def input_skymap(order1, d_order, fraction):
"""Construct a test multi-resolution sky map, with values that are
proportional to the NESTED pixel index.
To make the test more interesting by mixing together multiple resolutions,
part of the sky map is refined to a higher order.
Parameters
----------
order1 : int
The HEALPix resolution order.
d_order : int
The increase in orer for part of the sky map.
fraction : float
The fraction of the original pixels to refine.
"""
order2 = order1 + d_order
npix1 = ah.nside_to_npix(ah.level_to_nside(order1))
npix2 = ah.nside_to_npix(ah.level_to_nside(order2))
ipix1 = np.arange(npix1)
ipix2 = np.arange(npix2)
# Create a random sky map.
area = ah.nside_to_pixel_area(ah.level_to_nside(order1)).to_value(u.sr)
probdensity = np.random.uniform(0, 1, npix1)
prob = probdensity * area
normalization = prob.sum()
prob /= normalization
probdensity /= normalization
distmean = np.random.uniform(100, 110, npix1)
diststd = np.random.uniform(0, 1 / np.sqrt(3) - 0.1, npix1) * distmean
distmu, distsigma, distnorm = moments_to_parameters(distmean, diststd)
assert np.all(np.isfinite(distmu))
data1 = table.Table({
'UNIQ': moc.nest2uniq(order1, ipix1),
'PROBDENSITY': probdensity,
'DISTMU': distmu,
'DISTSIGMA': distsigma,
'DISTNORM': distnorm
})
# Add some upsampled pixels.
data2 = table.Table(np.repeat(data1, npix2 // npix1))
data2['UNIQ'] = moc.nest2uniq(order2, ipix2)
n = int(npix1 * (1 - fraction))
result = table.vstack((data1[:n], data2[n * npix2 // npix1:]))
# Add marginal distance mean and standard deviation.
rbar = (prob * distmean).sum()
r2bar = (prob * (np.square(diststd) + np.square(distmean))).sum()
result.meta['distmean'] = rbar
result.meta['diststd'] = np.sqrt(r2bar - np.square(rbar))
return result
def test_rasterize_downsample(order_in, d_order_in, fraction_in, order_out):
npix_in = ah.nside_to_npix(ah.level_to_nside(order_in))
npix_out = ah.nside_to_npix(ah.level_to_nside(order_out))
skymap_in = input_skymap(order_in, d_order_in, fraction_in)
skymap_out = moc.rasterize(skymap_in, order_out)
assert len(skymap_out) == npix_out
reps = npix_in // npix_out
expected = np.mean(np.arange(npix_in).reshape(-1, reps), axis=1)
np.testing.assert_array_equal(skymap_out['VALUE'], expected)
def test_rasterize_upsample(order_in, d_order_in, fraction_in, order_out):
npix_in = ah.nside_to_npix(ah.level_to_nside(order_in))
npix_out = ah.nside_to_npix(ah.level_to_nside(order_out))
skymap_in = input_skymap(order_in, d_order_in, fraction_in)
skymap_out = moc.rasterize(skymap_in, order_out)
assert len(skymap_out) == npix_out
ipix = np.arange(npix_in)
reps = npix_out // npix_in
for i in range(reps):
np.testing.assert_array_equal(skymap_out['VALUE'][i::reps], ipix)
def test_from_valued_healpix_cells_bayestar():
from astropy.io import fits
fits_image_filename = './resources/bayestar.multiorder.fits'
with fits.open(fits_image_filename) as hdul:
hdul.info()
hdul[1].columns
data = hdul[1].data
uniq = data['UNIQ']
probdensity = data['PROBDENSITY']
import astropy_healpix as ah
import astropy.units as u
level, ipix = ah.uniq_to_level_ipix(uniq)
area = ah.nside_to_pixel_area(ah.level_to_nside(level)).to_value(
u.steradian)
prob = probdensity * area
cumul_to = np.linspace(0.01, 2.0, num=10)
for b in cumul_to:
MOC.from_valued_healpix_cells(uniq,
prob,
12,
cumul_from=0.0,
cumul_to=b)
def main(args=None):
p = parser()
opts = parser().parse_args(args)
import astropy_healpix as ah
import astropy.units as u
try:
from mocpy import MOC
except ImportError:
p.error('This command-line tool requires mocpy >= 0.8.2. '
'Please install it by running "pip install mocpy".')
from ..io import read_sky_map
# Read multi-order sky map
skymap = read_sky_map(opts.input.name, moc=True)
uniq = skymap['UNIQ']
probdensity = skymap['PROBDENSITY']
level, ipix = ah.uniq_to_level_ipix(uniq)
area = ah.nside_to_pixel_area(
ah.level_to_nside(level)).to_value(u.steradian)
prob = probdensity * area
# Create MOC
contour_decimal = opts.contour / 100
moc = MOC.from_valued_healpix_cells(
uniq, prob, cumul_from=0.0, cumul_to=contour_decimal)
# Write MOC
moc.write(opts.output, format='fits', overwrite=True)
def _reconstruct_nested_breadthfirst(m, extra):
m = np.asarray(m)
max_npix = len(m)
max_nside = ah.npix_to_nside(max_npix)
max_order = ah.nside_to_level(max_nside)
seen = np.zeros(max_npix, dtype=bool)
for order in range(max_order + 1):
nside = ah.level_to_nside(order)
npix = ah.nside_to_npix(nside)
skip = max_npix // npix
if skip > 1:
b = m.reshape(-1, skip)
a = b[:, 0].reshape(-1, 1)
b = b[:, 1:]
aseen = seen.reshape(-1, skip)
eq = ((a == b) | ((a != a) & (b != b))).all(1) & (~aseen).all(1)
else:
eq = ~seen
for ipix in np.flatnonzero(eq):
ipix0 = ipix * skip
ipix1 = (ipix + 1) * skip
seen[ipix0:ipix1] = True
if extra:
yield _HEALPixTreeVisitExtra(nside, max_nside, ipix, ipix0,
ipix1, m[ipix0])
else:
yield _HEALPixTreeVisit(nside, ipix)
def flat_bitmap(self):
"""Return flattened HEALPix representation."""
m = np.empty(ah.nside_to_npix(ah.level_to_nside(self.order)))
for nside, full_nside, ipix, ipix0, ipix1, samples in self.visit():
pixarea = ah.nside_to_pixel_area(nside).to_value(u.sr)
m[ipix0:ipix1] = len(samples) / pixarea
return m
def input_skymap(order1, d_order, fraction):
"""Construct a test multi-resolution sky map, with values that are
proportional to the NESTED pixel index.
To make the test more interesting by mixing together multiple resolutions,
part of the sky map is refined to a higher order.
Parameters
----------
order1 : int
The HEALPix resolution order.
d_order : int
The increase in orer for part of the sky map.
fraction : float
The fraction of the original pixels to refine.
"""
order2 = order1 + d_order
npix1 = ah.nside_to_npix(ah.level_to_nside(order1))
npix2 = ah.nside_to_npix(ah.level_to_nside(order2))
ipix1 = np.arange(npix1)
ipix2 = np.arange(npix2)
data1 = table.Table({
'UNIQ': moc.nest2uniq(order1, ipix1),
'VALUE': ipix1.astype(float),
'VALUE2': np.pi * ipix1.astype(float)
})
data2 = table.Table({
'UNIQ':
moc.nest2uniq(order2, ipix2),
'VALUE':
np.repeat(ipix1, npix2 // npix1).astype(float),
'VALUE2':
np.pi * np.repeat(ipix1, npix2 // npix1).astype(float)
})
n = int(npix1 * (1 - fraction))
return table.vstack((data1[:n], data2[n * npix2 // npix1:]))
def _build_moc_map(self):
pts = np.column_stack((self._grb_phi, self._grb_theta))
self._kde_map = Clustered2DSkyKDE(pts, jobs=12)
data = self._kde_map.as_healpix(top_nside=self._npix)
self._uniq = data["UNIQ"]
self._prob_density = data["PROBDENSITY"]
level, ipix = ah.uniq_to_level_ipix(self._uniq)
area = ah.nside_to_pixel_area(ah.level_to_nside(level)).to_value(
u.steradian)
self._prob = self._prob_density * area
def test_rasterize_default(order):
npix = ah.nside_to_npix(ah.level_to_nside(order))
skymap_in = input_skymap(order, 0, 0)
skymap_out = moc.rasterize(skymap_in)
assert len(skymap_out) == npix
from astropy import units as u
from astropy_healpix import (level_to_nside, nside_to_pixel_area,
uniq_to_level_ipix, HEALPix)
from mocpy import MOC
from sqlalchemy import BigInteger, Column, Index
from sqlalchemy.ext.declarative import declared_attr
from sqlalchemy.ext.hybrid import hybrid_property
from sqlalchemy.orm import relationship
from sqlalchemy.orm.mapper import Mapper
from sqlalchemy.sql.expression import func
LEVEL = MOC.HPY_MAX_NORDER
"""Base HEALPix resolution. This is the maximum HEALPix level that can be
stored in a signed 8-byte integer data type."""
HPX = HEALPix(nside=level_to_nside(LEVEL), order='nested', frame=ICRS())
"""HEALPix projection object."""
PIXEL_AREA = HPX.pixel_area.to_value(u.sr)
"""Native pixel area in steradians."""
class Point:
"""Mixin class for a table that stores a HEALPix multiresolution point."""
nested = Column(BigInteger,
index=True,
nullable=False,
comment=f'HEALPix nested index at nside=2**{LEVEL}')
fits_image_filename = './../../resources/bayestar.multiorder.fits'
with fits.open(fits_image_filename) as hdul:
hdul.info()
hdul[1].columns
data = hdul[1].data
uniq=data['UNIQ']
probdensity=data['PROBDENSITY']
import astropy_healpix as ah
import astropy.units as u
level, ipix = ah.uniq_to_level_ipix(uniq)
area = ah.nside_to_pixel_area(ah.level_to_nside(level)).to_value(u.steradian)
prob = probdensity * area
from mocpy import MOC
import numpy as np
cumul_to = np.linspace(0.5, 0.9, 5)[::-1]
colors = ['blue', 'green', 'yellow', 'orange', 'red']
mocs = [MOC.from_valued_healpix_cells(uniq, prob, cumul_to=c) for c in cumul_to]
from mocpy import World2ScreenMPL
from astropy.coordinates import Angle, SkyCoord
import astropy.units as u
# Plot the MOC using matplotlib
def crossmatch(sky_map,
coordinates=None,
contours=(),
areas=(),
modes=False,
cosmology=False):
"""Cross match a sky map with a catalog of points.
Given a sky map and the true right ascension and declination (in radians),
find the smallest area in deg^2 that would have to be searched to find the
source, the smallest posterior mass, and the angular offset in degrees from
the true location to the maximum (mode) of the posterior. Optionally, also
compute the areas of and numbers of modes within the smallest contours
containing a given total probability.
Parameters
----------
sky_map : :class:`astropy.table.Table`
A multiresolution sky map, as returned by
:func:`ligo.skymap.io.fits.read_sky_map` called with the keyword
argument ``moc=True``.
coordinates : :class:`astropy.coordinates.SkyCoord`, optional
The catalog of target positions to match against.
contours : :class:`tuple`, optional
Credible levels between 0 and 1. If this argument is present, then
calculate the areas and volumes of the 2D and 3D credible regions that
contain these probabilities. For example, for ``contours=(0.5, 0.9)``,
then areas and volumes of the 50% and 90% credible regions.
areas : :class:`tuple`, optional
Credible areas in square degrees. If this argument is present, then
calculate the probability contained in the 2D credible levels that have
these areas. For example, for ``areas=(20, 100)``, then compute the
probability within the smallest credible levels of 20 deg² and 100
deg², respectively.
modes : :class:`bool`, optional
If True, then enable calculation of the number of distinct modes or
islands of probability. Note that this option may be computationally
expensive.
cosmology : :class:`bool`, optional
If True, then search space by descending probability density per unit
comoving volume. If False, then search space by descending probability
per luminosity distance cubed.
Returns
-------
result : :class:`~ligo.skymap.postprocess.crossmatch.CrossmatchResult`
Notes
-----
This function is also be used for injection finding; see
:doc:`/tool/ligo_skymap_stats`.
Examples
--------
First, some imports:
>>> from astroquery.vizier import VizierClass
>>> from astropy.coordinates import SkyCoord
>>> from ligo.skymap.io import read_sky_map
>>> from ligo.skymap.postprocess import crossmatch
Next, retrieve the GLADE catalog using Astroquery and get the coordinates
of all its entries:
>>> vizier = VizierClass(
... row_limit=-1, columns=['GWGC', '_RAJ2000', '_DEJ2000', 'Dist'])
>>> cat, = vizier.get_catalogs('VII/281/glade2')
>>> coordinates = SkyCoord(cat['_RAJ2000'], cat['_DEJ2000'], cat['Dist'])
Load the multiresolution sky map for S190814bv:
>>> url = 'https://gracedb.ligo.org/api/superevents/S190814bv/files/bayestar.multiorder.fits'
>>> skymap = read_sky_map(url, moc=True)
Perform the cross match:
>>> result = crossmatch(skymap, coordinates)
Using the cross match results, we can list the galaxies within the 90%
credible volume:
>>> print(cat[result.searched_prob_vol < 0.9])
GWGC _RAJ2000 _DEJ2000 Dist
deg deg Mpc
---------- -------------------- -------------------- --------------------
NGC0171 9.3396699999999999 -19.9342460000000017 57.56212553960000
--- 20.2009090000000064 -31.1146050000000010 137.16022925600001
ESO540-003 8.9144679999999994 -20.1252980000000008 49.07809291930000
--- 10.6762720000000009 -21.7740819999999999 276.46938505499998
--- 13.5855169999999994 -23.5523850000000010 138.44550704800000
--- 20.6362969999999990 -29.9825149999999958 160.23313164900000
--- 13.1923879999999993 -22.9750179999999986 236.96795954500001
--- 11.7813630000000007 -24.3706470000000017 244.25031189699999
--- 19.1711120000000008 -31.4339490000000019 152.13614001400001
--- 13.6367060000000002 -23.4948789999999974 141.25162979500001
... ... ... ...
--- 11.3517000000000010 -25.8596999999999966 335.73800000000000
--- 11.2073999999999998 -25.7149000000000001 309.02999999999997
--- 11.1875000000000000 -25.7503999999999991 295.12099999999998
--- 10.8608999999999991 -25.6904000000000003 291.07200000000000
--- 10.6938999999999975 -25.6778300000000002 323.59399999999999
--- 15.4935000000000009 -26.0304999999999964 304.78899999999999
--- 15.2794000000000008 -27.0410999999999966 320.62700000000001
--- 14.8323999999999980 -27.0459999999999994 320.62700000000001
--- 14.5341000000000005 -26.0949000000000026 307.61000000000001
--- 23.1280999999999963 -31.1109199999999966 320.62700000000001
Length = 1479 rows
""" # noqa: E501
# Astropy coordinates that are constructed without distance have
# a distance field that is unity (dimensionless).
if coordinates is None:
true_ra = true_dec = true_dist = None
else:
# Ensure that coordinates are in proper frame and representation
coordinates = SkyCoord(coordinates,
representation_type=SphericalRepresentation,
frame=ICRS)
true_ra = coordinates.ra.rad
true_dec = coordinates.dec.rad
if np.any(coordinates.distance != 1):
true_dist = coordinates.distance.to_value(u.Mpc)
else:
true_dist = None
contours = np.asarray(contours)
# Sort the pixels by descending posterior probability.
sky_map = np.flipud(np.sort(sky_map, order='PROBDENSITY'))
# Find the pixel that contains the injection.
order, ipix = moc.uniq2nest(sky_map['UNIQ'])
max_order = np.max(order)
max_nside = ah.level_to_nside(max_order)
max_ipix = ipix << np.int64(2 * (max_order - order))
if true_ra is not None:
true_theta = 0.5 * np.pi - true_dec
true_phi = true_ra
true_pix = hp.ang2pix(max_nside, true_theta, true_phi, nest=True)
i = np.argsort(max_ipix)
true_idx = i[np.digitize(true_pix, max_ipix[i]) - 1]
# Find the angular offset between the mode and true locations.
mode_theta, mode_phi = hp.pix2ang(ah.level_to_nside(order[0]),
ipix[0],
nest=True)
if true_ra is None:
offset = np.nan
else:
offset = np.rad2deg(
angle_distance(true_theta, true_phi, mode_theta, mode_phi))
# Calculate the cumulative area in deg2 and the cumulative probability.
dA = moc.uniq2pixarea(sky_map['UNIQ'])
dP = sky_map['PROBDENSITY'] * dA
prob = np.cumsum(dP)
area = np.cumsum(dA) * np.square(180 / np.pi)
if true_ra is None:
searched_area = searched_prob = probdensity = np.nan
else:
# Find the smallest area that would have to be searched to find
# the true location.
searched_area = area[true_idx]
# Find the smallest posterior mass that would have to be searched to
# find the true location.
searched_prob = prob[true_idx]
# Find the probability density.
probdensity = sky_map['PROBDENSITY'][true_idx]
# Find the contours of the given credible levels.
contour_idxs = np.digitize(contours, prob) - 1
# For each of the given confidence levels, compute the area of the
# smallest region containing that probability.
contour_areas = np.interp(contours,
prob,
area,
left=0,
right=4 * 180**2 / np.pi).tolist()
# For each listed area, find the probability contained within the
# smallest credible region of that area.
area_probs = np.interp(areas, area, prob, left=0, right=1).tolist()
if modes:
if true_ra is None:
searched_modes = np.nan
else:
# Count up the number of modes in each of the given contours.
searched_modes = count_modes_moc(sky_map['UNIQ'], true_idx)
contour_modes = [
count_modes_moc(sky_map['UNIQ'], i) for i in contour_idxs
]
else:
searched_modes = np.nan
contour_modes = np.nan
# Distance stats now...
if 'DISTMU' in sky_map.dtype.names:
dP_dA = sky_map['PROBDENSITY']
mu = sky_map['DISTMU']
sigma = sky_map['DISTSIGMA']
norm = sky_map['DISTNORM']
# Set up distance grid.
n_r = 1000
distmean, _ = distance.parameters_to_marginal_moments(dP, mu, sigma)
max_r = 6 * distmean
if true_dist is not None and np.size(true_dist) != 0 \
and np.max(true_dist) > max_r:
max_r = np.max(true_dist)
d_r = max_r / n_r
# Calculate searched_prob_dist and contour_dists.
r = d_r * np.arange(1, n_r)
P_r = distance.marginal_cdf(r, dP, mu, sigma, norm)
if true_dist is None:
searched_prob_dist = np.nan
else:
searched_prob_dist = np.interp(true_dist, r, P_r, left=0, right=1)
if len(contours) == 0:
contour_dists = []
else:
lo, hi = np.interp(np.row_stack(
(0.5 * (1 - contours), 0.5 * (1 + contours))),
P_r,
r,
left=0,
right=np.inf)
contour_dists = (hi - lo).tolist()
# Calculate volume of each voxel, defined as the region within the
# HEALPix pixel and contained within the two centric spherical shells
# with radii (r - d_r / 2) and (r + d_r / 2).
dV = (np.square(r) + np.square(d_r) / 12) * d_r * dA.reshape(-1, 1)
# Calculate probability within each voxel.
dP = np.exp(-0.5 * np.square(
(r.reshape(1, -1) - mu.reshape(-1, 1)) / sigma.reshape(-1, 1))) * (
dP_dA * norm /
(sigma * np.sqrt(2 * np.pi))).reshape(-1, 1) * dV
dP[np.isnan(dP)] = 0 # Suppress invalid values
# Calculate probability density per unit volume.
if cosmology:
dV *= dVC_dVL_for_DL(r)
dP_dV = dP / dV
i = np.flipud(np.argsort(dP_dV.ravel()))
P_flat = np.cumsum(dP.ravel()[i])
V_flat = np.cumsum(dV.ravel()[i])
contour_vols = np.interp(contours,
P_flat,
V_flat,
left=0,
right=np.inf).tolist()
P = np.empty_like(P_flat)
V = np.empty_like(V_flat)
P[i] = P_flat
V[i] = V_flat
P = P.reshape(dP.shape)
V = V.reshape(dV.shape)
if true_dist is None:
searched_vol = searched_prob_vol = probdensity_vol = np.nan
else:
i_radec = true_idx
i_dist = np.digitize(true_dist, r) - 1
probdensity_vol = dP_dV[i_radec, i_dist]
searched_prob_vol = P[i_radec, i_dist]
searched_vol = V[i_radec, i_dist]
else:
searched_vol = searched_prob_vol = searched_prob_dist \
= probdensity_vol = np.nan
contour_dists = [np.nan] * len(contours)
contour_vols = [np.nan] * len(contours)
# Done.
return CrossmatchResult(searched_area, searched_prob, offset,
searched_modes, contour_areas, area_probs,
contour_modes, searched_prob_dist, contour_dists,
searched_vol, searched_prob_vol, contour_vols,
probdensity, probdensity_vol)
Multiresolution HEALPix trees
"""
import astropy_healpix as ah
from astropy import units as u
import numpy as np
import healpy as hp
import collections
import itertools
__all__ = ('HEALPIX_MACHINE_ORDER', 'HEALPIX_MACHINE_NSIDE', 'HEALPixTree',
'adaptive_healpix_histogram', 'interpolate_nested',
'reconstruct_nested')
# Maximum 64-bit HEALPix resolution.
HEALPIX_MACHINE_ORDER = 29
HEALPIX_MACHINE_NSIDE = ah.level_to_nside(HEALPIX_MACHINE_ORDER)
_HEALPixTreeVisitExtra = collections.namedtuple(
'HEALPixTreeVisit', 'nside full_nside ipix ipix0 ipix1 value')
_HEALPixTreeVisit = collections.namedtuple('HEALPixTreeVisit', 'nside ipix')
class HEALPixTree:
"""Data structure used internally by the function
adaptive_healpix_histogram()."""
def __init__(self,
samples,
max_samples_per_pixel,
max_order,
order=0,
