def gmf(Mr=20, Nmock=500):
'''
Plot Group Multiplicty Function of fake observations
'''
prettyplot()
pretty_colors = prettycolors()
# import fake obs GMF
gmf, sig_gmf = Data.data_gmf(Mr=Mr, Nmock=Nmock)
# group richness bins
gmf_bin = Data.data_gmf_bins()
fig = plt.figure(1)
sub = fig.add_subplot(111)
sub.errorbar(
0.5*(gmf_bin[:-1]+gmf_bin[1:]), gmf, yerr=sig_gmf,
fmt="ok", capsize=1.0
)
sub.set_xlim([1, 60])
sub.set_yscale('log')
sub.set_ylabel(r"Group Multiplicity Function (h$^{3}$ Mpc$^{-3}$)", fontsize=20)
sub.set_xlabel(r"$\mathtt{Group\;\;Richness}$", fontsize=20)
# save to file
fig_file = ''.join([util.fig_dir(),
'gmf.Mr', str(Mr), '.Nmock', str(Nmock), '.png'])
fig.savefig(fig_file, bbox_inches='tight')
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 PlotCovariance(obvs, Mr=21, b_normal=0.25, inference='mcmc'):
''' Plot the covariance matrix for a specified obvs
'''
# import the covariance matrix
covar = Data.data_cov(Mr=Mr, b_normal=b_normal, inference=inference)
if obvs == 'xi':
obvs_cov = covar[1:16 , 1:16]
r_bin = Data.xi_binedges()
elif obvs == 'gmf':
obvs_cov = covar[17:, 17:]
binedges = Data.data_gmf_bins()
r_bin = 0.5 * (binedges[:-1] + binedges[1:])
n_bin = int(np.sqrt(obvs_cov.size))
# calculate the reduced covariance for plotting
red_covar = np.zeros([n_bin, n_bin])
for ii in range(n_bin):
for jj in range(n_bin):
red_covar[ii][jj] = obvs_cov[ii][jj]/np.sqrt(obvs_cov[ii][ii] * obvs_cov[jj][jj])
prettyplot()
fig = plt.figure()
sub = fig.add_subplot(111)
cont = sub.pcolormesh(r_bin, r_bin, red_covar, cmap=plt.cm.afmhot_r)
plt.colorbar(cont)
sub.set_xlim([r_bin[0], r_bin[-1]])
sub.set_ylim([r_bin[0], r_bin[-1]])
sub.set_xscale('log')
sub.set_yscale('log')
sub.set_xlabel(r'$\mathtt{r}\;[\mathtt{Mpc/h}$]', fontsize=25)
sub.set_ylabel(r'$\mathtt{r}\;[\mathtt{Mpc/h}$]', fontsize=25)
fig_file = ''.join([util.fig_dir(),
obvs.upper(), 'covariance',
'.Mr', str(Mr),
'.bnorm', str(round(b_normal,2)),
'.', inference, '_inf.png'])
fig.savefig(fig_file, bbox_inches='tight')
plt.close()
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()
approx_cell1_size = [rmax, rmax, rmax]
approx_cellran_size = [rmax, rmax, rmax]
if prior_range is None:
self.model.populate_mock(self.halocat, enforce_PBC=False)
pos = three_dim_pos_bundle(self.model.mock.galaxy_table, 'x', 'y',
'z')
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(len(pos) /
1000.**3.) # nbar of the galaxy catalog
elif obv == 'gmf':
nbar = len(pos) / 1000**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] / (1000.**3.)
obvs.append(gmf)
elif obv == 'xi':
greek_xi = tpcf(pos,
rbins,
pos,
randoms=randoms,
period=None,
max_sample_size=int(3e5),
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:
self.model.populate_mock(self.halocat)
pos = three_dim_pos_bundle(self.model.mock.galaxy_table,
'x', 'y', 'z')
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(len(pos) /
1000**3.) # nbar of the galaxy catalog
elif obv == 'gmf':
nbar = len(pos) / 1000**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] / (1000.**3.)
obvs.append(gmf)
elif obv == 'xi':
greek_xi = tpcf(
pos,
rbins,
pos,
randoms=randoms,
period=None,
max_sample_size=int(3e5),
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 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 plot_posterior_model(observable, abc_theta_file=None, data_dict={'Mr':20, 'b_normal': 0.25, 'Nmock':500},
clobber=False):
'''
Plot 1\sigma and 2\sigma model predictions from ABC-PMC posterior likelihood
Parameters
----------
observable : string
One of the following strings ['xi', 'scaledxi', 'gmf']
'''
# load the particles
if abc_theta_file is None:
raise ValueError("Please specify the theta output file from ABC-PMC run")
theta = np.loadtxt(abc_theta_file)
if observable == 'scaledxi':
obvs_str = 'xi'
else:
obvs_str = observable
obvs_file = ''.join(abc_theta_file.rsplit('.dat')[:-1] + ['.', observable, '.dat'])
print obvs_file
if not os.path.isfile(obvs_file) or clobber:
for i in xrange(len(theta)):
obv_i = HODsimulator(
theta[i], prior_range=None,
observables=[obvs_str], Mr=data_dict['Mr'])
try:
model_obv.append(obv_i[0])
except UnboundLocalError:
model_obv = [obv_i[0]]
model_obv = np.array(model_obv)
np.savetxt(obvs_file, model_obv)
else:
model_obv = np.loadtxt(obvs_file)
if 'xi' in observable:
r_bin = Data.data_xi_bins(Mr=data_dict['Mr'])
elif observable == 'gmf':
r_bin = Data.data_gmf_bins()
a, b, c, d, e = np.percentile(model_obv, [2.5, 16, 50, 84, 97.5], axis=0)
# plotting
fig = plt.figure(1)
ax = fig.add_subplot(111)
if observable == 'xi': # 2PCF
data_xi, data_xi_cov = Data.data_xi_full_cov(**data_dict) # data
ax.fill_between(r_bin, a, e, color="k", alpha=0.1, edgecolor="none")
ax.fill_between(r_bin, b, d, color="k", alpha=0.3, edgecolor="none")
#ax.plot(r_bin, c, "k", lw=1)
ax.errorbar(r_bin, data_xi, yerr = np.sqrt(np.diag(data_xi_cov)), fmt=".k",
capsize=0)
ax.set_xlabel(r'$r\;[\mathrm{Mpc}/h]$', fontsize=20)
ax.set_ylabel(r'$\xi_{\rm gg}$', fontsize=25)
ax.set_xscale('log')
ax.set_xlim([0.1, 20.])
elif observable == 'scaledxi': # Scaled 2PFC (r * xi)
data_xi, data_xi_cov = Data.data_xi_full_cov(**data_dict) # data
ax.fill_between(r_bin, r_bin*a, r_bin*e, color="k", alpha=0.1, edgecolor="none")
ax.fill_between(r_bin, r_bin*b, r_bin*d, color="k", alpha=0.3, edgecolor="none")
ax.errorbar(r_bin, r_bin*data_xi, yerr=r_bin*np.sqrt(np.diag(data_xi_cov)), fmt=".k",
capsize=0)
ax.set_xlabel(r'$r\;[\mathrm{Mpc}/h]$', fontsize=20)
ax.set_ylabel(r'$r \xi_{\rm gg}$', fontsize=25)
ax.set_xscale('log')
ax.set_xlim([0.1, 20.])
elif observable == 'gmf': # GMF
data_gmf, data_gmf_sigma = Data.data_gmf(**data_dict)
ax.fill_between(r_bin, a, e, color="k", alpha=0.1, edgecolor="none")
ax.fill_between(r_bin, b, d, color="k", alpha=0.3, edgecolor="none")
ax.errorbar(r_bin, data_gmf, yerr = data_gmf_sigma, fmt=".k",
capsize=0)
ax.set_xlabel(r'Group Richness', fontsize=25)
ax.set_ylabel(r'GMF $[\mathrm{h}^3\mathrm{Mpc}^{-3}]$', fontsize=25)
ax.set_yscale('log')
ax.set_xlim([1., 50.])
fig.savefig(
''.join([util.fig_dir(),
observable, '.posterior_prediction',
'.Mr', str(data_dict['Mr']), '_Nmock', str(data_dict['Nmock']),
'.pdf']),
bbox_inches='tight')
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()
approx_cell1_size = [rmax , rmax , rmax]
approx_cellran_size = [rmax , rmax , rmax]
if prior_range is None:
self.model.populate_mock(self.halocat)
pos =three_dim_pos_bundle(self.model.mock.galaxy_table, 'x', 'y', 'z')
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(len(pos) / 1000.**3.) # nbar of the galaxy catalog
elif obv == 'gmf':
nbar = len(pos) / 1000**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] / (1000.**3.)
obvs.append(gmf)
elif obv == 'xi':
greek_xi = tpcf(
pos, rbins,
period=self.model.mock.Lbox,
max_sample_size=int(3e5), estimator='Natural',
approx_cell1_size=approx_cell1_size)
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:
self.model.populate_mock(self.halocat)
pos=three_dim_pos_bundle(self.model.mock.galaxy_table, 'x', 'y', 'z')
obvs = []
for obv in observables:
if obv == 'nbar':
obvs.append(len(pos) / 1000**3.) # nbar of the galaxy catalog
elif obv == 'gmf':
nbar = len(pos) / 1000**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] / (1000.**3.)
obvs.append(gmf)
elif obv == 'xi':
greek_xi = tpcf(
pos, rbins, period=self.model.mock.Lbox,
max_sample_size=int(3e5), estimator='Natural',
approx_cell1_size=approx_cell1_size)
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 _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
def plot_posterior_model(observable,
abc_theta_file=None,
data_dict={
'Mr': 20,
'b_normal': 0.25,
'Nmock': 500
},
clobber=False):
'''
Plot 1\sigma and 2\sigma model predictions from ABC-PMC posterior likelihood
Parameters
----------
observable : string
One of the following strings ['xi', 'scaledxi', 'gmf']
'''
# load the particles
if abc_theta_file is None:
raise ValueError(
"Please specify the theta output file from ABC-PMC run")
theta = np.loadtxt(abc_theta_file)
if observable == 'scaledxi':
obvs_str = 'xi'
else:
obvs_str = observable
obvs_file = ''.join(
abc_theta_file.rsplit('.dat')[:-1] + ['.', observable, '.dat'])
print obvs_file
if not os.path.isfile(obvs_file) or clobber:
for i in xrange(len(theta)):
obv_i = HODsimulator(theta[i],
prior_range=None,
observables=[obvs_str],
Mr=data_dict['Mr'])
try:
model_obv.append(obv_i[0])
except UnboundLocalError:
model_obv = [obv_i[0]]
model_obv = np.array(model_obv)
np.savetxt(obvs_file, model_obv)
else:
model_obv = np.loadtxt(obvs_file)
if 'xi' in observable:
r_bin = Data.data_xi_bins(Mr=data_dict['Mr'])
elif observable == 'gmf':
r_bin = Data.data_gmf_bins()
a, b, c, d, e = np.percentile(model_obv, [2.5, 16, 50, 84, 97.5], axis=0)
# plotting
fig = plt.figure(1)
ax = fig.add_subplot(111)
if observable == 'xi': # 2PCF
data_xi, data_xi_cov = Data.data_xi_full_cov(**data_dict) # data
ax.fill_between(r_bin, a, e, color="k", alpha=0.1, edgecolor="none")
ax.fill_between(r_bin, b, d, color="k", alpha=0.3, edgecolor="none")
#ax.plot(r_bin, c, "k", lw=1)
ax.errorbar(r_bin,
data_xi,
yerr=np.sqrt(np.diag(data_xi_cov)),
fmt=".k",
capsize=0)
ax.set_xlabel(r'$r\;[\mathrm{Mpc}/h]$', fontsize=20)
ax.set_ylabel(r'$\xi_{\rm gg}$', fontsize=25)
ax.set_xscale('log')
ax.set_xlim([0.1, 20.])
elif observable == 'scaledxi': # Scaled 2PFC (r * xi)
data_xi, data_xi_cov = Data.data_xi_full_cov(**data_dict) # data
ax.fill_between(r_bin,
r_bin * a,
r_bin * e,
color="k",
alpha=0.1,
edgecolor="none")
ax.fill_between(r_bin,
r_bin * b,
r_bin * d,
color="k",
alpha=0.3,
edgecolor="none")
ax.errorbar(r_bin,
r_bin * data_xi,
yerr=r_bin * np.sqrt(np.diag(data_xi_cov)),
fmt=".k",
capsize=0)
ax.set_xlabel(r'$r\;[\mathrm{Mpc}/h]$', fontsize=20)
ax.set_ylabel(r'$r \xi_{\rm gg}$', fontsize=25)
ax.set_xscale('log')
ax.set_xlim([0.1, 20.])
elif observable == 'gmf': # GMF
data_gmf, data_gmf_sigma = Data.data_gmf(**data_dict)
ax.fill_between(r_bin, a, e, color="k", alpha=0.1, edgecolor="none")
ax.fill_between(r_bin, b, d, color="k", alpha=0.3, edgecolor="none")
ax.errorbar(r_bin, data_gmf, yerr=data_gmf_sigma, fmt=".k", capsize=0)
ax.set_xlabel(r'Group Richness', fontsize=25)
ax.set_ylabel(r'GMF $[\mathrm{h}^3\mathrm{Mpc}^{-3}]$', fontsize=25)
ax.set_yscale('log')
ax.set_xlim([1., 50.])
fig.savefig(''.join([
util.fig_dir(), observable, '.posterior_prediction', '.Mr',
str(data_dict['Mr']), '_Nmock',
str(data_dict['Nmock']), '.pdf'
]),
bbox_inches='tight')
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