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import contextlib
import warnings
from copy import deepcopy
import builtins
import dask.array as da
import numpy as np
from astropy.wcs.utils import proj_plane_pixel_area
from astropy.wcs import (WCSSUB_SPECTRAL, WCSSUB_LONGITUDE, WCSSUB_LATITUDE)
from astropy.wcs import WCS
from . import wcs_utils
from .utils import FITSWarning, AstropyUserWarning, WCSCelestialError
from astropy import log
from astropy.io import fits
from astropy.wcs.utils import is_proj_plane_distorted
from astropy.io.fits import BinTableHDU, Column
from astropy import units as u
import itertools
import re
from radio_beam import Beam
def _fix_spectral(wcs):
"""
Attempt to fix a cube with an invalid spectral axis definition. Only uses
well-known exceptions, e.g. CTYPE = 'VELOCITY'. For the rest, it will try
to raise a helpful error.
"""
axtypes = wcs.get_axis_types()
types = [a['coordinate_type'] for a in axtypes]
if wcs.naxis not in (3, 4):
raise TypeError("The WCS has {0} axes of types {1}".format(len(types),
types))
# sanitize noncompliant headers
if 'spectral' not in types:
log.warning("No spectral axis found; header may be non-compliant.")
for ind,tp in enumerate(types):
if tp not in ('celestial','stokes'):
if wcs.wcs.ctype[ind] in wcs_utils.bad_spectypes_mapping:
wcs.wcs.ctype[ind] = wcs_utils.bad_spectypes_mapping[wcs.wcs.ctype[ind]]
return wcs
def _split_stokes(array, wcs, beam_table=None):
"""
Given a 4-d data cube with 4-d WCS (spectral cube + stokes) return a
dictionary of data and WCS objects for each Stokes component
Parameters
----------
array : `~numpy.ndarray`
The input 3-d array with two position dimensions, one spectral
dimension, and a Stokes dimension.
wcs : `~astropy.wcs.WCS`
The input 3-d WCS with two position dimensions, one spectral
dimension, and a Stokes dimension.
beam_table : `~astropy.io.fits.hdu.table.BinTableHDU`
When multiple beams are present, a FITS table with the beam information
can be given to be split into the polarization components, consistent with
`array`.
"""
if array.ndim not in (3,4):
raise ValueError("Input array must be 3- or 4-dimensional for a"
" STOKES cube")
if wcs.wcs.naxis != 4:
raise ValueError("Input WCS must be 4-dimensional for a STOKES cube")
wcs = _fix_spectral(wcs)
# reverse from wcs -> numpy convention
axtypes = wcs.get_axis_types()[::-1]
types = [a['coordinate_type'] for a in axtypes]
try:
# Find stokes dimension
stokes_index = types.index('stokes')
except ValueError:
# stokes not in list, but we are 4d
if types.count('celestial') == 2 and types.count('spectral') == 1:
if None in types:
stokes_index = types.index(None)
log.warning("FITS file has no STOKES axis, but it has a blank"
" axis type at index {0} that is assumed to be "
"stokes.".format(4-stokes_index))
else:
for ii,tp in enumerate(types):
if tp not in ('celestial', 'spectral'):
stokes_index = ii
stokes_type = tp
log.warning("FITS file has no STOKES axis, but it has an axis"
" of type {1} at index {0} that is assumed to be "
"stokes.".format(4-stokes_index, stokes_type))
else:
raise IOError("There are 4 axes in the data cube but no STOKES "
"axis could be identified")
# TODO: make the stokes names more general
stokes_names = ["I", "Q", "U", "V"]
stokes_arrays = {}
if beam_table is not None:
beam_tables = {}
wcs_slice = wcs_utils.drop_axis(wcs, wcs.naxis - 1 - stokes_index)
if array.ndim == 4:
for i_stokes in range(array.shape[stokes_index]):
array_slice = [i_stokes if idim == stokes_index else slice(None)
for idim in range(array.ndim)]
stokes_arrays[stokes_names[i_stokes]] = array[tuple(array_slice)]
if beam_table is not None:
beam_pol_idx = beam_table['POL'] == i_stokes
beam_tables[stokes_names[i_stokes]] = beam_table[beam_pol_idx]
else:
# 3D array with STOKES as a 4th header parameter
stokes_arrays['I'] = array
if beam_table is not None:
beam_tables['I'] = beam_table
if beam_table is not None:
return stokes_arrays, wcs_slice, beam_tables
else:
return stokes_arrays, wcs_slice
def _orient(array, wcs):
"""
Given a 3-d spectral cube and WCS, swap around the axes so that the
spectral axis cube is the first in Numpy notation, and the last in WCS
notation.
Parameters
----------
array : `~numpy.ndarray`
The input 3-d array with two position dimensions and one spectral
dimension.
wcs : `~astropy.wcs.WCS`
The input 3-d WCS with two position dimensions and one spectral
dimension.
"""
if array.ndim != 3:
raise ValueError("Input array must be 3-dimensional")
if wcs.wcs.naxis != 3:
raise ValueError("Input WCS must be 3-dimensional")
wcs = wcs_utils.diagonal_wcs_to_cdelt(_fix_spectral(wcs))
# reverse from wcs -> numpy convention
axtypes = wcs.get_axis_types()[::-1]
types = [a['coordinate_type'] for a in axtypes]
n_celestial = types.count('celestial')
if n_celestial == 0:
raise ValueError('No celestial axes found in WCS')
elif n_celestial != 2:
raise ValueError('WCS should contain 2 celestial dimensions but '
'contains {0}'.format(n_celestial))
n_spectral = types.count('spectral')
if n_spectral == 0:
raise ValueError('No spectral axes found in WCS')
elif n_spectral != 1:
raise ValueError('WCS should contain one spectral dimension but '
'contains {0}'.format(n_spectral))
nums = [None if a['coordinate_type'] != 'celestial' else a['number']
for a in axtypes]
if 'stokes' in types:
raise ValueError("Input WCS should not contain stokes")
t = [types.index('spectral'), nums.index(1), nums.index(0)]
if t == [0, 1, 2]:
result_array = array
else:
result_array = array.transpose(t)
result_wcs = wcs.sub([WCSSUB_LONGITUDE, WCSSUB_LATITUDE, WCSSUB_SPECTRAL])
return result_array, result_wcs
def slice_syntax(f):
"""
This decorator wraps a function that accepts a tuple of slices.
After wrapping, the function acts like a property that accepts
bracket syntax (e.g., p[1:3, :, :])
Parameters
----------
f : function
"""
def wrapper(self):
result = SliceIndexer(f, self)
result.__doc__ = f.__doc__
return result
wrapper.__doc__ = slice_doc.format(f.__doc__ or '',
f.__name__)
result = property(wrapper)
return result
slice_doc = """
{0}
Notes
-----
Supports efficient Numpy slice notation,
like ``{1}[0:3, :, 2:4]``
"""
class SliceIndexer(object):
def __init__(self, func, _other):
self._func = func
self._other = _other
def __getitem__(self, view):
result = self._func(self._other, view)
if isinstance(result, da.Array):
result = result.compute()
return result
@property
def size(self):
return self._other.size
@property
def ndim(self):
return self._other.ndim
@property
def shape(self):
return self._other.shape
def __iter__(self):
raise Exception("You need to specify a slice (e.g. ``[:]`` or "
"``[0,:,:]`` in order to access this property.")
# TODO: make this into a proper configuration item
# TODO: make threshold depend on memory?
MEMORY_THRESHOLD=1e8
def is_huge(cube):
if cube.size < MEMORY_THRESHOLD: # smallish
return False
else:
return True
def iterator_strategy(cube, axis=None):
"""
Guess the most efficient iteration strategy
for iterating over a cube, given its size and layout
Parameters
----------
cube : SpectralCube instance
The cube to iterate over
axis : [0, 1, 2]
For reduction methods, the axis that is
being collapsed
Returns
-------
strategy : ['cube' | 'ray' | 'slice']
The recommended iteration strategy.
*cube* recommends working with the entire array in memory
*slice* recommends working with one slice at a time
*ray* recommends working with one ray at a time
"""
# pretty simple for now
if cube.size < 1e8: # smallish
return 'cube'
return 'slice'
def try_load_beam(header):
'''
Try loading a beam from a FITS header.
'''
try:
beam = Beam.from_fits_header(header)
return beam
except Exception as ex:
# We don't emit a warning if no beam was found since it's ok for
# cubes to not have beams
# if 'No BMAJ' not in str(ex):
# warnings.warn("Could not parse beam information from header."
# " Exception was: {0}".format(ex.__repr__()),
# FITSWarning
# )
# Avoid warning since cubes don't have a beam
# Warning now provided when `SpectralCube.beam` is None
beam = None
return beam
def try_load_beams(data):
'''
Try loading a beam table from a FITS HDU list.
'''
try:
from radio_beam import Beam
except ImportError:
warnings.warn("radio_beam is not installed. No beam "
"can be created.",
ImportError
)
if isinstance(data, fits.BinTableHDU):
if 'BPA' in data.data.names:
beam_table = data.data
return beam_table
else:
raise ValueError("No beam table found")
elif isinstance(data, fits.HDUList):
for ihdu, hdu_item in enumerate(data):
if isinstance(hdu_item, (fits.PrimaryHDU, fits.ImageHDU)):
beam = try_load_beams(hdu_item.header)
elif isinstance(hdu_item, fits.BinTableHDU):
if 'BPA' in hdu_item.data.names:
beam_table = hdu_item.data
return beam_table
try:
# if there was a beam in a header, but not a beam table
return beam
except NameError:
# if the for loop has completed, we didn't find a beam table
raise ValueError("No beam table found")
elif isinstance(data, (fits.PrimaryHDU, fits.ImageHDU)):
return try_load_beams(data.header)
elif isinstance(data, fits.Header):
try:
beam = Beam.from_fits_header(data)
return beam
except Exception as ex:
# warnings.warn("Could not parse beam information from header."
# " Exception was: {0}".format(ex.__repr__()),
# FITSWarning
# )
# Avoid warning since cubes don't have a beam
# Warning now provided when `SpectralCube.beam` is None
beam = None
else:
raise ValueError("How did you get here? This is some sort of error.")
def beams_to_bintable(beams):
"""
Convert a list of beams to a CASA-style BinTableHDU
"""
c1 = Column(name='BMAJ', format='1E', array=[bm.major.to(u.arcsec).value for bm in beams], unit=u.arcsec.to_string('FITS'))
c2 = Column(name='BMIN', format='1E', array=[bm.minor.to(u.arcsec).value for bm in beams], unit=u.arcsec.to_string('FITS'))
c3 = Column(name='BPA', format='1E', array=[bm.pa.to(u.deg).value for bm in beams], unit=u.deg.to_string('FITS'))
#c4 = Column(name='CHAN', format='1J', array=[bm.meta['CHAN'] if 'CHAN' in bm.meta else 0 for bm in beams])
c4 = Column(name='CHAN', format='1J', array=np.arange(len(beams)))
c5 = Column(name='POL', format='1J', array=[bm.meta['POL'] if 'POL' in bm.meta else 0 for bm in beams])
bmhdu = BinTableHDU.from_columns([c1, c2, c3, c4, c5])
bmhdu.header['EXTNAME'] = 'BEAMS'
bmhdu.header['EXTVER'] = 1
bmhdu.header['XTENSION'] = 'BINTABLE'
bmhdu.header['NCHAN'] = len(beams)
bmhdu.header['NPOL'] = len(set([bm.meta['POL'] for bm in beams if 'POL' in bm.meta]))
return bmhdu
def beam_props(beams, includemask=None):
'''
Returns separate quantities for the major, minor, and PA of a list of
beams.
'''
if includemask is None:
includemask = itertools.cycle([True])
major = u.Quantity([bm.major for bm, incl in zip(beams, includemask)
if incl], u.deg)
minor = u.Quantity([bm.minor for bm, incl in zip(beams, includemask)
if incl], u.deg)
pa = u.Quantity([bm.pa for bm, incl in zip(beams, includemask)
if incl], u.deg)
return major, minor, pa
def largest_beam(beams, includemask=None):
"""
Returns the largest beam (by area) in a list of beams.
"""
from radio_beam import Beam
major, minor, pa = beam_props(beams, includemask)
largest_idx = (major * minor).argmax()
new_beam = Beam(major=major[largest_idx], minor=minor[largest_idx],
pa=pa[largest_idx])
return new_beam
def smallest_beam(beams, includemask=None):
"""
Returns the smallest beam (by area) in a list of beams.
"""
from radio_beam import Beam
major, minor, pa = beam_props(beams, includemask)
smallest_idx = (major * minor).argmin()
new_beam = Beam(major=major[smallest_idx], minor=minor[smallest_idx],
pa=pa[smallest_idx])
return new_beam
@contextlib.contextmanager
def _map_context(numcores):
"""
Mapping context manager to allow parallel mapping or regular mapping
depending on the number of cores specified.
The builtin map is overloaded to handle python3 problems: python3 returns a
generator, while ``multiprocessing.Pool.map`` actually runs the whole thing
"""
if numcores is not None and numcores > 1:
try:
from joblib import Parallel, delayed
from joblib.pool import has_shareable_memory
map = lambda x,y: Parallel(n_jobs=numcores)(delayed(has_shareable_memory)(x))(y)
parallel = True
except ImportError:
map = lambda x,y: list(builtins.map(x,y))
warnings.warn("Could not import joblib. "
"map will be non-parallel.",
ImportError
)
parallel = False
else:
parallel = False
map = lambda x,y: list(builtins.map(x,y))
yield map
def convert_bunit(bunit):
'''
Convert a BUNIT string to a quantity
Parameters
----------
bunit : str
String to convert to an `~astropy.units.Unit`
Returns
-------
unit : `~astropy.unit.Unit`
Corresponding unit.
'''
# special case: CASA (sometimes) makes non-FITS-compliant jy/beam headers
bunit_lower = re.sub(r"\s", "", bunit.lower())
if bunit_lower == 'jy/beam':
unit = u.Jy / u.beam
else:
try:
unit = u.Unit(bunit)
except ValueError:
warnings.warn("Could not parse unit {0}. "
"If you know the correct unit, try "
"u.add_enabled_units(u.def_unit(['{0}'], represents=u.<correct_unit>))".format(bunit),
AstropyUserWarning)
unit = None
return unit
def world_take_along_axis(cube, position_plane, axis):
'''
Convert a 2D plane of pixel positions to the equivalent WCS coordinates.
For example, this will convert `argmax`
along the spectral axis to the equivalent spectral value (e.g., velocity at
peak intensity).
Parameters
----------
cube : SpectralCube
A spectral cube.
position_plane : 2D numpy.ndarray
2D array of pixel positions along `axis`. For example, `position_plane` can
be the output of `argmax` or `argmin` along an axis.
axis : int
The axis that `position_plane` is collapsed along.
Returns
-------
out : astropy.units.Quantity
2D array of WCS coordinates.
'''
if wcs_utils.is_pixel_axis_to_wcs_correlated(cube.wcs, axis):
raise WCSCelestialError("world_take_along_axis requires the celestial axes"
" to be aligned along image axes.")
# Get 1D slice along that axis.
world_slice = [0, 0]
world_slice.insert(axis, slice(None))
world_coords = cube.world[tuple(world_slice)][axis]
world_newaxis = [np.newaxis] * 2
world_newaxis.insert(axis, slice(None))
world_newaxis = tuple(world_newaxis)
plane_newaxis = [slice(None), slice(None)]
plane_newaxis.insert(axis, np.newaxis)
plane_newaxis = tuple(plane_newaxis)
out = np.take_along_axis(world_coords[world_newaxis],
position_plane[plane_newaxis], axis=axis)
out = out.squeeze()
return out
def _has_beam(obj):
if hasattr(obj, '_beam'):
return obj._beam is not None
else:
return False
def _has_beams(obj):
if hasattr(obj, '_beams'):
return obj._beams is not None
else:
return False
def bunit_converters(obj, unit, equivalencies=(), freq=None):
'''
Handler for all brightness unit conversions, including: K, Jy/beam, Jy/pix, Jy/sr.
This also includes varying resolution spectral cubes, where the beam size varies along
the frequency axis.
Parameters
----------
obj : {SpectralCube, LowerDimensionalObject}
A spectral cube or any other lower dimensional object.
unit : `~astropy.units.Unit`
Unit to convert `obj` to.
equivalencies : tuple, optional
Initial list of equivalencies.
freq : `~astropy.unit.Quantity`, optional
Frequency to use for spectral conversions. If the spectral axis is available, the
frequencies will already be defined.
Outputs
-------
factor : `~numpy.ndarray`
Array of factors for the unit conversion.
'''
# Add a simple check it the new unit is already equivalent, and so we don't need
# any additional unit equivalencies
if obj.unit.is_equivalent(unit):
# return equivalencies
factor = obj.unit.to(unit, equivalencies=equivalencies)
return np.array([factor])
# Determine the bunit "type". This will determine what information we need for the unit conversion.
has_btemp = obj.unit.is_equivalent(u.K) or unit.is_equivalent(u.K)
has_perbeam = obj.unit.is_equivalent(u.Jy/u.beam) or unit.is_equivalent(u.Jy/u.beam)
has_perangarea = obj.unit.is_equivalent(u.Jy/u.sr) or unit.is_equivalent(u.Jy/u.sr)
has_perpix = obj.unit.is_equivalent(u.Jy/u.pix) or unit.is_equivalent(u.Jy/u.pix)
# Is there any beam object defined?
has_beam = _has_beam(obj) or _has_beams(obj)
# Set if this is a varying resolution object
has_beams = _has_beams(obj)
# Define freq, if needed:
if any([has_perangarea, has_perbeam, has_btemp]):
# Create a beam equivalency for brightness temperature
# This requires knowing the frequency along the spectral axis.
if freq is None:
try:
freq = obj.with_spectral_unit(u.Hz).spectral_axis
except AttributeError:
raise TypeError("Object of type {0} has no spectral "
"information. `freq` must be provided for"
" unit conversion from Jy/beam"
.format(type(obj)))
else:
if not freq.unit.is_equivalent(u.Hz):
raise u.UnitsError("freq must be given in equivalent "
"frequency units.")
freq = freq.reshape((-1,))
else:
freq = [None]
# To handle varying resolution objects, loop through "channels"
# Default to a single iteration for a 2D spatial object or when a beam is not defined
# This allows handling all 1D, 2D, and 3D data products.
if has_beams:
iter = range(len(obj.beams))
beams = obj.beams
elif has_beam:
iter = range(0, 1)
beams = [obj.beam]
else:
iter = range(0, 1)
beams = [None]
# Append the unit conversion factors
factors = []
# Iterate through spectral channels.
for ii in iter:
beam = beams[ii]
# Use the range of frequencies when the beam does not change. Otherwise, select the
# frequency corresponding to this beam.
if has_beams:
thisfreq = freq[ii]
else:
thisfreq = freq
# Changes in beam require a new equivalency for each.
this_equivalencies = deepcopy(equivalencies)
# Equivalencies for Jy per ang area.
if has_perangarea:
bmequiv_angarea = u.brightness_temperature(thisfreq)
this_equivalencies = list(this_equivalencies) + bmequiv_angarea
# Beam area equivalencies for Jy per beam and/or Jy per ang area
if has_perbeam:
# create a beam equivalency for brightness temperature
bmequiv = beam.jtok_equiv(thisfreq)
# NOTE: `beamarea_equiv` was included in the radio-beam v0.3.3 release
# The if/else here handles potential cases where earlier releases are installed.
if hasattr(beam, 'beamarea_equiv'):
bmarea_equiv = beam.beamarea_equiv
else:
bmarea_equiv = u.beam_angular_area(beam.sr)
this_equivalencies = list(this_equivalencies) + bmequiv + bmarea_equiv
# Equivalencies for Jy per pixel area.
if has_perpix:
if not obj.wcs.has_celestial:
raise ValueError("Spatial WCS information is required for unit conversions"
" involving spatial areas (e.g., Jy/pix, Jy/sr)")
pix_area = (proj_plane_pixel_area(obj.wcs.celestial) * u.deg**2).to(u.sr)
pix_area_equiv = [(u.Jy / u.pix, u.Jy / u.sr,
lambda x: x / pix_area.value,
lambda x: x * pix_area.value)]
this_equivalencies = list(this_equivalencies) + pix_area_equiv
# Define full from brightness temp to Jy / pix.
# Otherwise isn't working in 1 step
if has_btemp:
if not has_beam:
raise ValueError("Conversions between K and Jy/beam or Jy/pix"
"requires the cube to have a beam defined.")
jtok_factor = beam.jtok(thisfreq) / (u.Jy / u.beam)
# We're going to do this piecemeal because it's easier to conceptualize
# We specifically anchor these conversions based on the beam area. So from
# beam to pix, this is beam -> angular area -> area per pixel
# Altogether:
# K -> Jy/beam -> Jy /sr - > Jy / pix
forward_factor = 1 / (jtok_factor * (beam.sr / u.beam) / (pix_area / u.pix))
reverse_factor = jtok_factor * (beam.sr / u.beam) / (pix_area / u.pix)
pix_area_btemp_equiv = [(u.K, u.Jy / u.pix,
lambda x: x * forward_factor.value,
lambda x: x * reverse_factor.value)]
this_equivalencies = list(this_equivalencies) + pix_area_btemp_equiv
# Equivalencies between pixel and angular areas.
if has_perbeam:
if not has_beam:
raise ValueError("Conversions between Jy/beam or Jy/pix"
"requires the cube to have a beam defined.")
beam_area = beam.sr
pix_area_btemp_equiv = [(u.Jy / u.pix, u.Jy / u.beam,
lambda x: x * (beam_area / pix_area).value,
lambda x: x * (pix_area / beam_area).value)]
this_equivalencies = list(this_equivalencies) + pix_area_btemp_equiv
factor = obj.unit.to(unit, equivalencies=this_equivalencies)
factors.append(factor)
if has_beams:
return factors
else:
# Slice along first axis to return a 1D array.
return factors[0]
def combine_headers(header1, header2, **kwargs):
'''
Given two Header objects, this function returns a fits Header of the optimal wcs.
Parameters
----------
header1 : astropy.io.fits.Header
A Header.
header2 : astropy.io.fits.Header
A Header.
Returns
-------
header : astropy.io.fits.Header
A header object of a field containing both initial headers.
'''
from reproject.mosaicking import find_optimal_celestial_wcs
# Get wcs and shape of both headers
w1 = WCS(header1).celestial
s1 = w1.array_shape
w2 = WCS(header2).celestial
s2 = w2.array_shape
# Get the optimal wcs and shape for both fields together
wcs_opt, shape_opt = find_optimal_celestial_wcs([(s1, w1), (s2, w2)], auto_rotate=False,
**kwargs)
# Make a new header using the optimal wcs and information from cubes
header = header1.copy()
header['NAXIS'] = 3
header['NAXIS1'] = shape_opt[1]
header['NAXIS2'] = shape_opt[0]
header['NAXIS3'] = header1['NAXIS3']
header.update(wcs_opt.to_header())
header['WCSAXES'] = 3
return header
def mosaic_cubes(cubes, spectral_block_size=100, combine_header_kwargs={}, **kwargs):
'''
This function reprojects cubes onto a common grid and combines them to a single field.
Parameters
----------
cubes : iterable
Iterable list of SpectralCube objects to reproject and add together.
spectral_block_size : int
Block size so that reproject does not run out of memory.
combine_header_kwargs : dict
Keywords passed to `~reproject.mosaicking.find_optimal_celestial_wcs`
via `combine_headers`.
Outputs
-------
cube : SpectralCube
A spectral cube with the list of cubes mosaicked together.
'''
cube1 = cubes[0]
header = cube1.header
# Create a header for a field containing all cubes
for cu in cubes[1:]:
header = combine_headers(header, cu.header, **combine_header_kwargs)
# Prepare an array and mask for the final cube
shape_opt = (header['NAXIS3'], header['NAXIS2'], header['NAXIS1'])
final_array = np.zeros(shape_opt)
mask_opt = np.zeros(shape_opt[1:])
for cube in cubes:
# Reproject cubes to the header
try:
if spectral_block_size is not None:
cube_repr = cube.reproject(header,
block_size=[spectral_block_size,
cube.shape[1],
cube.shape[2]],
**kwargs)
else:
cube_repr = cube.reproject(header, **kwargs)
except TypeError:
warnings.warn("The block_size argument is not accepted by `reproject`. "
"A more recent version may be needed.")
cube_repr = cube.reproject(header, **kwargs)
# Create weighting mask (2D)
mask = (cube_repr[0:1].get_mask_array()[0])
mask_opt += mask.astype(float)
# Go through each slice of the cube, add it to the final array
for ii in range(final_array.shape[0]):
slice1 = np.nan_to_num(cube_repr.unitless_filled_data[ii])
final_array[ii] = final_array[ii] + slice1
# Dividing by the mask throws errors where it is zero
with np.errstate(divide='ignore'):
# Use weighting mask to average where cubes overlap
for ss in range(final_array.shape[0]):
final_array[ss] /= mask_opt
# Create Cube
cube = cube1.__class__(data=final_array * cube1.unit, wcs=WCS(header))
return cube
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