def fit_King_prof(nchains,
nruns,
nburn,
x,
y,
cl_cent,
field_dens,
cl_rad,
n_memb_i,
rt_max_f,
N_integ=1000,
ndim=2,
N_conv=1000,
tau_stable=0.05):
"""
rt_max_f: factor that caps the maximum tidal radius, given the previously
estimated cluster radius.
HARDCODED:
N_integ : number of values used in the tidal radius array.
N_conv
tau_stable
"""
from emcee import ensemble
from emcee import moves
# HARDCODED
# mv = moves.StretchMove()
# mv = moves.KDEMove()
mv = [
(moves.DESnookerMove(), 0.1),
(moves.DEMove(), 0.9 * 0.9),
(moves.DEMove(gamma0=1.0), 0.9 * 0.1),
]
# HARDCODED
# Steps to store Bayes params.
KP_steps = int(nruns * .01)
xy = np.array((x, y)).T
# area_tot = np.ptp(x) * np.ptp(y)
# cx, cy = cl_cent
# # Frame limits
# x0, x1 = min(xy.T[0]), max(xy.T[0])
# y0, y1 = min(xy.T[1]), max(xy.T[1])
# dx0, dx1 = abs(cl_cent[0] - x0), abs(cl_cent[0] - x1)
# dy0, dy1 = abs(cl_cent[1] - y0), abs(cl_cent[1] - y1)
# dxy = min(dx0, dx1, dy0, dy1)
# # Parameters used to estimate the fraction of cluster area inside the
# # frame if it spills outside of it.
# circarea_pars = (dxy, x0, x1, y0, y1, N_MC, rand_01_MC, cos_t, sin_t)
# This assumes that the tidal radius can not be larger than 'rt_max' times
# the estimated cluster radius.
rt_max = rt_max_f * cl_rad
# Tidal radius array. Used for integrating
rt_rang = np.linspace(0., rt_max, int(rt_max_f * N_integ))
# if ndim == 2:
# Dimensions: rc, rt
# Initial guesses.
rc_pos0 = np.random.uniform(.05 * rt_max, rt_max, nchains)
rt_pos0 = np.random.uniform(rc_pos0, rt_max, nchains)
pos0 = np.array([rc_pos0, rt_pos0]).T
# Stars inside the cut-out given by the 'rt_max' value.
xy_cent_dist = spatial.distance.cdist([cl_cent], xy)[0]
msk = xy_cent_dist <= rt_max
r_in = xy_cent_dist[msk]
# Fixed values
fd, N_memb = field_dens, n_memb_i
# elif KP_mode == 3:
# # Dimensions: fd, rc, rt
# ndim = 3
# # Initial guesses.
# fd_pos0 = np.random.uniform(.5 * fd, 2. * fd, nchains)
# rc_pos0 = np.random.uniform(.05 * rt_max, rt_max, nchains)
# rt_pos0 = np.random.uniform(rc_pos0, rt_max, nchains)
# pos0 = np.array([fd_pos0, rc_pos0, rt_pos0]).T
# # Stars inside the cut-out given by the 'rt_max' value.
# xy_cent_dist = spatial.distance.cdist([cl_cent], xy)[0]
# msk = xy_cent_dist <= rt_max
# r_in = xy_cent_dist[msk]
# fd, N_memb, fd_max = None, None, r_in.size / rt_max**2
# elif ndim == 4:
# # Dimensions: cent_x, cent_y, rc, rt
# ndim = 4
# # Initial guesses.
# cx_pos0 = np.random.uniform(
# cx - .9 * cl_rad, cx + .9 * cl_rad, nchains)
# cy_pos0 = np.random.uniform(
# cy - .9 * cl_rad, cy + .9 * cl_rad, nchains)
# rc_pos0 = np.random.uniform(.05 * rt_max, rt_max, nchains)
# rt_pos0 = np.random.uniform(rc_pos0, rt_max, nchains)
# pos0 = np.array([cx_pos0, cy_pos0, rc_pos0, rt_pos0]).T
# r_in = []
args = {
'rt_max': rt_max,
'rt_rang': rt_rang,
'fd': fd,
'N_memb': N_memb,
'r_in': r_in
}
# emcee sampler
sampler = ensemble.EnsembleSampler(nchains,
ndim,
lnprob,
kwargs=args,
moves=mv)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
tau_index, autocorr_vals, afs = 0, np.empty(nruns), np.empty(nruns)
old_tau = np.inf
for i, (pos, prob,
stat) in enumerate(sampler.sample(pos0, iterations=nruns)):
# Every X steps
if i % KP_steps and i < (nruns - 1):
continue
afs[tau_index] = np.mean(sampler.acceptance_fraction)
tau = np.mean(sampler.get_autocorr_time(tol=0))
autocorr_vals[tau_index] = tau
tau_index += 1
# Check convergence
converged = tau * (N_conv / nchains) < i * nburn
converged &= np.abs(old_tau - tau) / tau < tau_stable
if converged:
print("")
break
old_tau = tau
update_progress.updt(nruns, i + 1)
KP_mean_afs = afs[:tau_index]
KP_tau_autocorr = autocorr_vals[:tau_index]
nburn = int(i * nburn)
samples = sampler.get_chain(discard=nburn, flat=True)
# if ndim == 4:
# cx, cy, rc, rt = np.mean(samples, 0)
# print(cx, cy)
# e_cx, e_cy, e_rc, e_rt = np.percentile(samples, (16, 84), 0).T
# if ndim == 2:
rc, rt = np.mean(samples, 0)
rc_16, rc_50, rc_84, rt_16, rt_50, rt_84 = np.percentile(
samples, (16, 50, 84), 0).T.flatten()
# Mode and KDE to plot
# This simulates the 'fundam_params and 'varIdxs' arrays.
fp, vi = [[-np.inf, np.inf], [-np.inf, np.inf]], [0, 1]
KP_Bys_mode, KP_Bayes_kde = modeKDE(fp, vi, samples.T)
# Store: 16, median, 84, mean, mode
KP_Bys_rc = np.array([rc_16, rc_50, rc_84, rc, KP_Bys_mode[0]])
KP_Bys_rt = np.array([rt_16, rt_50, rt_84, rt, KP_Bys_mode[1]])
# Effective sample size
KP_ESS = samples.shape[0] / np.mean(sampler.get_autocorr_time(tol=0))
# For plotting, (nsteps, nchains, ndim)
KP_samples = sampler.get_chain()
# Central density, for plotting.
# if ndim == 4:
# N_memb = rMmembN(
# fd, rt_max, rt, xy, area_tot, (cx, cy), circarea_pars)[-1]
KP_cd = centDens(N_memb, rc, rt, rt_rang)
return KP_cd, KP_steps, KP_mean_afs, KP_tau_autocorr, KP_ESS, KP_samples,\
KP_Bys_rc, KP_Bys_rt, KP_Bayes_kde
def test_uniform_de_snooker(**kwargs):
_test_uniform(moves.DESnookerMove(), **kwargs)
def fit_King_prof(nchains,
nruns,
nburn,
x,
y,
cl_cent,
field_dens,
cl_rad,
n_memb_i,
rt_max_f,
N_integ=1000,
N_conv=1000,
tau_stable=0.05):
"""
rt_max_f: factor that caps the maximum tidal radius, given the previously
estimated cluster radius.
"""
from emcee import ensemble
from emcee import moves
# HARDCODED ##########################
# Move used by emcee
mv = [
(moves.DESnookerMove(), 0.1),
(moves.DEMove(), 0.9 * 0.9),
(moves.DEMove(gamma0=1.0), 0.9 * 0.1),
]
# mv = moves.StretchMove()
# mv = moves.KDEMove()
# Steps to store Bayes params.
KP_steps = int(nruns * .01)
# Field density and estimated number of members (previously
# obtained)
fd = field_dens
# Fix N_memb
N_memb = n_memb_i
# Estimate N_memb with each sampler step
# N_memb = None
# Select the number of parameters to fit:
# ndim = 2 fits (rc, rt)
# ndim = 4 fits (rc, rt, ecc, theta)
ndim = 2
# HARDCODED ##########################
# The tidal radius can not be larger than 'rt_max' times the estimated
# "optimal" cluster radius. Used as a prior.
rt_max = rt_max_f * cl_rad
# Tidal radius array. Used for integrating
rt_rang = np.linspace(0., rt_max, int(rt_max_f * N_integ))
# Initial positions for the sampler.
if ndim == 2:
# Dimensions: rc, rt
rc_pos0 = np.random.uniform(.05 * rt_max, rt_max, nchains)
rt_pos0 = np.random.uniform(rc_pos0, rt_max, nchains)
pos0 = np.array([rc_pos0, rt_pos0]).T
elif ndim == 4:
# Dimensions: rc, rt, ecc, theta
rc_pos0 = np.random.uniform(.05 * rt_max, rt_max, nchains)
rt_pos0 = np.random.uniform(rc_pos0, rt_max, nchains)
ecc = np.random.uniform(0., 1., nchains)
theta = np.random.uniform(0., np.pi, nchains)
pos0 = np.array([rc_pos0, rt_pos0, ecc, theta]).T
# Identify stars inside the cut-out given by the 'rt_max' value. Only these
# stars will be processed below.
xy = np.array((x, y)).T
xy_cent_dist = spatial.distance.cdist([cl_cent], xy)[0]
msk = xy_cent_dist <= rt_max
xy_in = xy[msk].T
r_in = xy_cent_dist[msk]
args = {
'ndim': ndim,
'rt_max': rt_max,
'cl_cent': cl_cent,
'fd': fd,
'N_memb': N_memb,
'rt_rang': rt_rang,
'xy_in': xy_in,
'r_in': r_in
}
# emcee sampler
sampler = ensemble.EnsembleSampler(nchains,
ndim,
lnprob,
kwargs=args,
moves=mv)
# Run the smpler hiding some warnings
with warnings.catch_warnings():
warnings.simplefilter("ignore")
tau_index, autocorr_vals, afs = 0, np.empty(nruns), np.empty(nruns)
old_tau = np.inf
for i, (pos, prob,
stat) in enumerate(sampler.sample(pos0, iterations=nruns)):
# Every X steps
if i % KP_steps and i < (nruns - 1):
continue
afs[tau_index] = np.mean(sampler.acceptance_fraction)
tau = np.mean(sampler.get_autocorr_time(tol=0))
autocorr_vals[tau_index] = tau
tau_index += 1
# Check convergence
converged = tau * (N_conv / nchains) < i * nburn
converged &= np.abs(old_tau - tau) / tau < tau_stable
if converged:
print("")
break
old_tau = tau
update_progress.updt(nruns, i + 1)
KP_mean_afs = afs[:tau_index]
KP_tau_autocorr = autocorr_vals[:tau_index]
# Remove burn-in
nburn = int(i * nburn)
samples = sampler.get_chain(discard=nburn, flat=True)
# Extract mean, median, mode, 16th, 84th percentiles for each parameter
rc, rt = np.mean(samples[:, :2], 0)
rc_16, rc_50, rc_84, rt_16, rt_50, rt_84 = np.percentile(
samples[:, :2], (16, 50, 84), 0).T.flatten()
if ndim == 2:
ecc, theta = 0., 0.
ecc_16, ecc_50, ecc_84, theta_16, theta_50, theta_84 =\
[np.array([np.nan] * 3) for _ in range(6)]
# Mode and KDE to plot
# This simulates the 'fundam_params and 'varIdxs' arrays.
fp, vi = [[-np.inf, np.inf], [-np.inf, np.inf]], [0, 1]
KP_Bys_mode, KP_Bayes_kde = modeKDE(fp, vi, samples.T)
KP_Bys_mode += [0., 0.]
KP_Bayes_kde += [[], []]
elif ndim == 4:
ecc = np.mean(samples[:, 2], 0)
theta = circmean(samples[:, 3] * u.rad).value
# Beware: the median and percentiles for theta might not be
# properly defined.
ecc_16, ecc_50, ecc_84, theta_16, theta_50, theta_84 =\
np.percentile(samples[:, 2:], (16, 50, 84), 0).T.flatten()
# Estimate the mode
fp, vi = [[-np.inf, np.inf], [-np.inf, np.inf], [-np.inf, np.inf],
[-np.inf, np.inf]], [0, 1, 2, 3]
KP_Bys_mode, KP_Bayes_kde = modeKDE(fp, vi, samples.T)
# Store: 16th, median, 84th, mean, mode
KP_Bys_rc = np.array([rc_16, rc_50, rc_84, rc, KP_Bys_mode[0]])
KP_Bys_rt = np.array([rt_16, rt_50, rt_84, rt, KP_Bys_mode[1]])
KP_Bys_ecc = np.array([ecc_16, ecc_50, ecc_84, ecc, KP_Bys_mode[2]])
KP_Bys_theta = np.array(
[theta_16, theta_50, theta_84, theta, KP_Bys_mode[3]])
# Effective sample size
KP_ESS = samples.shape[0] / np.mean(sampler.get_autocorr_time(tol=0))
# For plotting, (nsteps, nchains, ndim)
KP_samples = sampler.get_chain()
# Central density, for plotting. Use mean values for all the parameters.
KP_cd = lnlike((rc, rt, ecc, theta), ndim, rt_max, cl_cent, fd, N_memb,
xy_in, r_in, rt_rang, True)
return KP_cd, KP_steps, KP_mean_afs, KP_tau_autocorr, KP_ESS, KP_samples,\
KP_Bys_rc, KP_Bys_rt, KP_Bys_ecc, KP_Bys_theta, KP_Bayes_kde
def test_normal_de_snooker(**kwargs):
kwargs["nsteps"] = 4000
_test_normal(moves.DESnookerMove(), **kwargs)
def test_normal_de_snooker(**kwargs):
_test_normal(moves.DESnookerMove(), **kwargs)