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 _interpolate_level(m):
"""Recursive multi-resolution interpolation. Modifies `m` in place."""
# Determine resolution.
npix = len(m)
if npix > 12:
# Determine which pixels comprise multi-pixel tiles.
ipix = np.flatnonzero((m[0::4] == m[1::4]) & (m[0::4] == m[2::4])
& (m[0::4] == m[3::4]))
if len(ipix):
ipix = 4 * ipix + np.expand_dims(np.arange(4, dtype=np.intp), 1)
ipix = ipix.T.ravel()
nside = ah.npix_to_nside(npix)
# Downsample.
m_lores = hp.ud_grade(m,
nside // 2,
order_in='NESTED',
order_out='NESTED')
# Interpolate recursively.
_interpolate_level(m_lores)
# Record interpolated multi-pixel tiles.
m[ipix] = hp.get_interp_val(m_lores,
*hp.pix2ang(nside, ipix, nest=True),
nest=True)
def test_combine(tmpdir):
"""Test ligo-skymap-combine."""
fn1 = str(tmpdir / 'skymap1.fits.gz')
fn2 = str(tmpdir / 'skymap2.fits.gz')
fn3 = str(tmpdir / 'joint_skymap.fits.gz')
# generate a hemisphere of constant probability
nside1 = 32
npix1 = ah.nside_to_npix(nside1)
m1 = np.zeros(npix1)
disc_idx = hp.query_disc(nside1, (1, 0, 0), np.pi / 2)
m1[disc_idx] = 1
m1 /= m1.sum()
hp.write_map(fn1,
m1,
column_names=['PROBABILITY'],
extra_header=[('INSTRUME', 'X1')])
# generate another hemisphere of constant probability
# but with higher resolution and rotated 90 degrees
nside2 = 64
npix2 = ah.nside_to_npix(nside2)
m2 = np.zeros(npix2)
disc_idx = hp.query_disc(nside2, (0, 1, 0), np.pi / 2)
m2[disc_idx] = 1
m2 /= m2.sum()
hp.write_map(fn2,
m2,
column_names=['PROBABILITY'],
extra_header=[('INSTRUME', 'Y1')])
run_entry_point('ligo-skymap-combine', fn1, fn2, fn3)
m3 = hp.read_map(fn3, nest=True)
npix3 = len(m3)
nside3 = ah.npix_to_nside(npix3)
pix_area3 = ah.nside_to_pixel_area(nside3).to_value(u.sr)
# resolution must match the highest original resolution
assert npix3 == npix2
# probability must be normalized to 1
assert m3.sum() == pytest.approx(1)
# support must be ¼ of the sphere
tolerance = 10 * ah.nside_to_pixel_area(nside1).to_value(u.sr)
assert sum(m3 > 0) * pix_area3 == pytest.approx(np.pi, abs=tolerance)
# generate a BAYESTAR-like map with mock distance information
d_mu = np.zeros_like(m1)
d_sigma = np.ones_like(m1)
d_norm = np.ones_like(m1)
io.write_sky_map(fn1, [m1, d_mu, d_sigma, d_norm])
run_entry_point('ligo-skymap-combine', fn1, fn2, fn3)
m3, meta3 = io.read_sky_map(fn3, nest=True, distances=True)
# check that marginal distance moments match what was simulated
mean, std, _ = distance.parameters_to_moments(d_mu[0], d_sigma[0])
assert meta3['distmean'] == pytest.approx(mean)
assert meta3['diststd'] == pytest.approx(std)
def main(args=None):
opts = parser().parse_args(args)
# Late imports
from ..io import fits
import astropy_healpix as ah
from astropy.coordinates import SkyCoord
from astropy.table import Table
from astropy import units as u
import healpy as hp
import numpy as np
prob, meta = fits.read_sky_map(opts.input.name, nest=None)
npix = len(prob)
nside = ah.npix_to_nside(npix)
ipix = np.arange(npix)
ra, dec = hp.pix2ang(nside, ipix, lonlat=True, nest=meta['nest'])
coord = SkyCoord(ra * u.deg, dec * u.deg)
table = Table({
'prob': prob,
'constellation': coord.get_constellation()
},
copy=False)
table = table.group_by('constellation').groups.aggregate(np.sum)
table.sort('prob')
table.reverse()
table.write(opts.output, format='ascii.tab')
def posterior_mean(prob, nest=False):
npix = len(prob)
nside = ah.npix_to_nside(npix)
xyz = hp.pix2vec(nside, np.arange(npix), nest=nest)
mean_xyz = np.average(xyz, axis=1, weights=prob)
pos = SkyCoord(*mean_xyz, representation_type=CartesianRepresentation)
pos.representation_type = UnitSphericalRepresentation
return pos
def principal_axes(prob, distmu, distsigma, nest=False):
npix = len(prob)
nside = ah.npix_to_nside(npix)
good = np.isfinite(prob) & np.isfinite(distmu) & np.isfinite(distsigma)
ipix = np.flatnonzero(good)
distmean, diststd, _ = parameters_to_moments(distmu[good], distsigma[good])
mass = prob[good] * (np.square(diststd) + np.square(distmean))
xyz = np.asarray(hp.pix2vec(nside, ipix, nest=nest))
cov = np.dot(xyz * mass, xyz.T)
L, V = np.linalg.eigh(cov)
if np.linalg.det(V) < 0:
V = -V
return V
def count_modes(m, nest=False):
"""Count the number of modes in a binary HEALPix image by repeatedly
applying the flood-fill algorithm.
WARNING: The input array is clobbered in the process.
"""
npix = len(m)
nside = ah.npix_to_nside(npix)
for nmodes in range(npix):
nonzeroipix = np.flatnonzero(m)
if len(nonzeroipix):
flood_fill(nside, nonzeroipix[0], m, nest=nest)
else:
break
return nmodes
def main(args=None):
opts = parser().parse_args(args)
# Late imports
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams
from ..io import fits
from .. import plot
from .. import postprocess
import astropy_healpix as ah
from astropy.coordinates import SkyCoord
from astropy.time import Time
from astropy import units as u
skymap, metadata = fits.read_sky_map(opts.input.name, nest=None)
nside = ah.npix_to_nside(len(skymap))
# Convert sky map from probability to probability per square degree.
deg2perpix = ah.nside_to_pixel_area(nside).to_value(u.deg**2)
probperdeg2 = skymap / deg2perpix
axes_args = {}
if opts.geo:
axes_args['projection'] = 'geo'
obstime = Time(metadata['gps_time'], format='gps').utc.isot
axes_args['obstime'] = obstime
else:
axes_args['projection'] = 'astro'
axes_args['projection'] += ' ' + opts.projection
if opts.projection_center is not None:
axes_args['center'] = SkyCoord(opts.projection_center)
if opts.zoom_radius is not None:
axes_args['radius'] = opts.zoom_radius
ax = plt.axes(**axes_args)
ax.grid()
# Plot sky map.
vmax = probperdeg2.max()
img = ax.imshow_hpx((probperdeg2, 'ICRS'),
nested=metadata['nest'],
vmin=0.,
vmax=vmax)
# Add colorbar.
if opts.colorbar:
cb = plot.colorbar(img)
cb.set_label(r'prob. per deg$^2$')
# Add contours.
if opts.contour:
cls = 100 * postprocess.find_greedy_credible_levels(skymap)
cs = ax.contour_hpx((cls, 'ICRS'),
nested=metadata['nest'],
colors='k',
linewidths=0.5,
levels=opts.contour)
fmt = r'%g\%%' if rcParams['text.usetex'] else '%g%%'
plt.clabel(cs, fmt=fmt, fontsize=6, inline=True)
# Add continents.
if opts.geo:
plt.plot(*plot.coastlines(),
color='0.5',
linewidth=0.5,
transform=ax.get_transform('world'))
radecs = opts.radec
if opts.inj_database:
query = '''SELECT DISTINCT longitude, latitude FROM sim_inspiral AS si
INNER JOIN coinc_event_map AS cm1
ON (si.simulation_id = cm1.event_id)
INNER JOIN coinc_event_map AS cm2
ON (cm1.coinc_event_id = cm2.coinc_event_id)
WHERE cm2.event_id = ?
AND cm1.table_name = 'sim_inspiral'
AND cm2.table_name = 'coinc_event'
'''
(ra,
dec), = opts.inj_database.execute(query,
(metadata['objid'], )).fetchall()
radecs.append(np.rad2deg([ra, dec]).tolist())
# Add markers (e.g., for injections or external triggers).
for ra, dec in radecs:
ax.plot_coord(SkyCoord(ra, dec, unit='deg'),
'*',
markerfacecolor='white',
markeredgecolor='black',
markersize=10)
# Add a white outline to all text to make it stand out from the background.
plot.outline_text(ax)
if opts.annotate:
text = []
try:
objid = metadata['objid']
except KeyError:
pass
else:
text.append('event ID: {}'.format(objid))
if opts.contour:
pp = np.round(opts.contour).astype(int)
ii = np.round(
np.searchsorted(np.sort(cls), opts.contour) *
deg2perpix).astype(int)
for i, p in zip(ii, pp):
# FIXME: use Unicode symbol instead of TeX '$^2$'
# because of broken fonts on Scientific Linux 7.
text.append('{:d}% area: {:,d} deg²'.format(p, i))
ax.text(1, 1, '\n'.join(text), transform=ax.transAxes, ha='right')
# Show or save output.
opts.output()
def main(args=None):
args = parser().parse_args(args)
import numpy as np
import astropy_healpix as ah
from astropy.io import fits
from astropy.time import Time
import healpy as hp
from ..distance import parameters_to_marginal_moments
from ..io import read_sky_map, write_sky_map
input_skymaps = []
dist_mu = dist_sigma = dist_norm = None
for input_file in args.input:
with fits.open(input_file) as hdus:
header = hdus[0].header.copy()
header.extend(hdus[1].header)
has_distance = 'DISTMU' in hdus[1].columns.names
data, meta = read_sky_map(hdus, nest=True, distances=has_distance)
if has_distance:
if dist_mu is not None:
raise RuntimeError('only one input localization can have'
' distance information')
dist_mu = data[1]
dist_sigma = data[2]
dist_norm = data[3]
else:
data = (data, )
nside = ah.npix_to_nside(len(data[0]))
input_skymaps.append((nside, data[0], meta, header))
max_nside = max(x[0] for x in input_skymaps)
# upsample sky posteriors to maximum resolution and combine them
combined_prob = None
for nside, prob, _, _ in input_skymaps:
if nside < max_nside:
prob = hp.ud_grade(prob,
max_nside,
order_in='NESTED',
order_out='NESTED')
if combined_prob is None:
combined_prob = np.ones_like(prob)
combined_prob *= prob
# normalize joint posterior
norm = combined_prob.sum()
if norm == 0:
raise RuntimeError('input sky localizations are disjoint')
combined_prob /= norm
out_kwargs = {'gps_creation_time': Time.now().gps, 'nest': True}
if args.origin is not None:
out_kwargs['origin'] = args.origin
# average the various input event times
input_gps = [x[2]['gps_time'] for x in input_skymaps if 'gps_time' in x[2]]
if input_gps:
out_kwargs['gps_time'] = np.mean(input_gps)
# combine instrument tags
out_instruments = set()
for x in input_skymaps:
if 'instruments' in x[2]:
out_instruments.update(x[2]['instruments'])
out_kwargs['instruments'] = ','.join(out_instruments)
# update marginal distance posterior, if available
if dist_mu is not None:
if ah.npix_to_nside(len(dist_mu)) < max_nside:
dist_mu = hp.ud_grade(dist_mu,
max_nside,
order_in='NESTED',
order_out='NESTED')
dist_sigma = hp.ud_grade(dist_sigma,
max_nside,
order_in='NESTED',
order_out='NESTED')
dist_norm = hp.ud_grade(dist_norm,
max_nside,
order_in='NESTED',
order_out='NESTED')
distmean, diststd = parameters_to_marginal_moments(
combined_prob, dist_mu, dist_sigma)
out_data = (combined_prob, dist_mu, dist_sigma, dist_norm)
out_kwargs['distmean'] = distmean
out_kwargs['diststd'] = diststd
else:
out_data = combined_prob
# save input headers in output history
out_kwargs['HISTORY'] = []
for i, x in enumerate(input_skymaps):
out_kwargs['HISTORY'].append('')
out_kwargs['HISTORY'].append(
'Headers of HDUs 0 and 1 of input file {:d}:'.format(i))
out_kwargs['HISTORY'].append('')
out_kwargs['HISTORY'] += [
'{} = {}'.format(k, v) for k, v in x[3].items()
]
write_sky_map(args.output, out_data, **out_kwargs)
def healpix_to_image(healpix_data,
coord_system_in,
wcs_out,
shape_out,
order='bilinear',
nested=False):
"""
Convert image in HEALPIX format to a normal FITS projection image (e.g.
CAR or AIT).
Parameters
----------
healpix_data : `numpy.ndarray`
HEALPIX data array
coord_system_in : str or `~astropy.coordinates.BaseCoordinateFrame`
The coordinate system for the input HEALPIX data, as an Astropy
coordinate frame or corresponding string alias (e.g. ``'icrs'`` or
``'galactic'``)
wcs_out : `~astropy.wcs.WCS`
The WCS of the output array
shape_out : tuple
The shape of the output array
order : int or str, optional
The order of the interpolation (if ``mode`` is set to
``'interpolation'``). This can be either one of the following strings:
* 'nearest-neighbor'
* 'bilinear'
or an integer. A value of ``0`` indicates nearest neighbor
interpolation.
nested : bool
The order of the healpix_data, either nested or ring. Stored in
FITS headers in the ORDERING keyword.
Returns
-------
reprojected_data : `numpy.ndarray`
HEALPIX image resampled onto the reference image
footprint : `~numpy.ndarray`
Footprint of the input array in the output array. Values of 0 indicate
no coverage or valid values in the input image, while values of 1
indicate valid values.
"""
healpix_data = np.asarray(healpix_data, dtype=float)
# Look up lon, lat of pixels in reference system
yinds, xinds = np.indices(shape_out)
lon_out, lat_out = wcs_out.wcs_pix2world(xinds, yinds, 0)
# Convert between celestial coordinates
coord_system_in = parse_coord_system(coord_system_in)
with np.errstate(invalid='ignore'):
lon_in, lat_in = convert_world_coordinates(
lon_out, lat_out, wcs_out, (coord_system_in, u.deg, u.deg))
lon_in = u.Quantity(lon_in, unit=u.deg, copy=False)
lat_in = u.Quantity(lat_in, unit=u.deg, copy=False)
if isinstance(order, six.string_types):
order = ORDER[order]
nside = npix_to_nside(len(healpix_data))
hp = HEALPix(nside=nside, order='nested' if nested else 'ring')
if order == 1:
data = hp.interpolate_bilinear_lonlat(lon_in, lat_in, healpix_data)
elif order == 0:
ipix = hp.lonlat_to_healpix(lon_in, lat_in)
data = healpix_data[ipix]
else:
raise ValueError(
"Only nearest-neighbor and bilinear interpolation are supported")
footprint = np.ones(data.shape, bool)
return data, footprint
def gsm_sky_model(freqs, resolution="hi", nside=None):
"""
Return a pyradiosky SkyModel object populated with a Global Sky Model datacube in
healpix format.
Parameters
----------
freqs : array_like
Frequency array, in Hz.
resolution : str, optional
Whether to use the high or low resolution pygdsm maps. Options are 'hi' or 'low'.
nside : int, optional
Healpix nside to up- or down-sample the GSM sky model to. Default: `None` (use the
default from `pygdsm`, which is 1024).
Returns
-------
sky_model : pyradiosky.SkyModel
SkyModel object.
"""
import pygdsm
# Initialise GSM object
gsm = pygdsm.GlobalSkyModel2016(data_unit="TRJ", resolution=resolution, freq_unit="Hz")
# Construct GSM datacube
hpmap = gsm.generate(freqs=freqs) # FIXME: nside=1024, ring ordering, galactic coords
hpmap_units = "K"
# Set nside or resample
nside_gsm = int(astropy_healpix.npix_to_nside(hpmap.shape[-1]))
if nside is None:
# Use default nside from pygdsm map
nside = nside_gsm
else:
# Transform to a user-selected nside
hpmap_new = np.zeros((hpmap.shape[0], astropy_healpix.nside_to_npix(nside)),
dtype=hpmap.dtype)
for i in range(hpmap.shape[0]):
hpmap_new[i,:] = hp.ud_grade(hpmap[i,:],
nside_out=nside,
order_in="RING",
order_out="RING")
hpmap = hpmap_new
# Get datacube properties
npix = astropy_healpix.nside_to_npix(nside)
indices = np.arange(npix)
history = "pygdsm.GlobalSkyModel2016, data_unit=TRJ, resolution=low, freq_unit=MHz"
freq = units.Quantity(freqs, "hertz")
# hmap is in K
stokes = units.Quantity(np.zeros((4, len(freq), len(indices))), hpmap_units)
stokes[0] = hpmap * units.Unit(hpmap_units)
# Construct pyradiosky SkyModel
sky_model = pyradiosky.SkyModel(
nside=nside,
hpx_inds=indices,
stokes=stokes,
spectral_type="full",
freq_array=freq,
history=history,
frame="galactic",
hpx_order="ring"
)
sky_model.healpix_interp_transform(frame='icrs', full_sky=True, inplace=True) # do coord transform
assert sky_model.component_type == "healpix"
return sky_model
def read_sky_map(filename, nest=False, distances=False, moc=False, **kwargs):
"""Read a LIGO/Virgo-type sky map and return a tuple of the HEALPix array
and a dictionary of metadata from the header.
Parameters
----------
filename: string
Path to the optionally gzip-compressed FITS file.
nest: bool, optional
If omitted or False, then detect the pixel ordering in the FITS file
and rearrange if necessary to RING indexing before returning.
If True, then detect the pixel ordering and rearrange if necessary to
NESTED indexing before returning.
If None, then preserve the ordering from the FITS file.
Regardless of the value of this option, the ordering used in the FITS
file is indicated as the value of the 'nest' key in the metadata
dictionary.
distances: bool, optional
If true, then read also read the additional HEALPix layers representing
the conditional mean and standard deviation of distance as a function
of sky location.
moc: bool, optional
If true, then preserve multi-order structure if present.
Examples
--------
Test that we can read a legacy IDL-compatible file
(https://bugs.ligo.org/redmine/issues/5168):
>>> import tempfile
>>> with tempfile.NamedTemporaryFile(suffix='.fits') as f:
... nside = 512
... npix = ah.nside_to_npix(nside)
... ipix_nest = np.arange(npix)
... hp.write_map(f.name, ipix_nest, nest=True, column_names=['PROB'])
... m, meta = read_sky_map(f.name)
... np.testing.assert_array_equal(m, hp.ring2nest(nside, ipix_nest))
"""
m = Table.read(filename, format='fits', **kwargs)
# Remove some keys that we do not need
for key in ('PIXTYPE', 'EXTNAME', 'NSIDE', 'FIRSTPIX', 'LASTPIX',
'INDXSCHM', 'MOCORDER'):
m.meta.pop(key, None)
if m.meta.pop('COORDSYS', 'C') != 'C':
raise ValueError('ligo.skymap only reads and writes sky maps in '
'equatorial coordinates.')
try:
value = m.meta.pop('ORDERING')
except KeyError:
pass
else:
if value == 'RING':
m.meta['nest'] = False
elif value == 'NESTED':
m.meta['nest'] = True
elif value == 'NUNIQ':
pass
else:
raise ValueError(
'ORDERING card in header has unknown value: {0}'.format(value))
for fits_key, rows in itertools.groupby(FITS_META_MAPPING,
lambda row: row[1]):
try:
value = m.meta.pop(fits_key)
except KeyError:
pass
else:
for row in rows:
key, _, _, _, from_fits = row
if from_fits is not None:
m.meta[key] = from_fits(value)
# FIXME: Fermi GBM HEALPix maps use the column name 'PROBABILITY',
# instead of the LIGO/Virgo convention of 'PROB'.
#
# Fermi may change to our convention in the future, but for now we
# rename the column.
if 'PROBABILITY' in m.colnames:
m.rename_column('PROBABILITY', 'PROB')
# For a long time, we produced files with a UNIQ column that was an
# unsigned integer. Cast it here to a signed integer so that the user
# can handle old or new sky maps the same way.
if 'UNIQ' in m.colnames:
m['UNIQ'] = m['UNIQ'].astype(np.int64)
if 'UNIQ' not in m.colnames:
m = Table([col.ravel() for col in m.columns.values()], meta=m.meta)
if 'UNIQ' in m.colnames and not moc:
from ..bayestar import rasterize
m = rasterize(m)
m.meta['nest'] = True
elif 'UNIQ' not in m.colnames and moc:
from ..bayestar import derasterize
if not m.meta['nest']:
npix = len(m)
nside = ah.npix_to_nside(npix)
m = m[hp.nest2ring(nside, np.arange(npix))]
m = derasterize(m)
m.meta.pop('nest', None)
if 'UNIQ' not in m.colnames:
npix = len(m)
nside = ah.npix_to_nside(npix)
if nest is None:
pass
elif m.meta['nest'] and not nest:
m = m[hp.ring2nest(nside, np.arange(npix))]
elif not m.meta['nest'] and nest:
m = m[hp.nest2ring(nside, np.arange(npix))]
if moc:
return m
elif distances:
return tuple(np.asarray(m[name])
for name in DEFAULT_NESTED_NAMES), m.meta
else:
return np.asarray(m[DEFAULT_NESTED_NAMES[0]]), m.meta
def write_sky_map(filename, m, **kwargs):
"""Write a gravitational-wave sky map to a file, populating the header
with optional metadata.
Parameters
----------
filename: str
Path to the optionally gzip-compressed FITS file.
m : `astropy.table.Table`, `numpy.array`
If a Numpy record array or astorpy.table.Table instance, and has a
column named 'UNIQ', then interpret the input as NUNIQ-style
multi-order map [1]_. Otherwise, interpret as a NESTED or RING ordered
map.
**kwargs
Additional metadata to add to FITS header. If m is an
`astropy.table.Table` instance, then the header is initialized from
both `m.meta` and `kwargs`.
References
----------
.. [1] Górski, K.M., Wandelt, B.D., Hivon, E., Hansen, F.K., & Banday, A.J.
2017. The HEALPix Primer. The Unique Identifier scheme.
http://healpix.sourceforge.net/html/intronode4.htm#SECTION00042000000000000000
Examples
--------
Test header contents:
>>> order = 9
>>> nside = 2 ** order
>>> npix = ah.nside_to_npix(nside)
>>> prob = np.ones(npix, dtype=np.float) / npix
>>> import tempfile
>>> from ligo.skymap import version
>>> with tempfile.NamedTemporaryFile(suffix='.fits') as f:
... write_sky_map(f.name, prob, nest=True,
... vcs_version='foo 1.0', vcs_revision='bar',
... build_date='2018-01-01T00:00:00')
... for card in fits.getheader(f.name, 1).cards:
... print(str(card).rstrip())
XTENSION= 'BINTABLE' / binary table extension
BITPIX = 8 / array data type
NAXIS = 2 / number of array dimensions
NAXIS1 = 8 / length of dimension 1
NAXIS2 = 3145728 / length of dimension 2
PCOUNT = 0 / number of group parameters
GCOUNT = 1 / number of groups
TFIELDS = 1 / number of table fields
TTYPE1 = 'PROB '
TFORM1 = 'D '
TUNIT1 = 'pix-1 '
PIXTYPE = 'HEALPIX ' / HEALPIX pixelisation
ORDERING= 'NESTED ' / Pixel ordering scheme: RING, NESTED, or NUNIQ
COORDSYS= 'C ' / Ecliptic, Galactic or Celestial (equatorial)
NSIDE = 512 / Resolution parameter of HEALPIX
INDXSCHM= 'IMPLICIT' / Indexing: IMPLICIT or EXPLICIT
VCSVERS = 'foo 1.0 ' / Software version
VCSREV = 'bar ' / Software revision (Git)
DATE-BLD= '2018-01-01T00:00:00' / Software build date
>>> uniq = moc.nest2uniq(np.uint8(order), np.arange(npix))
>>> probdensity = prob / hp.nside2pixarea(nside)
>>> moc_data = np.rec.fromarrays(
... [uniq, probdensity], names=['UNIQ', 'PROBDENSITY'])
>>> with tempfile.NamedTemporaryFile(suffix='.fits') as f:
... write_sky_map(f.name, moc_data,
... vcs_version='foo 1.0', vcs_revision='bar',
... build_date='2018-01-01T00:00:00')
... for card in fits.getheader(f.name, 1).cards:
... print(str(card).rstrip())
XTENSION= 'BINTABLE' / binary table extension
BITPIX = 8 / array data type
NAXIS = 2 / number of array dimensions
NAXIS1 = 16 / length of dimension 1
NAXIS2 = 3145728 / length of dimension 2
PCOUNT = 0 / number of group parameters
GCOUNT = 1 / number of groups
TFIELDS = 2 / number of table fields
TTYPE1 = 'UNIQ '
TFORM1 = 'K '
TTYPE2 = 'PROBDENSITY'
TFORM2 = 'D '
TUNIT2 = 'sr-1 '
PIXTYPE = 'HEALPIX ' / HEALPIX pixelisation
ORDERING= 'NUNIQ ' / Pixel ordering scheme: RING, NESTED, or NUNIQ
COORDSYS= 'C ' / Ecliptic, Galactic or Celestial (equatorial)
MOCORDER= 9 / MOC resolution (best order)
INDXSCHM= 'EXPLICIT' / Indexing: IMPLICIT or EXPLICIT
VCSVERS = 'foo 1.0 ' / Software version
VCSREV = 'bar ' / Software revision (Git)
DATE-BLD= '2018-01-01T00:00:00' / Software build date
""" # noqa: E501
log.debug('normalizing metadata')
if isinstance(m, Table) or (isinstance(m, np.ndarray) and m.dtype.names):
m = Table(m, copy=False)
else:
if np.ndim(m) == 1:
m = [m]
m = Table(m, names=DEFAULT_NESTED_NAMES[:len(m)], copy=False)
m.meta.update(kwargs)
if 'UNIQ' in m.colnames:
default_names = DEFAULT_NUNIQ_NAMES
default_units = DEFAULT_NUNIQ_UNITS
extra_header = [
('PIXTYPE', 'HEALPIX', 'HEALPIX pixelisation'),
('ORDERING', 'NUNIQ',
'Pixel ordering scheme: RING, NESTED, or NUNIQ'),
('COORDSYS', 'C', 'Ecliptic, Galactic or Celestial (equatorial)'),
('MOCORDER', moc.uniq2order(m['UNIQ'].max()),
'MOC resolution (best order)'),
('INDXSCHM', 'EXPLICIT', 'Indexing: IMPLICIT or EXPLICIT')
]
# Ignore nest keyword argument if present
m.meta.pop('nest', False)
else:
default_names = DEFAULT_NESTED_NAMES
default_units = DEFAULT_NESTED_UNITS
ordering = 'NESTED' if m.meta.pop('nest', False) else 'RING'
extra_header = [
('PIXTYPE', 'HEALPIX', 'HEALPIX pixelisation'),
('ORDERING', ordering,
'Pixel ordering scheme: RING, NESTED, or NUNIQ'),
('COORDSYS', 'C', 'Ecliptic, Galactic or Celestial (equatorial)'),
('NSIDE', ah.npix_to_nside(len(m)),
'Resolution parameter of HEALPIX'),
('INDXSCHM', 'IMPLICIT', 'Indexing: IMPLICIT or EXPLICIT')
]
for key, rows in itertools.groupby(FITS_META_MAPPING, lambda row: row[0]):
try:
value = m.meta.pop(key)
except KeyError:
pass
else:
for row in rows:
_, fits_key, fits_comment, to_fits, _ = row
if to_fits is not None:
extra_header.append(
(fits_key, to_fits(value), fits_comment))
for default_name, default_unit in zip(default_names, default_units):
try:
col = m[default_name]
except KeyError:
pass
else:
if not col.unit:
col.unit = default_unit
log.debug('converting from Astropy table to FITS HDU list')
hdu = fits.table_to_hdu(m)
hdu.header.extend(extra_header)
hdulist = fits.HDUList([fits.PrimaryHDU(), hdu])
log.debug('saving')
hdulist.writeto(filename, overwrite=True)
def contour(m, levels, nest=False, degrees=False, simplify=True):
"""Calculate contours from a HEALPix dataset.
Parameters
----------
m : `numpy.ndarray`
The HEALPix dataset.
levels : list
The list of contour values.
nest : bool, default=False
Indicates whether the input sky map is in nested rather than
ring-indexed HEALPix coordinates (default: ring).
degrees : bool, default=False
Whether the contours are in degrees instead of radians.
simplify : bool, default=True
Whether to simplify the paths.
Returns
-------
list
A list with the same length as `levels`.
Each item is a list of disjoint polygons, of which each item is a
list of points, of which each is a list consisting of the right
ascension and declination.
Examples
--------
A very simply example sky map...
>>> nside = 32
>>> npix = ah.nside_to_npix(nside)
>>> ra, dec = hp.pix2ang(nside, np.arange(npix), lonlat=True)
>>> m = dec
>>> contour(m, [10, 20, 30], degrees=True)
[[[[..., ...], ...], ...], ...]
"""
# Infrequently used import
import networkx as nx
# Determine HEALPix resolution.
npix = len(m)
nside = ah.npix_to_nside(npix)
min_area = 0.4 * ah.nside_to_pixel_area(nside).to_value(u.sr)
neighbors = hp.get_all_neighbours(nside, np.arange(npix), nest=nest).T
# Loop over the requested contours.
paths = []
for level in levels:
# Find credible region.
indicator = (m >= level)
# Find all faces that lie on the boundary.
# This speeds up the doubly nested ``for`` loop below by allowing us to
# skip the vast majority of faces that are on the interior or the
# exterior of the contour.
tovisit = np.flatnonzero(
np.any(indicator.reshape(-1, 1) != indicator[neighbors[:, ::2]],
axis=1))
# Construct a graph of the edges of the contour.
graph = nx.Graph()
face_pairs = set()
for ipix1 in tovisit:
neighborhood = neighbors[ipix1]
for _ in range(4):
neighborhood = np.roll(neighborhood, 2)
ipix2 = neighborhood[4]
# Skip this pair of faces if we have already examined it.
new_face_pair = frozenset((ipix1, ipix2))
if new_face_pair in face_pairs:
continue
face_pairs.add(new_face_pair)
# Determine if this pair of faces are on a boundary of the
# credible level.
if indicator[ipix1] == indicator[ipix2]:
continue
# Add the common edge of this pair of faces.
# Label each vertex with the set of faces that they share.
graph.add_edge(frozenset((ipix1, *neighborhood[2:5])),
frozenset((ipix1, *neighborhood[4:7])))
graph = nx.freeze(graph)
# Find contours by detecting cycles in the graph.
cycles = nx.cycle_basis(graph)
# Construct the coordinates of the vertices by averaging the
# coordinates of the connected faces.
cycles = [[
np.sum(hp.pix2vec(nside, [i for i in v if i != -1], nest=nest), 1)
for v in cycle
] for cycle in cycles]
# Simplify paths if requested.
if simplify:
cycles = [_simplify(cycle, min_area) for cycle in cycles]
cycles = [cycle for cycle in cycles if len(cycle) > 2]
# Convert to angles.
cycles = [
_vec2radec(cycle, degrees=degrees).tolist() for cycle in cycles
]
# Add to output paths.
paths.append([cycle + [cycle[0]] for cycle in cycles])
return paths
def posterior_max(prob, nest=False):
npix = len(prob)
nside = ah.npix_to_nside(npix)
i = np.argmax(prob)
return SkyCoord(
*hp.pix2ang(nside, i, nest=nest, lonlat=True), unit=u.deg)
def find_ellipse(prob, cl=90, projection='ARC', nest=False):
"""For a HEALPix map, find an ellipse that contains a given probability.
The orientation is defined as the angle of the semimajor axis
counterclockwise from west on the plane of the sky. If you think of the
semimajor distance as the width of the ellipse, then the orientation is the
clockwise rotation relative to the image x-axis. Equivalently, the
orientation is the position angle of the semi-minor axis.
These conventions match the definitions used in DS9 region files [1]_ and
Aladin drawing commands [2]_.
Parameters
----------
prob : np.ndarray, astropy.table.Table
The HEALPix probability map, either as a full rank explicit array
or as a multi-order map.
cl : float
The desired credible level (default: 90).
projection : str, optional
The WCS projection (default: 'ARC', or zenithal equidistant).
For a list of possible values, see the Astropy documentation [3]_.
nest : bool
HEALPix pixel ordering (default: False, or ring ordering).
Returns
-------
ra : float
The ellipse center right ascension in degrees.
dec : float
The ellipse center right ascension in degrees.
a : float
The lenth of the semimajor axis in degrees.
b : float
The length of the semiminor axis in degrees.
pa : float
The orientation of the ellipse axis on the plane of the sky in degrees.
area : float
The area of the ellipse in square degrees.
Notes
-----
The center of the ellipse is the median a posteriori sky position. The
length and orientation of the semi-major and semi-minor axes are measured
as follows:
1. The sky map is transformed to a WCS projection that may be specified by
the caller. The default projection is ``ARC`` (zenithal equidistant), in
which radial distances are proportional to the physical angular
separation from the center point.
2. A 1-sigma ellipse is estimated by calculating the covariance matrix in
the projected image plane using three rounds of sigma clipping to reject
distant outlier points.
3. The 1-sigma ellipse is inflated until it encloses an integrated
probability of ``cl`` (default: 90%).
The function returns a tuple of the right ascension, declination,
semi-major distance, semi-minor distance, and orientation angle, all in
degrees.
References
----------
.. [1] http://ds9.si.edu/doc/ref/region.html
.. [2] http://aladin.u-strasbg.fr/java/AladinScriptManual.gml#draw
.. [3] http://docs.astropy.org/en/stable/wcs/index.html#supported-projections
Examples
--------
**Example 1**
First, we need some imports.
>>> from astropy.io import fits
>>> from astropy.utils.data import download_file
>>> from astropy.wcs import WCS
>>> import healpy as hp
>>> from reproject import reproject_from_healpix
>>> import subprocess
Next, we download the BAYESTAR sky map for GW170817 from the
LIGO Document Control Center.
>>> url = 'https://dcc.ligo.org/public/0146/G1701985/001/bayestar.fits.gz' # doctest: +SKIP
>>> filename = download_file(url, cache=True, show_progress=False) # doctest: +SKIP
>>> _, healpix_hdu = fits.open(filename) # doctest: +SKIP
>>> prob = hp.read_map(healpix_hdu, verbose=False) # doctest: +SKIP
Then, we calculate ellipse and write it to a DS9 region file.
>>> ra, dec, a, b, pa, area = find_ellipse(prob) # doctest: +SKIP
>>> print(*np.around([ra, dec, a, b, pa, area], 5)) # doctest: +SKIP
195.03732 -19.29358 8.66545 1.1793 63.61698 32.07665
>>> s = 'fk5;ellipse({},{},{},{},{})'.format(ra, dec, a, b, pa) # doctest: +SKIP
>>> open('ds9.reg', 'w').write(s) # doctest: +SKIP
Then, we reproject a small patch of the HEALPix map, and save it to a file.
>>> wcs = WCS() # doctest: +SKIP
>>> wcs.wcs.ctype = ['RA---ARC', 'DEC--ARC'] # doctest: +SKIP
>>> wcs.wcs.crval = [ra, dec] # doctest: +SKIP
>>> wcs.wcs.crpix = [128, 128] # doctest: +SKIP
>>> wcs.wcs.cdelt = [-0.1, 0.1] # doctest: +SKIP
>>> img, _ = reproject_from_healpix(healpix_hdu, wcs, [256, 256]) # doctest: +SKIP
>>> img_hdu = fits.ImageHDU(img, wcs.to_header()) # doctest: +SKIP
>>> img_hdu.writeto('skymap.fits') # doctest: +SKIP
Now open the image and region file in DS9. You should find that the ellipse
encloses the probability hot spot. You can load the sky map and region file
from the command line:
.. code-block:: sh
$ ds9 skymap.fits -region ds9.reg
Or you can do this manually:
1. Open DS9.
2. Open the sky map: select "File->Open..." and choose ``skymap.fits``
from the dialog box.
3. Open the region file: select "Regions->Load Regions..." and choose
``ds9.reg`` from the dialog box.
Now open the image and region file in Aladin.
1. Open Aladin.
2. Open the sky map: select "File->Load Local File..." and choose
``skymap.fits`` from the dialog box.
3. Open the sky map: select "File->Load Local File..." and choose
``ds9.reg`` from the dialog box.
You can also compare the original HEALPix file with the ellipse in Aladin:
1. Open Aladin.
2. Open the HEALPix file by pasting the URL from the top of this
example in the Command field at the top of the window and hitting
return, or by selecting "File->Load Direct URL...", pasting the URL,
and clicking "Submit."
3. Open the sky map: select "File->Load Local File..." and choose
``ds9.reg`` from the dialog box.
**Example 2**
This example shows that we get approximately the same answer for GW171087
if we read it in as a multi-order map.
>>> from ..io import read_sky_map # doctest: +SKIP
>>> skymap_moc = read_sky_map(healpix_hdu, moc=True) # doctest: +SKIP
>>> ellipse = find_ellipse(skymap_moc) # doctest: +SKIP
>>> print(*np.around(ellipse, 5)) # doctest: +SKIP
195.03709 -19.27589 8.67611 1.18167 63.60454 32.08015
**Example 3**
I'm not showing the `ra` or `pa` output from the examples below because
the right ascension is arbitary when dec=90° and the position angle is
arbitrary when a=b; their arbitrary values may vary depending on your math
library. Also, I add 0.0 to the outputs because on some platforms you tend
to get values of dec or pa that get rounded to -0.0, which is within
numerical precision but would break the doctests (see
https://stackoverflow.com/questions/11010683).
This is an example sky map that is uniform in sin(theta) out to a given
radius in degrees. The 90% credible radius should be 0.9 * radius. (There
will be deviations for small radius due to finite resolution.)
>>> def make_uniform_in_sin_theta(radius, nside=512):
... npix = ah.nside_to_npix(nside)
... theta, phi = hp.pix2ang(nside, np.arange(npix))
... theta_max = np.deg2rad(radius)
... prob = np.where(theta <= theta_max, 1 / np.sin(theta), 0)
... return prob / prob.sum()
...
>>> prob = make_uniform_in_sin_theta(1)
>>> ra, dec, a, b, pa, area = find_ellipse(prob)
>>> dec, a, b, area # doctest: +FLOAT_CMP
(89.90862520480792, 0.8703361458208101, 0.8703357768874356, 2.3788811576269793)
>>> prob = make_uniform_in_sin_theta(10)
>>> ra, dec, a, b, pa, area = find_ellipse(prob)
>>> dec, a, b, area # doctest: +FLOAT_CMP
(89.90827657529562, 9.024846562072119, 9.024842703023802, 255.11972196535515)
>>> prob = make_uniform_in_sin_theta(120)
>>> ra, dec, a, b, pa, area = find_ellipse(prob)
>>> dec, a, b, area # doctest: +FLOAT_CMP
(90.0, 107.9745037610576, 107.97450376105758, 26988.70467497216)
**Example 4**
These are approximately Gaussian distributions.
>>> from scipy import stats
>>> def make_gaussian(mean, cov, nside=512):
... npix = ah.nside_to_npix(nside)
... xyz = np.transpose(hp.pix2vec(nside, np.arange(npix)))
... dist = stats.multivariate_normal(mean, cov)
... prob = dist.pdf(xyz)
... return prob / prob.sum()
...
This one is centered at RA=45°, Dec=0° and has a standard deviation of ~1°.
>>> prob = make_gaussian(
... [1/np.sqrt(2), 1/np.sqrt(2), 0],
... np.square(np.deg2rad(1)))
...
>>> find_ellipse(prob) # doctest: +FLOAT_CMP
(45.0, 0.0, 2.1424077148886744, 2.1420790721225518, 90.0, 14.467701995920123)
This one is centered at RA=45°, Dec=0°, and is elongated in the north-south
direction.
>>> prob = make_gaussian(
... [1/np.sqrt(2), 1/np.sqrt(2), 0],
... np.diag(np.square(np.deg2rad([1, 1, 10]))))
...
>>> find_ellipse(prob) # doctest: +FLOAT_CMP
(44.99999999999999, 0.0, 13.58768882719899, 2.0829846178241853, 90.0, 88.57796576937031)
This one is centered at RA=0°, Dec=0°, and is elongated in the east-west
direction.
>>> prob = make_gaussian(
... [1, 0, 0],
... np.diag(np.square(np.deg2rad([1, 10, 1]))))
...
>>> find_ellipse(prob) # doctest: +FLOAT_CMP
(0.0, 0.0, 13.583918022027149, 2.0823769912401433, 0.0, 88.54622940628761)
This one is centered at RA=0°, Dec=0°, and has its long axis tilted about
10° to the west of north.
>>> prob = make_gaussian(
... [1, 0, 0],
... [[0.1, 0, 0],
... [0, 0.1, -0.15],
... [0, -0.15, 1]])
...
>>> find_ellipse(prob) # doctest: +FLOAT_CMP
(0.0, 0.0, 64.7713312709293, 33.50754131182681, 80.78231196786838, 6372.344658663038)
This one is centered at RA=0°, Dec=0°, and has its long axis tilted about
10° to the east of north.
>>> prob = make_gaussian(
... [1, 0, 0],
... [[0.1, 0, 0],
... [0, 0.1, 0.15],
... [0, 0.15, 1]])
...
>>> find_ellipse(prob) # doctest: +FLOAT_CMP
(0.0, 0.0, 64.77133127093047, 33.50754131182745, 99.21768803213159, 6372.344658663096)
This one is centered at RA=0°, Dec=0°, and has its long axis tilted about
80° to the east of north.
>>> prob = make_gaussian(
... [1, 0, 0],
... [[0.1, 0, 0],
... [0, 1, 0.15],
... [0, 0.15, 0.1]])
...
>>> find_ellipse(prob) # doctest: +FLOAT_CMP
(0.0, 0.0, 64.7756448603915, 33.509863018519894, 170.78252287327365, 6372.425731592412)
This one is centered at RA=0°, Dec=0°, and has its long axis tilted about
80° to the west of north.
>>> prob = make_gaussian(
... [1, 0, 0],
... [[0.1, 0, 0],
... [0, 1, -0.15],
... [0, -0.15, 0.1]])
...
>>> find_ellipse(prob) # doctest: +FLOAT_CMP
(0.0, 0.0, 64.77564486039148, 33.50986301851987, 9.217477126726322, 6372.42573159241)
""" # noqa: E501
try:
prob['UNIQ']
except (IndexError, KeyError, ValueError):
npix = len(prob)
nside = ah.npix_to_nside(npix)
ipix = range(npix)
area = ah.nside_to_pixel_area(nside).to_value(u.deg**2)
else:
order, ipix = moc.uniq2nest(prob['UNIQ'])
nside = 1 << order.astype(int)
ipix = ipix.astype(int)
area = ah.nside_to_pixel_area(nside).to_value(u.sr)
prob = prob['PROBDENSITY'] * area
area *= np.square(180 / np.pi)
nest = True
# Find median a posteriori sky position.
xyz0 = [
quantile(x, 0.5, weights=prob)
for x in hp.pix2vec(nside, ipix, nest=nest)
]
(ra, ), (dec, ) = hp.vec2ang(np.asarray(xyz0), lonlat=True)
# Construct WCS with the specified projection
# and centered on mean direction.
w = WCS()
w.wcs.crval = [ra, dec]
w.wcs.ctype = ['RA---' + projection, 'DEC--' + projection]
# Transform HEALPix to zenithal equidistant coordinates.
xy = w.wcs_world2pix(
np.transpose(hp.pix2ang(nside, ipix, nest=nest, lonlat=True)), 1)
# Keep only values that were inside the projection.
keep = np.logical_and.reduce(np.isfinite(xy), axis=1)
xy = xy[keep]
prob = prob[keep]
if not np.isscalar(area):
area = area[keep]
# Find covariance matrix, performing three rounds of sigma-clipping
# to reject outliers.
keep = np.ones(len(xy), dtype=bool)
for _ in range(3):
c = np.cov(xy[keep], aweights=prob[keep], rowvar=False)
nsigmas = np.sqrt(np.sum(xy.T * np.linalg.solve(c, xy.T), axis=0))
keep &= (nsigmas < 3)
# Find the number of sigma that enclose the cl% credible level.
i = np.argsort(nsigmas)
nsigmas = nsigmas[i]
cls = np.cumsum(prob[i])
if np.isscalar(area):
careas = np.arange(1, len(i) + 1) * area
else:
careas = np.cumsum(area[i])
nsigma = np.interp(1e-2 * cl, cls, nsigmas)
area = np.interp(1e-2 * cl, cls, careas)
# If the credible level is not within the projection,
# then stop here and return all nans.
if 1e-2 * cl > cls[-1]:
return np.nan, np.nan, np.nan, np.nan, np.nan
# Find the eigendecomposition of the covariance matrix.
w, v = np.linalg.eigh(c)
# Find the semi-minor and semi-major axes.
b, a = nsigma * np.sqrt(w)
# Find the position angle.
pa = np.rad2deg(np.arctan2(*v[0]))
# An ellipse is symmetric under rotations of 180°.
# Return the smallest possible positive position angle.
pa %= 180
# Done!
return ra, dec, a, b, pa, area
def healpix_to_image(healpix_data, coord_system_in, wcs_out, shape_out,
order='bilinear', nested=False):
"""
Convert image in HEALPIX format to a normal FITS projection image (e.g.
CAR or AIT).
Parameters
----------
healpix_data : `numpy.ndarray`
HEALPIX data array
coord_system_in : str or `~astropy.coordinates.BaseCoordinateFrame`
The coordinate system for the input HEALPIX data, as an Astropy
coordinate frame or corresponding string alias (e.g. ``'icrs'`` or
``'galactic'``)
wcs_out : `~astropy.wcs.WCS`
The WCS of the output array
shape_out : tuple
The shape of the output array
order : int or str, optional
The order of the interpolation (if ``mode`` is set to
``'interpolation'``). This can be either one of the following strings:
* 'nearest-neighbor'
* 'bilinear'
or an integer. A value of ``0`` indicates nearest neighbor
interpolation.
nested : bool
The order of the healpix_data, either nested or ring. Stored in
FITS headers in the ORDERING keyword.
Returns
-------
reprojected_data : `numpy.ndarray`
HEALPIX image resampled onto the reference image
footprint : `~numpy.ndarray`
Footprint of the input array in the output array. Values of 0 indicate
no coverage or valid values in the input image, while values of 1
indicate valid values.
"""
healpix_data = np.asarray(healpix_data, dtype=float)
# Look up lon, lat of pixels in reference system
yinds, xinds = np.indices(shape_out)
lon_out, lat_out = wcs_out.wcs_pix2world(xinds, yinds, 0)
# Convert between celestial coordinates
coord_system_in = parse_coord_system(coord_system_in)
with np.errstate(invalid='ignore'):
lon_in, lat_in = convert_world_coordinates(lon_out, lat_out, wcs_out, (coord_system_in, u.deg, u.deg))
lon_in = u.Quantity(lon_in, unit=u.deg, copy=False)
lat_in = u.Quantity(lat_in, unit=u.deg, copy=False)
if isinstance(order, six.string_types):
order = ORDER[order]
nside = npix_to_nside(len(healpix_data))
hp = HEALPix(nside=nside, order='nested' if nested else 'ring')
if order == 1:
data = hp.interpolate_bilinear_lonlat(lon_in, lat_in, healpix_data)
elif order == 0:
ipix = hp.lonlat_to_healpix(lon_in, lat_in)
data = healpix_data[ipix]
else:
raise ValueError("Only nearest-neighbor and bilinear interpolation are supported")
footprint = np.ones(data.shape, bool)
return data, footprint
