,
'data_icov': fake_obs_icov,
'observables': observables,
'Mr': data_dict['Mr']
}
sampler = emcee.EnsembleSampler(Nwalkers,
Ndim,
lnPost,
pool=pool,
kwargs=hod_kwargs)
# Initializing Walkers
for result in sampler.sample(pos0, iterations=Nchain, storechain=False):
position = result[0]
#print position
f = open(chain_file, 'a')
for k in range(position.shape[0]):
output_str = '\t'.join(position[k].astype('str')) + '\n'
f.write(output_str)
f.close()
pool.close()
def mcmc_mpi(
Nwalkers,
Nchains,
observables=["nbar", "xi"],
data_dict={"Mr": 21, "b_normal": 0.25},
prior_name="first_try",
mcmcrun=None,
):
"""
Standard MCMC implementaion
Parameters
-----------
- Nwalker :
Number of walkers
- Nchains :
Number of MCMC chains
- observables :
list of observables. Options are: ['nbar','xi'],['nbar','gmf'],['xi']
- data_dict : dictionary that specifies the observation keywords
"""
# Initializing the vector of observables and inverse covariance matrix
if observables == ["xi"]:
fake_obs = Data.data_xi(**data_dict)
# fake_obs_icov = Data.data_inv_cov('xi', **data_dict)
fake_obs_icov = Data.data_cov(inference="mcmc", **data_dict)[1:16, 1:16]
if observables == ["nbar", "xi"]:
fake_obs = np.hstack([Data.data_nbar(**data_dict), Data.data_xi(**data_dict)])
fake_obs_icov = Data.data_cov(inference="mcmc", **data_dict)[:16, :16]
if observables == ["nbar", "gmf"]:
##### FIRST BIN OF GMF DROPPED ###############
# CAUTION: hardcoded
fake_obs = np.hstack([Data.data_nbar(**data_dict), Data.data_gmf(**data_dict)[1:]])
fake_obs_icov = np.zeros((10, 10))
# print Data.data_cov(**data_dict)[17: , 17:].shape
# Covariance matrix being adjusted accordingly
fake_obs_icov[1:, 1:] = Data.data_cov(inference="mcmc", **data_dict)[17:, 17:]
fake_obs_icov[0, 1:] = Data.data_cov(inference="mcmc", **data_dict)[0, 17:]
fake_obs_icov[1:, 0] = Data.data_cov(inference="mcmc", **data_dict)[17:, 0]
fake_obs_icov[0, 0] = Data.data_cov(inference="mcmc", **data_dict)[0, 0]
# True HOD parameters
data_hod_dict = Data.data_hod_param(Mr=data_dict["Mr"])
data_hod = np.array(
[
data_hod_dict["logM0"], # log M0
np.log(data_hod_dict["sigma_logM"]), # log(sigma)
data_hod_dict["logMmin"], # log Mmin
data_hod_dict["alpha"], # alpha
data_hod_dict["logM1"], # log M1
]
)
Ndim = len(data_hod)
# Priors
prior_min, prior_max = PriorRange(prior_name)
prior_range = np.zeros((len(prior_min), 2))
prior_range[:, 0] = prior_min
prior_range[:, 1] = prior_max
# mcmc chain output file
chain_file = "".join([util.mcmc_dir(), util.observable_id_flag(observables), ".", mcmcrun, ".mcmc_chain.dat"])
# print chain_file
if os.path.isfile(chain_file) and continue_chain:
print "Continuing previous MCMC chain!"
sample = np.loadtxt(chain_file)
Nchain = Niter - (len(sample) / Nwalkers) # Number of chains left to finish
if Nchain > 0:
pass
else:
raise ValueError
print Nchain, " iterations left to finish"
# Initializing Walkers from the end of the chain
pos0 = sample[-Nwalkers:]
else:
# new chain
f = open(chain_file, "w")
f.close()
Nchain = Niter
# Initializing Walkers
random_guess = data_hod
pos0 = np.repeat(random_guess, Nwalkers).reshape(Ndim, Nwalkers).T + 5.0e-2 * np.random.randn(
Ndim * Nwalkers
).reshape(Nwalkers, Ndim)
# print pos0.shape
# Initializing MPIPool
pool = MPIPool()
if not pool.is_master():
pool.wait()
sys.exit(0)
# Initializing the emcee sampler
hod_kwargs = {
"prior_range": prior_range,
"data": fake_obs,
"data_icov": fake_obs_icov,
"observables": observables,
"Mr": data_dict["Mr"],
}
sampler = emcee.EnsembleSampler(Nwalkers, Ndim, lnPost, pool=pool, kwargs=hod_kwargs)
# Initializing Walkers
for result in sampler.sample(pos0, iterations=Nchain, storechain=False):
position = result[0]
# print position
f = open(chain_file, "a")
for k in range(position.shape[0]):
output_str = "\t".join(position[k].astype("str")) + "\n"
f.write(output_str)
f.close()
pool.close()
def PosteriorObservable(Mr=21, b_normal=0.25, clobber=False):
''' Plot 1\sigma and 2\sigma model predictions from ABC-PMC posterior likelihood
'''
prettyplot()
pretty_colors=prettycolors()
fig = plt.figure(1, figsize=(16,12))
gs = gridspec.GridSpec(2, 2, height_ratios=[2.5, 1], width_ratios=[1,1])
for obvs in ['nbargmf', 'nbarxi']:
if obvs == 'nbargmf':
result_dir = ''.join([ut.dat_dir(), 'paper/ABC', obvs, '/run1/',])
theta_file = lambda tt: ''.join([result_dir, 'nbar_gmf_theta_t', str(tt), '.ABCnbargmf.dat'])
tf = 8
obvs_list = ['gmf']
elif obvs == 'nbarxi':
result_dir = ''.join([ut.dat_dir(), 'paper/ABC', obvs, '/'])
theta_file = lambda tt: ''.join([result_dir, 'nbar_xi_theta_t', str(tt), '.abc.dat'])
tf = 9
obvs_list = ['xi']
else:
raise ValueError
theta = np.loadtxt(theta_file(tf)) # import thetas
#theta = theta[:10]
obvs_file = ''.join(theta_file(tf).rsplit('.dat')[:-1] + ['.', obvs_list[0], '.p'])
print obvs_file
HODsimulator = ABC_HODsim(Mr=Mr, b_normal=b_normal)
if not os.path.isfile(obvs_file) or clobber:
model_obv = []
for i in xrange(len(theta)):
print i
obv_i = HODsimulator(
theta[i],
prior_range=None,
observables=obvs_list)
model_obv.append(obv_i[0])
model_obv = np.array(model_obv)
pickle.dump(model_obv, open(obvs_file, 'wb'))
else:
model_obv = pickle.load(open(obvs_file, 'rb'))
if 'xi' in obvs:
r_bin = Data.data_xi_bin(Mr=Mr)
elif 'gmf' in obvs:
r_binedge = Data.data_gmf_bins()
r_bin = 0.5 * (r_binedge[:-1] + r_binedge[1:])
a, b, c, d, e = np.percentile(model_obv, [2.5, 16, 50, 84, 97.5], axis=0)
# plotting
if obvs == 'nbarxi':
ax = plt.subplot(gs[0])
elif obvs == 'nbargmf':
ax = plt.subplot(gs[1])
if 'xi' in obvs: # 2PCF
xi_data = Data.data_xi(Mr=Mr, b_normal=b_normal)
cov_data = Data.data_cov(Mr=Mr, b_normal=b_normal, inference='mcmc')
data_xi_cov = cov_data[1:16, 1:16]
ax.fill_between(r_bin, a, e, color=pretty_colors[3], alpha=0.3, edgecolor="none")
ax.fill_between(r_bin, b, d, color=pretty_colors[3], alpha=0.5, edgecolor="none")
ax.errorbar(r_bin, xi_data, yerr = np.sqrt(np.diag(data_xi_cov)), fmt="o", color='k',
markersize=0, lw=0, capsize=3, elinewidth=1.5)
ax.scatter(r_bin, xi_data, c='k', s=10, lw=0)
ax.set_ylabel(r'$\xi_\mathtt{gg}(\mathtt{r})$', fontsize=27)
ax.set_yscale('log')
ax.set_xscale('log')
ax.set_xticklabels([])
ax.set_xlim([0.1, 20.])
ax.set_ylim([0.09, 1000.])
ax = plt.subplot(gs[2])
ax.fill_between(r_bin, a/xi_data, e/xi_data, color=pretty_colors[3], alpha=0.3, edgecolor="none")
ax.fill_between(r_bin, b/xi_data, d/xi_data, color=pretty_colors[3], alpha=0.5, edgecolor="none")
ax.errorbar(r_bin, np.repeat(1., len(xi_data)), yerr=np.sqrt(np.diag(data_xi_cov))/xi_data,
fmt="o", color='k', markersize=0, lw=0, capsize=3, elinewidth=1.5)
ax.plot(np.arange(0.1, 20., 0.1), np.repeat(1., len(np.arange(0.1, 20, 0.1))), c='k', ls='--', lw=2)
ax.set_xlim([0.1, 20.])
ax.set_xscale('log')
ax.set_ylim([0.5, 1.5])
ax.set_xlabel(r'$\mathtt{r}\;[\mathtt{Mpc}/h]$', fontsize=25)
ax.set_ylabel(r'$\xi_\mathtt{gg}/\xi_\mathtt{gg}^\mathtt{obvs}$', fontsize=25)
elif 'gmf' in obvs: # GMF
data_gmf = Data.data_gmf(Mr=Mr, b_normal=b_normal)
cov_data = Data.data_cov(Mr=Mr, b_normal=b_normal, inference='mcmc')
data_gmf_cov = cov_data[16:, 16:]
ax.fill_between(r_bin, a, e, color=pretty_colors[3], alpha=0.3, edgecolor="none")
ax.fill_between(r_bin, b, d, color=pretty_colors[3], alpha=0.5, edgecolor="none", label='ABC Posterior')
ax.errorbar(r_bin, data_gmf, yerr=np.sqrt(np.diag(data_gmf_cov)), fmt="o", color='k',
markersize=0, lw=0, capsize=4, elinewidth=2)
ax.scatter(r_bin, data_gmf, s=15, lw=0, c='k', label='Mock Observation')
ax.legend(loc='upper right', scatterpoints=1, prop={'size': 25}, borderpad=1.0)
ax.yaxis.tick_right()
ax.yaxis.set_ticks_position('both')
ax.yaxis.set_label_position('right')
ax.set_ylabel(r'$\zeta$ $[(\mathrm{h}/\mathtt{Mpc})^{3}]$', fontsize=25)
ax.set_yscale('log')
ax.set_xlim([1., 20.])
ax.set_xticklabels([])
ax.set_ylim([10.**-7.2, 2*10**-4.])
ax = plt.subplot(gs[3])
ax.fill_between(r_bin, a/data_gmf, e/data_gmf, color=pretty_colors[3], alpha=0.3, edgecolor="none")
ax.fill_between(r_bin, b/data_gmf, d/data_gmf, color=pretty_colors[3], alpha=0.5, edgecolor="none")
ax.errorbar(r_bin, np.repeat(1., len(data_gmf)), yerr=np.sqrt(np.diag(data_gmf_cov))/data_gmf,
fmt="o", color='k', markersize=0, lw=0, capsize=3, elinewidth=1.5)
ax.plot(np.arange(1., 20., 1), np.repeat(1., len(np.arange(1., 20, 1))), c='k', ls='--', lw=1.75)
ax.yaxis.tick_right()
ax.yaxis.set_label_position('right')
ax.set_ylim([-0.1, 2.1])
ax.set_ylabel(r'$\zeta/\zeta^\mathtt{obvs}$', fontsize=25)
ax.set_xlim([1., 20.])
ax.set_xlabel(r'$\mathtt{N}$ [Group Richness]', fontsize=25)
fig.subplots_adjust(wspace=0.05, hspace=0.0)
fig_name = ''.join([ut.fig_dir(),
'paper',
'.ABCposterior',
'.pdf'])
fig.savefig(fig_name, bbox_inches='tight')
plt.close()
return None