def localize_emcee(logl,
loglargs,
logp,
logpargs,
xmin,
xmax,
nside=-1,
chain_dump=None):
# Set up sampler
import emcee
from sky_area.sky_area_clustering import Clustered3DKDEPosterior
ntemps = 20
nwalkers = 100
nburnin = 1000
nthin = 10
niter = 10000 + nburnin
ndim = len(xmin)
sampler = emcee.PTSampler(ntemps=ntemps,
nwalkers=nwalkers,
dim=ndim,
logl=logl,
logp=logp,
loglargs=loglargs,
logpargs=logpargs)
# Draw initial state from multivariate uniform distribution
p0 = np.random.uniform(xmin, xmax, (ntemps, nwalkers, ndim))
# Collect samples. The .copy() is important because PTSampler.sample()
# reuses p on every iteration.
chain = np.vstack([
p[0, :, :].copy() for p, _, _ in itertools.islice(
sampler.sample(p0, iterations=niter, storechain=False), nburnin,
niter, nthin)
])
# Extract polar coordinates. For all likelihoodds, the first two parameters
# are ra, sin(dec).
theta = np.arccos(chain[:, 1])
phi = chain[:, 0]
dist = chain[:, 2]
ra = phi
dec = 0.5 * np.pi - theta
pts = np.column_stack((ra, dec, dist))
# Pass a random subset of 1000 points to the KDE, to save time.
pts = np.random.permutation(pts)[:1000, :]
ckde = Clustered3DKDEPosterior(pts)
_, nside, ipix = zip(*ckde._bayestar_adaptive_grid())
uniq = (4 * np.square(nside) + ipix).astype(np.uint64)
pts = np.transpose(hp.pix2vec(nside, ipix, nest=True))
datasets = [kde.dataset for kde in ckde.kdes]
inverse_covariances = [kde.inv_cov for kde in ckde.kdes]
weights = ckde.weights
# Compute marginal probability, conditional mean, and conditional
# standard deviation in all directions.
probdensity, distmean, diststd = np.transpose([
distance.cartesian_kde_to_moments(pt, datasets, inverse_covariances,
weights) for pt in pts
])
# Optionally save posterior sample chain to file.
# Read back in with np.load().
if chain_dump:
# Undo numerical conditioning of distances; convert back to Mpc
names = 'ra sin_dec distance cos_inclination twopsi time'.split(
)[:ndim]
np.save(chain_dump, np.rec.fromrecords(chain, names=names))
# Done!
return Table([uniq, probdensity, distmean, diststd],
names='UNIQ PROBDENSITY DISTMEAN DISTSTD'.split())
def emcee_sky_map(logl,
loglargs,
logp,
logpargs,
xmin,
xmax,
nside=-1,
kde=False,
chain_dump=None,
max_horizon=1.0):
# Set up sampler
import emcee
ntemps = 20
nwalkers = 100
nburnin = 1000
nthin = 10
niter = 10000 + nburnin
ndim = len(xmin)
sampler = emcee.PTSampler(ntemps=ntemps,
nwalkers=nwalkers,
dim=ndim,
logl=logl,
logp=logp,
loglargs=loglargs,
logpargs=logpargs)
# Draw initial state from multivariate uniform distribution
p0 = np.random.uniform(xmin, xmax, (ntemps, nwalkers, ndim))
# Collect samples. The .copy() is important because PTSampler.sample()
# reuses p on every iteration.
chain = np.vstack([
p[0, :, :].copy() for p, _, _ in itertools.islice(
sampler.sample(p0, iterations=niter, storechain=False), nburnin,
niter, nthin)
])
# Extract polar coordinates. For all likelihoodds, the first two parameters
# are ra, sin(dec).
theta = np.arccos(chain[:, 1])
phi = chain[:, 0]
dist = chain[:, 2]
# Do adaptive histogram binning if the user has not selected the KDE,
# or if the user has selected the KDE but we need to guess the resolution.
if nside == -1 or not kde:
samples_per_bin = int(np.ceil(0.005 * len(chain)))
prob = postprocess.adaptive_healpix_histogram(theta,
phi,
samples_per_bin,
nside=nside,
nest=True)
# Determine what nside what actually used.
nside = hp.npix2nside(len(prob))
# Go one level finer, because the KDE will find more detail.
nside *= 2
if kde:
from sky_area.sky_area_clustering import Clustered3DKDEPosterior
ra = phi
dec = 0.5 * np.pi - theta
pts = np.column_stack((ra, dec, dist))
# Pass a random subset of 1000 points to the KDE, to save time.
pts = np.random.permutation(pts)[:1000, :]
prob = Clustered3DKDEPosterior(pts).as_healpix(nside)
# Optionally save posterior sample chain to file.
# Read back in with np.load().
if chain_dump:
# Undo numerical conditioning of distances; convert back to Mpc
chain[:, 2] *= max_horizon
names = 'ra sin_dec distance cos_inclination twopsi time'.split(
)[:ndim]
np.save(chain_dump, np.rec.fromrecords(chain, names=names))
# Done!
return prob