def test_sample(self):
N = 10
T = 2
postfn = lambda theta: None
dist = 1.0
distfn = lambda X, Y: dist
prior = abcpmc.TophatPrior([0], [100])
sampler = abcpmc.Sampler(N, 0, postfn, distfn)
eps = 10
eps_proposal = abcpmc.ConstEps(T, eps)
for i, pool in enumerate(sampler.sample(prior, eps_proposal)):
assert pool is not None
assert pool.t == i
assert pool.ratio == 1.0
assert pool.eps == eps
assert len(pool.thetas) == N
assert np.all(pool.thetas != 0.0)
assert len(pool.dists) == N
assert np.all(pool.dists == dist)
assert len(pool.ws) == N
assert np.allclose(np.sum(pool.ws), 1.0)
assert i + 1 == T
def sample(T, eps_val, eps_min):
abcpmc_sampler = abcpmc.Sampler(N=1000,
Y=data,
postfn=simz,
dist=distance,
pool=mpi_pool)
abcpmc_sampler.particle_proposal_cls = abcpmc.OLCMParticleProposal
eps = abcpmc.ConstEps(T, eps_val)
pools = []
for pool in abcpmc_sampler.sample(prior, eps):
print("T: {0}, eps: {1:>.4f}, ratio: {2:>.4f}".format(
pool.t, eps(pool.t), pool.ratio))
plot_thetas(pool.thetas, pool.ws, pool.t)
if (pool.t < 5):
eps.eps = np.percentile(pool.dists, 50)
else:
eps.eps = np.percentile(pool.dists, 75)
if eps.eps < eps_min:
eps.eps = eps_min
pools.append(pool)
#abcpmc_sampler.close()
return pools
def test_ConstEps():
eps_val = 0.5
T = 5
eps = abcpmc.ConstEps(T, eps_val)
for i, e in enumerate(eps):
assert e == eps_val
assert i + 1 == T
def abc(pewl, name=None, niter=None, npart=None, restart=None):
if restart is not None:
# read pool
theta_init = np.loadtxt(
os.path.join(abc_dir, 'theta.t%i.dat' % restart))
rho_init = np.loadtxt(
os.path.join(abc_dir, 'rho.t%i.dat' % restart))
w_init = np.loadtxt(
os.path.join(abc_dir, 'w.t%i.dat' % restart))
init_pool = abcpmc.PoolSpec(restart, None, None, theta_init, rho_init, w_init)
npart = len(theta_init)
print('%i particles' % npart)
else:
init_pool = None
#--- inference with ABC-PMC below ---
# prior
prior = abcpmc.TophatPrior(prior_min, prior_max)
# sampler
abcpmc_sampler = abcpmc.Sampler(
N=npart, # N_particles
Y=x_obs, # data
postfn=_sumstat_model_wrap, # simulator
dist=_distance_metric_wrap, # distance metric
pool=pewl,
postfn_kwargs={'dem': dem}#, dist_kwargs={'method': 'L2', 'phi_err': phi_err}
)
# threshold
eps = abcpmc.ConstEps(niter, eps0)
print('eps0', eps.eps)
for pool in abcpmc_sampler.sample(prior, eps, pool=init_pool):
eps_str = ", ".join(["{0:>.4f}".format(e) for e in pool.eps])
print("T: {0}, eps: [{1}], ratio: {2:>.4f}".format(pool.t, eps_str, pool.ratio))
for i, (mean, std) in enumerate(zip(*abcpmc.weighted_avg_and_std(pool.thetas, pool.ws, axis=0))):
print(u" theta[{0}]: {1:>.4f} \u00B1 {2:>.4f}".format(i, mean,std))
print('dist', pool.dists)
# write out theta, weights, and distances to file
dustInfer.writeABC('eps', pool, abc_dir=abc_dir)
dustInfer.writeABC('theta', pool, abc_dir=abc_dir)
dustInfer.writeABC('w', pool, abc_dir=abc_dir)
dustInfer.writeABC('rho', pool, abc_dir=abc_dir)
# update epsilon based on median thresholding
eps.eps = np.median(pool.dists, axis=0)
print('eps%i' % pool.t, eps.eps)
print('----------------------------------------')
#if pool.ratio <0.2: break
abcpmc_sampler.close()
return None
def test_sample(self):
N = 10
T = 2
postfn = lambda theta: None
dist = lambda X, Y: 0
prior = abcpmc.TophatPrior([0], [100])
sampler = abcpmc.Sampler(N, 0, postfn, dist)
eps_proposal = abcpmc.ConstEps(T, 10)
for i, pool in enumerate(sampler.sample(prior, eps_proposal)):
assert pool is not None
assert len(pool.thetas) == N
assert i + 1 == T
def launch(threads):
eps = abcpmc.ConstEps(T, eps_start)
pools = []
# pool is a namedtuple representing the values of one iteration
for pool in sampler.sample(prior, eps):
print("T: {0}, eps: {1:>.4f}, ratio: {2:>.4f}".format(
pool.t, eps(pool.eps), pool.ratio))
for i, (mean, std) in enumerate(
zip(*abcpmc.weighted_avg_and_std(pool.thetas, pool.ws,
axis=0))):
print(u" theta[{0}]: {1:>.4f} \u00B1 {2:>.4f}".format(
i, mean, std))
# reduce the eps value to the alpha-th percentile of the sorted distances
eps.eps = np.percentile(pool.dists, alpha)
pools.append(pool)
sampler.close()
return pools
def sample(T, eps_val, eps_min):
prior = abcpmc.TophatPrior([10., np.log(.1), 11.02, .8, 13.],
[13., np.log(.7), 13.02, 1.3, 14.])
abcpmc_sampler = abcpmc.Sampler(N=1000,
Y=data,
postfn=simz,
dist=distance,
pool=mpi_pool)
abcpmc_sampler.particle_proposal_cls = abcpmc.ParticleProposal
#abcpmc.Sampler.particle_proposal_kwargs = {'k': 50}
#abcpmc_sampler.particle_proposal_cls = abcpmc.KNNParticleProposal
eps = abcpmc.ConstEps(T, [1.e13, 1.e13])
pools = []
for pool in abcpmc_sampler.sample(prior, eps):
print("T:{0},ratio: {1:>.4f}".format(pool.t, pool.ratio))
print eps(pool.t)
plot_thetas(pool.thetas, pool.ws, pool.t)
np.savetxt(
"/home/mj/public_html/nbar_gmf5_Mr20_theta_t" + str(t) + ".dat",
theta)
np.savetxt("/home/mj/public_html/nbar_gmf5_Mr20_w_t" + str(t) + ".dat",
w)
if pool.t < 3:
eps.eps = np.percentile(np.atleast_2d(pool.dists), 50, axis=0)
elif (pool.t > 2) and (pool.t < 20):
eps.eps = np.percentile(np.atleast_2d(pool.dists), 75, axis=0)
abcpmc_sampler.particle_proposal_cls = abcpmc.ParticleProposal
else:
eps.eps = np.percentile(np.atleast_2d(pool.dists), 90, axis=0)
abcpmc_sampler.particle_proposal_cls = abcpmc.ParticleProposal
#if eps.eps < eps_min:
# eps.eps = eps_min
pools.append(pool)
#abcpmc_sampler.close()
return pools
def config(self):
try:
import abcpmc
except ImportError:
raise ValueError("To use ABC PMC you need to install it with pip install abcpmc")
global abc_pipeline
abc_pipeline = self.pipeline
self.threshold = self.read_ini("threshold",str, 'LinearEps')
self.metric_kw = self.read_ini("metric",str, 'chi2') #mean, chi2 or other
if self.metric_kw =='other':
self.distance_func = self.read_ini("distance_func",str, None) #only for other metric,
self.metric = self.distance_func[1:-1]
self.epimax = self.read_ini('epimax', float,5.0)
self.epimin = self.read_ini('epimin',float, 1.0)
self.part_prop = self.read_ini("particle_prop",str,'weighted_cov')
self.set_prior = self.read_ini("set_prior",str,'uniform')
self.param_cov = self.read_ini("param_cov_file",str,'None')
self.knn = self.read_ini("num_nn",int, 10)
self.npart = self.read_ini("npart",int,100)
self.niter = self.read_ini("niter",int,2)
self.ngauss = self.read_ini("ngauss",int,4)
self.run_multigauss = self.read_ini("run_multigauss",bool,False)
self.diag_cov = self.read_ini("diag_cov",bool,False)
self.ndim = len(self.pipeline.varied_params)
#options for decreasing threshold
if self.threshold == 'ConstEps':
self.eps = abcpmc.ConstEps(self.niter, self.epimax)
elif self.threshold == 'ExpEps':
self.eps = abcpmc.ExponentialEps(self.niter, self.epimax,self.epimin)
else:
self.eps = abcpmc.LinearEps(self.niter, self.epimax, self.epimin)
print("\nRunning ABC PMC")
print("with %d particles, %s prior, %s threshold, %d iterations over (%f,%f), %s kernal \n" % (self.npart,self.set_prior,self.threshold,self.niter,self.epimax,self.epimin,self.part_prop))
#Initial positions for all of the parameters
self.p0 = np.array([param.start for param in self.pipeline.varied_params])
#Data file is read for use in dist() for each step
#parameter covariance used in the prior
self.data, self.cov, self.invcov = self.load_data()
#At the moment the same prior (with variable hyperparameters) is
# used for all parameters - would be nice to change this to be more flexible
self.pmin = np.zeros(self.ndim)
self.pmax = np.zeros(self.ndim)
for i,pi in enumerate(self.pipeline.varied_params):
self.pmin[i] = pi.limits[0]
self.pmax[i] = pi.limits[1]
if self.set_prior.lower() == 'uniform':
self.prior = abcpmc.TophatPrior(self.pmin,self.pmax)
elif self.set_prior.lower() == 'gaussian':
sigma2 = np.loadtxt(self.param_cov)
if len(np.atleast_2d(sigma2)[0][:]) != self.ndim:
raise ValueError("Cov matrix for Gaussian prior has %d columns for %d params" % len(np.atleast_2d(sigma2)[0][:]), self.ndim)
else:
self.prior = abcpmc.GaussianPrior(self.p0, np.atleast_2d(sigma2))
else:
raise ValueError("Please set the ABC option 'set_prior' to either 'uniform' or 'gaussian'. At the moment only 'uniform' works in the general case.")
#create sampler
self.sampler = abcpmc.Sampler(N=self.npart, Y=self.data, postfn=abc_model, dist=self.dist)
#set particle proposal kernal
abcpmc.Sampler.particle_proposal_kwargs = {}
if self.part_prop == 'KNN':
abcpmc.Sampler.particle_proposal_kwargs = {'k':self.knn}
self.sampler.particle_proposal_cls = abcpmc.KNNParticleProposal
elif self.part_prop == 'OLCM':
self.sampler.particle_proposal_cls = abcpmc.OLCMParticleProposal
self.converged = False
def std(x, y):
return abs(np.std(x) - np.std(y))
''' Setup '''
# 'Best' guess about the distribution, uniform distribution
prior = abcpmc.TophatPrior([0.0, 1.0], [2.0, 3.0])
# As threshold for accepting draws from the prior we use the alpha-th percentile
# of the sorted distances of the particles of the current iteration
alpha = 75
T = 2 # sample for T iterations
eps_start = 20.0 # sufficiently high starting threshold (like 5x the variability or more)
eps = abcpmc.ConstEps(T, eps_start)
''' Sampling function '''
def launch(threads):
eps = abcpmc.ConstEps(T, eps_start)
pools = []
# pool is a namedtuple representing the values of one iteration
for pool in sampler.sample(prior, eps):
print("T: {0}, eps: {1:>.4f}, ratio: {2:>.4f}".format(
pool.t, eps(pool.eps), pool.ratio))
for i, (mean, std) in enumerate(
zip(*abcpmc.weighted_avg_and_std(pool.thetas, pool.ws,
axis=0))):
def ABC(T,
eps_input,
Npart=1000,
cen_tf=None,
cen_prior_name=None,
cen_abcrun=None):
''' ABC-PMC implementation.
Parameters
----------
T : (int)
Number of iterations
eps_input : (float)
Starting epsilon threshold value
N_part : (int)
Number of particles
prior_name : (string)
String that specifies what prior to use.
abcrun : (string)
String that specifies abc run information
'''
abcinh = ABCInherit(cen_tf, abcrun=cen_abcrun, prior_name=cen_prior_name)
# Data (Group Catalog Satellite fQ)
grpcat = GroupCat(Mrcut=18, position='satellite')
grpcat.Read()
qfrac = Fq()
m_bin = np.array([9.7, 10.1, 10.5, 10.9, 11.3])
M_mid = 0.5 * (m_bin[:-1] + m_bin[1:])
sfq = qfrac.Classify(grpcat.mass,
grpcat.sfr,
np.median(grpcat.z),
sfms_prop=abcinh.sim_kwargs['sfr_prop']['sfms'])
ngal, dum = np.histogram(grpcat.mass, bins=m_bin)
ngal_q, dum = np.histogram(grpcat.mass[sfq == 'quiescent'], bins=m_bin)
data_sum = [M_mid, ngal_q.astype('float') / ngal.astype('float')]
# Simulator
cen_assigned_sat_file = ''.join([
'/data1/hahn/pmc_abc/pickle/', 'satellite', '.cenassign', '.',
cen_abcrun, '_ABC', '.', cen_prior_name, '_prior', '.p'
])
if not os.path.isfile(cen_assigned_sat_file):
sat_cen = AssignCenSFR(cen_tf,
abcrun=cen_abcrun,
prior_name=cen_prior_name)
pickle.dump(sat_cen, open(cen_assigned_sat_file, 'wb'))
else:
sat_cen = pickle.load(open(cen_assigned_sat_file, 'rb'))
def Simz(tt): # Simulator (forward model)
tqdel_dict = {'name': 'explin', 'm': tt[0], 'b': tt[1]}
sat_evol = EvolveSatSFR(sat_cen, tqdelay_dict=tqdel_dict)
sfq_sim = qfrac.Classify(sat_evol.mass,
sat_evol.sfr,
sat_evol.zsnap,
sfms_prop=sat_evol.sfms_prop)
ngal_sim, dum = np.histogram(sat_evol.mass, bins=m_bin)
ngal_q_sim, dum = np.histogram(sat_evol.mass[sfq_sim == 'quiescent'],
bins=m_bin)
sim_sum = [
M_mid,
ngal_q_sim.astype('float') / ngal_sim.astype('float')
]
return sim_sum
# Priors
prior_min = [-11.75, 2.]
prior_max = [-10.25, 4.]
prior = abcpmc.TophatPrior(prior_min, prior_max) # ABCPMC prior object
def rho(simum, datum):
datum_dist = datum[1]
simum_dist = simum[1]
drho = np.sum((datum_dist - simum_dist)**2)
return drho
abcrun_flag = cen_abcrun + '_central'
theta_file = lambda pewl: ''.join([
code_dir(), 'dat/pmc_abc/', 'Satellite.tQdelay.theta_t',
str(pewl), '_', abcrun_flag, '.dat'
])
w_file = lambda pewl: ''.join([
code_dir(), 'dat/pmc_abc/', 'Satellite.tQdelay.w_t',
str(pewl), '_', abcrun_flag, '.dat'
])
dist_file = lambda pewl: ''.join([
code_dir(), 'dat/pmc_abc/', 'Satellite.tQdelay.dist_t',
str(pewl), '_', abcrun_flag, '.dat'
])
eps_file = ''.join([
code_dir(), 'dat/pmc_abc/Satellite.tQdelay.epsilon_', abcrun_flag,
'.dat'
])
eps = abcpmc.ConstEps(T, eps_input)
try:
mpi_pool = mpi_util.MpiPool()
abcpmc_sampler = abcpmc.Sampler(
N=Npart, # N_particles
Y=data_sum, # data
postfn=Simz, # simulator
dist=rho, # distance function
pool=mpi_pool)
except AttributeError:
abcpmc_sampler = abcpmc.Sampler(
N=Npart, # N_particles
Y=data_sum, # data
postfn=Simz, # simulator
dist=rho) # distance function
abcpmc_sampler.particle_proposal_cls = abcpmc.ParticleProposal
pools = []
f = open(eps_file, "w")
f.close()
eps_str = ''
for pool in abcpmc_sampler.sample(prior, eps, pool=None):
print '----------------------------------------'
print 'eps ', pool.eps
new_eps_str = '\t' + str(pool.eps) + '\n'
if eps_str != new_eps_str: # if eps is different, open fiel and append
f = open(eps_file, "a")
eps_str = new_eps_str
f.write(eps_str)
f.close()
print("T:{0},ratio: {1:>.4f}".format(pool.t, pool.ratio))
print eps(pool.t)
# write theta, weights, and distances to file
np.savetxt(theta_file(pool.t),
pool.thetas,
header='tQdelay_slope, tQdelay_offset')
np.savetxt(w_file(pool.t), pool.ws)
np.savetxt(dist_file(pool.t), pool.dists)
# update epsilon based on median thresholding
eps.eps = np.median(pool.dists)
pools.append(pool)
return pools
def main_abcpmc_MUSIC2(conf, test=False):
"""
config should contain
[][]: a list etc.
eps_start is actually important as the next iteration will only start if the number of computed trials within these boundaries will be Nw.
So in one case I had to draw and compute twice as many particles than Nw.
About the treads: 14-16 treads are fine, as more treats wont be fully used and just sit in the taskqueue
"""
# Loads the real data to compare with (and if neccessary also test data)
data = iom.unpickleObject(conf['paths']['surveyreal'])
if test:
dataMUSIC2 = iom.unpickleObject(conf['paths']['surveysim'])
print(type(dataMUSIC2.Rmodel), conf['paths']['surveysim'])
surmet.abcpmc_dist_severalMetrices(dataMUSIC2, data, metrics=json.loads(conf['metrics']['used']),
delal=False, stochdrop=conf['flavor']['stochdrop'],
phoenixdrop = conf['flavor']['phoenixdrop'], outpath='/data/')
return 0
""" The abcpmc part starts: Define thetas i.e. parameter values to be inferred and priors"""
if conf['prior']['type'] == 'tophat':
bounds = json.loads(conf['prior']['bounds'])
prior = abcpmc.TophatPrior(bounds[0], bounds[1])
elif conf['prior']['type'] == 'gaussian':
means = json.loads(conf['prior']['means'])
COV = json.loads(conf['prior']['covariance'])
prior = abcpmc.GaussianPrior(mu=means, sigma=COV)
else:
print('inference_abcpmc::main_abcpmc_MUSIC2: prior %s is unknown!' % (conf['prior']['type']))
return 0
eps = abcpmc.ConstEps(conf.getint('pmc', 'T'), json.loads(conf['metrics']['eps_startlimits']))
if test:
sampler = abcpmc.Sampler(N=conf.getint('pmc', 'Nw'), Y=data, postfn=testrand, dist=testmetric,
threads=conf.getint('mp', 'Nthreads'), maxtasksperchild=conf.getint('mp', 'maxtasksperchild'))
else:
sampler = abcpmc.Sampler(N=conf.getint('pmc', 'Nw'), Y=data, postfn=partial(music2run.main_ABC, parfile=conf['simulation']['parfile']),
dist=partial(surmet.abcpmc_dist_severalMetrices, metrics=json.loads(conf['metrics']['used']),
outpath=conf['paths']['abcpmc'], stochdrop=conf['flavor']['stochdrop'],
phoenixdrop = conf['flavor']['phoenixdrop']),
threads=conf.getint('mp', 'Nthreads'), maxtasksperchild=conf.getint('mp', 'maxtasksperchild'))
# Prepares the file for counting
with open(conf['paths']['abcpmc'] + 'count.txt', 'w+') as f:
f.write('0')
sampler.particle_proposal_cls = abcpmc.OLCMParticleProposal
""" compare with AstroABC
sampler = astroabc.ABC_class(Ndim,walkers,data,tlevels,niter,priors,**prop)
sampler.sample(music2run.main_astroABC)
"""
# startfrom=iom.unpickleObject('/data/ClusterBuster-Output/MUSIC_NVSS02_Test01/launch_pools')
pool = None #startfrom[-1]
launch(sampler, prior, conf.getfloat('pmc','alpha'), eps, surveypath=conf['paths']['abcpmc'], pool=pool)
def FixedTauABC(T, eps_input, fixtau='satellite', Npart=1000, prior_name='try0',
observables=['fqz_multi'], abcrun=None,
restart=False, t_restart=None, eps_restart=None, **sim_kwargs):
''' Run ABC-PMC analysis for central galaxy SFH model with *FIXED* quenching
timescale
Parameters
----------
T : (int)
Number of iterations
eps_input : (float)
Starting epsilon threshold value
N_part : (int)
Number of particles
prior_name : (string)
String that specifies what prior to use.
abcrun : (string)
String that specifies abc run information
'''
if isinstance(eps_input, list):
if len(eps_input) != len(observables):
raise ValueError
if len(observables) > 1 and isinstance(eps_input, float):
raise ValueError
# output abc run details
sfinherit_kwargs, abcrun_flag = MakeABCrun(
abcrun=abcrun, Niter=T, Npart=Npart, prior_name=prior_name,
eps_val=eps_input, restart=restart, **sim_kwargs)
# Data
data_sum = DataSummary(observables=observables)
# Priors
prior_min, prior_max = PriorRange(prior_name)
prior = abcpmc.TophatPrior(prior_min, prior_max) # ABCPMC prior object
def Simz(tt): # Simulator (forward model)
gv_slope = tt[0]
gv_offset = tt[1]
fudge_slope = tt[2]
fudge_offset = tt[3]
sim_kwargs = sfinherit_kwargs.copy()
sim_kwargs['sfr_prop']['gv'] = {'slope': gv_slope, 'fidmass': 10.5, 'offset': gv_offset}
sim_kwargs['evol_prop']['fudge'] = {'slope': fudge_slope, 'fidmass': 10.5, 'offset': fudge_offset}
sim_kwargs['evol_prop']['tau'] = {'name': fixtau}
sim_output = SimSummary(observables=observables, **sim_kwargs)
return sim_output
theta_file = lambda pewl: ''.join([code_dir(),
'dat/pmc_abc/', 'CenQue_theta_t', str(pewl), '_', abcrun_flag,
'.fixedtau.', fixtau, '.dat'])
w_file = lambda pewl: ''.join([code_dir(),
'dat/pmc_abc/', 'CenQue_w_t', str(pewl), '_', abcrun_flag,
'.fixedtau.', fixtau, '.dat'])
dist_file = lambda pewl: ''.join([code_dir(),
'dat/pmc_abc/', 'CenQue_dist_t', str(pewl), '_', abcrun_flag,
'.fixedtau.', fixtau, '.dat'])
eps_file = ''.join([code_dir(),
'dat/pmc_abc/epsilon_', abcrun_flag,
'.fixedtau.', fixtau, '.dat'])
distfn = RhoFq
if restart:
if t_restart is None:
raise ValueError
last_thetas = np.loadtxt(theta_file(t_restart))
last_ws = np.loadtxt(w_file(t_restart))
last_dist = np.loadtxt(dist_file(t_restart))
init_pool = abcpmc.PoolSpec(t_restart, None, None, last_thetas, last_dist, last_ws)
else:
init_pool = None
eps = abcpmc.ConstEps(T, eps_input)
try:
mpi_pool = mpi_util.MpiPool()
abcpmc_sampler = abcpmc.Sampler(
N=Npart, # N_particles
Y=data_sum, # data
postfn=Simz, # simulator
dist=distfn, # distance function
pool=mpi_pool)
except AttributeError:
abcpmc_sampler = abcpmc.Sampler(
N=Npart, # N_particles
Y=data_sum, # data
postfn=Simz, # simulator
dist=distfn) # distance function
abcpmc_sampler.particle_proposal_cls = abcpmc.ParticleProposal
pools = []
if init_pool is None:
f = open(eps_file, "w")
f.close()
eps_str = ''
for pool in abcpmc_sampler.sample(prior, eps, pool=init_pool):
print '----------------------------------------'
print 'eps ', pool.eps
new_eps_str = str(pool.eps)+'\t'+str(pool.ratio)+'\n'
if eps_str != new_eps_str: # if eps is different, open fiel and append
f = open(eps_file, "a")
eps_str = new_eps_str
f.write(eps_str)
f.close()
print("T:{0},ratio: {1:>.4f}".format(pool.t, pool.ratio))
print eps(pool.t)
# write theta, weights, and distances to file
np.savetxt(theta_file(pool.t), pool.thetas,
header='gv_slope, gv_offset, fudge_slope, fudge_offset')
np.savetxt(w_file(pool.t), pool.ws)
np.savetxt(dist_file(pool.t), pool.dists)
# update epsilon based on median thresholding
if len(observables) == 1:
eps.eps = np.median(pool.dists)
else:
#print pool.dists
print np.median(np.atleast_2d(pool.dists), axis = 0)
eps.eps = np.median(np.atleast_2d(pool.dists), axis = 0)
print '----------------------------------------'
pools.append(pool)
return pools
