def plot_xi_model(file_name="infered_hod_file_name", observables=['xi'],
Mr=20 , data_dict={'Mr':20, 'Nmock':500} , smooth = "False"):
"""
2PCF model 1\sigma & 2\sigma model predictions
"""
#load the data
theta = np.loadtxt(file_name+".dat")[:3]
for obv in observables:
if obv == 'xi':
# import xir and full covariance matrix of xir
data_xi, data_xi_cov = Data.data_xi_full_cov(**data_dict)
xi_gg = []
for i in xrange(len(theta)):
#mod = PrebuiltHodModelFactory('zheng07', threshold=-1*Mr)
#mod.param_dict["logM0"] = theta[i][0]
#mod.param_dict["sigma_logM"] = np.exp(theta[i][1])
#mod.param_dict["logMmin"] = theta[i][2]
#mod.param_dict["alpha"] = theta[i][3]
#mod.param_dict["logM1"] = theta[i][4]
#mod.populate_mock()
""" if we want to make a smooth plot, we do this:"""
#rr , xi = mod.compute_average_compute_average_galaxy_clustering(rbins = xi_binedges() , num_iterations = 6 )
"""else"""
HODsimulator(theta[i], prior_range=None, observables=['xi'], Mr=20)
xi_gg.append(xi)
xi_gg = np.array(xi_gg)
a, b, c, d, e = np.percentile(xi_gg, [2.5, 16, 50, 84, 97.5], axis=0)
fig1 = plt.figure()
ax = fig1.add_subplot(111)
ax.fill_between(rr, a, e, color="k", alpha=0.1, edgecolor="none")
ax.fill_between(rr, b, d, color="k", alpha=0.3, edgecolor="none")
ax.plot(rr, c, "k", lw=1)
ax.errorbar(rr, data_xi, yerr = np.sqrt(np.diag(data_xi_cov)), fmt=".k",
capsize=0)
xlabel = ax.set_xlabel(r'$r[\mathrm{Mpc}h^{-1}]$', fontsize=20)
ylabel = ax.set_ylabel(r'$\xi_{\rm gg}$', fontsize=25)
plt.xscale('log')
plt.xlim(xmin = .1 , xmax = 15)
fig1.savefig('../figs/xi_posterior_prediction'+str(Mr)+'.pdf',
bbox_extra_artists=[xlabel, ylabel], bbox_inches='tight')
fig2 = plt.figure()
ax = fig2.add_subplot(111)
ax.fill_between(rr, rr*a, rr*e, color="k", alpha=0.1, edgecolor="none")
ax.fill_between(rr, rr*b, rr*d, color="k", alpha=0.3, edgecolor="none")
#ax.plot(rr, c, "k", lw=1) we don't care about the best fit here
ax.errorbar(rr, rr*data_xi, yerr = rr*np.sqrt(np.diag(data_xi_cov)), fmt=".k",
capsize=0)
xlabel = ax.set_xlabel(r'$r[\mathrm{Mpc}h^{-1}]$', fontsize=20)
ylabel = ax.set_ylabel(r'$r\xi_{\rm gg}$', fontsize=25)
plt.xscale('log')
plt.xlim(xmin = .1 , xmax = 15)
fig2.savefig('../figs/xi_scaled_posterior_prediction'+str(Mr)+'.pdf',
bbox_extra_artists=[xlabel, ylabel], bbox_inches='tight')
fig3 = plt.figure()
ax = fig3.add_subplot(111)
ax.fill_between(rr, a - data_xi, e-data_xi, color="k", alpha=0.1, edgecolor="none")
ax.fill_between(rr, b - data_xi, d-data_xi, color="k", alpha=0.3, edgecolor="none")
#ax.plot(rr, c, "k", lw=1) we don't care about the best fit here
ax.errorbar(rr, data_xi - data_xi, yerr = np.sqrt(np.diag(data_xi_cov)), fmt=".k",
capsize=0)
xlabel = ax.set_xlabel(r'$r[\mathrm{Mpc}h^{-1}]$', fontsize=20)
ylabel = ax.set_ylabel(r'$\Delta \xi_{\rm gg}$', fontsize=25)
plt.xscale('log')
plt.xlim(xmin = .1 , xmax = 15)
fig3.savefig('../figs/xi_residual_posterior_prediction'+str(Mr)+'.pdf',
bbox_extra_artists=[xlabel, ylabel], bbox_inches='tight')
fig4, axes = pl.subplots(2, 1, figsize=(10, 8) , sharex = True)
fig4.subplots_adjust(wspace=0.0 , hspace=0.4)
ax1 = axes[0,0]
ax1.fill_between(rr, a, e, color="k", alpha=0.1, edgecolor="none")
ax1.fill_between(rr, b, d, color="k", alpha=0.3, edgecolor="none")
#ax1.plot(rr, c, "k", lw=1)
ax1.errorbar(rr, data_xi, yerr = np.sqrt(np.diag(data_xi_cov)), fmt=".k",
capsize=0)
ylabel = ax1.set_ylabel(r'$\xi_{\rm gg}$', fontsize=25)
ax1.set_xscale("log")
ax1.set_yscale("log")
ax1_set.xlim(xmin = .1 , xmax = 15)
ax2 = axes[0,0]
ax2.fill_between(rr, a - data_xi, e- data_xi, color="k", alpha=0.1, edgecolor="none")
ax2.fill_between(rr, b- data_xi, d- data_xi, color="k", alpha=0.3, edgecolor="none")
#ax2.plot(rr, c, "k", lw=1)
ax2.errorbar(rr, data_xi- data_xi , yerr = np.sqrt(np.diag(data_xi_cov)), fmt=".k",
capsize=0)
ylabel = ax2.set_ylabel(r'$\Delta \xi_{\rm gg}$', fontsize=25)
ax2.set_xscale("log")
ax2_set.xlim(xmin = .1 , xmax = 15)
fig4.savefig('../figs/xi&residual_posterior_prediction'+str(Mr)+'.pdf',
bbox_extra_artists=[xlabel, ylabel], bbox_inches='tight')
fig5, axes = pl.subplots(2, 1, figsize=(10, 8) , sharex = True)
fig5.subplots_adjust(wspace=0.0 , hspace=0.4)
ax1 = axes[0,0]
ax1.fill_between(rr,rr* a, rr* e, color="k", alpha=0.1, edgecolor="none")
ax1.fill_between(rr, rr* b, rr* d, color="k", alpha=0.3, edgecolor="none")
#ax1.plot(rr, c, "k", lw=1)
ax1.errorbar(rr, rr* data_xi, yerr = rr*np.sqrt(np.diag(data_xi_cov)), fmt=".k",
capsize=0)
ylabel = ax1.set_ylabel(r'$r\xi_{\rm gg}$', fontsize=25)
ax1.set_xscale("log")
ax1.set_yscale("log")
ax1_set.xlim(xmin = .1 , xmax = 15)
ax2 = axes[0,0]
ax2.fill_between(rr, rr* a - rr* data_xi, rr* e- rr* data_xi, color="k", alpha=0.1, edgecolor="none")
ax2.fill_between(rr, rr* b- rr* data_xi, rr* d- rr* data_xi, color="k", alpha=0.3, edgecolor="none")
#ax2.plot(rr, c, "k", lw=1)
ax2.errorbar(rr, rr*data_xi- rr* data_xi , yerr = rr* np.sqrt(np.diag(data_xi_cov)), fmt=".k",
capsize=0)
ylabel = ax2.set_ylabel(r'$\Delta(r\xi_{\rm gg})$', fontsize=25)
ax2.set_xscale("log")
ax2_set.xlim(xmin = .1 , xmax = 15)
fig5.savefig('../figs/xi&residual_scaled_posterior_prediction'+str(Mr)+'.pdf',
bbox_extra_artists=[xlabel, ylabel], bbox_inches='tight')
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 mcmc_ipython_par(Nwalkers, Nchains_burn, Nchains_pro, observables=['nbar', 'xi'],
data_dict={'Mr':20, 'Nmock':500}, prior_name = 'first_try', threads=1):
'''
Standard MCMC implementaion
Parameters
-----------
- Nwalker :
Number of walkers
- Nchains_burn :
Number of burn-in chains
- Nchains_pro :
Number of production chains
- observables :
list of observables. Options are 'nbar', 'gmf', 'xi'
- data_dict : dictionary that specifies the observation keywords
'''
# data observables
fake_obs = [] # list of observables
fake_obs_cov = []
for obv in observables:
if obv == 'nbar':
data_nbar, data_nbar_var = Data.data_nbar(**data_dict)
fake_obs.append(data_nbar)
fake_obs_cov.append(data_nbar_var)
if obv == 'gmf':
data_gmf, data_gmf_sigma = Data.data_gmf(**data_dict)
fake_obs.append(data_gmf)
fake_obs_cov.append(data_gmf)
if obv == 'xi':
# import xir and full covariance matrix of xir
data_xi, data_xi_cov = Data.data_xi_full_cov(**data_dict)
data_xi_invcov = Data.data_xi_inv_cov(**data_dict)
fake_obs.append(data_xi)
fake_obs_cov.append(data_xi_invcov)
# 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
# Initializing Walkers
random_guess = np.array([11. , np.log(.4) , 11.5 , 1.0 , 13.5])
pos0 = np.repeat(random_guess, Nwalkers).reshape(Ndim, Nwalkers).T + \
1e-1 * np.random.randn(Ndim * Nwalkers).reshape(Nwalkers, Ndim)
# Initializing the emcee sampler
hod_kwargs = {
'prior_range': prior_range,
'data': fake_obs,
'data_cov': fake_obs_cov,
'observables': observables,
'Mr': data_dict['Mr']
}
# Set up the interface to the ipcluster.
c = Client()
view = c[:]
view.push({"lnPost": lnPost})
# Modules necessary in posterior calculation should be called here
view.execute("import numpy as np")
view.execute("from hod_sim import HODsimulator")
# Setting up the Sampler
sampler = emcee.EnsembleSampler(Nwalkers, Ndim, lnPost, kwargs=hod_kwargs, pool = view)
# Setting up a file for saving the chains
chain_file = ''.join([util.dat_dir(),
util.observable_id_flag(observables),
'_Mr', str(data_dict["Mr"]), '_theta.mcmc_chain.dat'])
f = open(chain_file, "w")
f.close()
# Running the Sampler and writing out the chains
for result in sampler.sample(pos0, iterations=Nchains_burn + Nchains_pro, storechain=False):
position = result[0]
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()
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 mcmc_ipython_par(Nwalkers,
Nchains_burn,
Nchains_pro,
observables=['nbar', 'xi'],
data_dict={
'Mr': 20,
'Nmock': 500
},
prior_name='first_try',
threads=1):
'''
Standard MCMC implementaion
Parameters
-----------
- Nwalker :
Number of walkers
- Nchains_burn :
Number of burn-in chains
- Nchains_pro :
Number of production chains
- observables :
list of observables. Options are 'nbar', 'gmf', 'xi'
- data_dict : dictionary that specifies the observation keywords
'''
# data observables
fake_obs = [] # list of observables
fake_obs_cov = []
for obv in observables:
if obv == 'nbar':
data_nbar, data_nbar_var = Data.data_nbar(**data_dict)
fake_obs.append(data_nbar)
fake_obs_cov.append(data_nbar_var)
if obv == 'gmf':
data_gmf, data_gmf_sigma = Data.data_gmf(**data_dict)
fake_obs.append(data_gmf)
fake_obs_cov.append(data_gmf)
if obv == 'xi':
# import xir and full covariance matrix of xir
data_xi, data_xi_cov = Data.data_xi_full_cov(**data_dict)
data_xi_invcov = Data.data_xi_inv_cov(**data_dict)
fake_obs.append(data_xi)
fake_obs_cov.append(data_xi_invcov)
# 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
# Initializing Walkers
random_guess = np.array([11., np.log(.4), 11.5, 1.0, 13.5])
pos0 = np.repeat(random_guess, Nwalkers).reshape(Ndim, Nwalkers).T + \
1e-1 * np.random.randn(Ndim * Nwalkers).reshape(Nwalkers, Ndim)
# Initializing the emcee sampler
hod_kwargs = {
'prior_range': prior_range,
'data': fake_obs,
'data_cov': fake_obs_cov,
'observables': observables,
'Mr': data_dict['Mr']
}
# Set up the interface to the ipcluster.
c = Client()
view = c[:]
view.push({"lnPost": lnPost})
# Modules necessary in posterior calculation should be called here
view.execute("import numpy as np")
view.execute("from hod_sim import HODsimulator")
# Setting up the Sampler
sampler = emcee.EnsembleSampler(Nwalkers,
Ndim,
lnPost,
kwargs=hod_kwargs,
pool=view)
# Setting up a file for saving the chains
chain_file = ''.join([
util.dat_dir(),
util.observable_id_flag(observables), '_Mr',
str(data_dict["Mr"]), '_theta.mcmc_chain.dat'
])
f = open(chain_file, "w")
f.close()
# Running the Sampler and writing out the chains
for result in sampler.sample(pos0,
iterations=Nchains_burn + Nchains_pro,
storechain=False):
position = result[0]
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()
Nwalkers = 10
Nchains_burn = 1
Nchains_pro = 1
# data observables
fake_obs = [] # list of observables
for obv in observables:
if obv == 'nbar':
data_nbar, data_nbar_var = Data.data_nbar(**data_dict)
fake_obs.append(data_nbar)
if obv == 'gmf':
data_gmf, data_gmf_sigma = Data.data_gmf(**data_dict)
fake_obs.append(data_gmf)
if obv == 'xi':
# import xir and full covariance matrix of xir
data_xi, data_xi_cov = Data.data_xi_full_cov(**data_dict)
# take the inverse of the covariance matrix
data_xi_invcov = solve(np.eye(len(data_xi)) , data_xi_cov)
fake_obs.append(data_xi)
# '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)
Nwalkers = 10
Nchains_burn = 1
Nchains_pro = 1
# data observables
fake_obs = [] # list of observables
for obv in observables:
if obv == 'nbar':
data_nbar, data_nbar_var = Data.data_nbar(**data_dict)
fake_obs.append(data_nbar)
if obv == 'gmf':
data_gmf, data_gmf_sigma = Data.data_gmf(**data_dict)
fake_obs.append(data_gmf)
if obv == 'xi':
# import xir and full covariance matrix of xir
data_xi, data_xi_cov = Data.data_xi_full_cov(**data_dict)
# take the inverse of the covariance matrix
data_xi_invcov = solve(np.eye(len(data_xi)), data_xi_cov)
fake_obs.append(data_xi)
# '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)