def _slice0(cube, axis, scale):
"""
0th moment along an axis, calculated slicewise
Parameters
----------
cube : SpectralCube
axis : int
scale : float
Returns
-------
moment0_error : array
"""
shp = _moment_shp(cube, axis)
result = np.zeros(shp)
view = [slice(None)] * 3
valid = np.zeros(shp, dtype=np.bool)
for i in range(cube.shape[axis]):
view[axis] = i
plane = cube._mask.include(data=cube._data, wcs=cube._wcs, view=view)
valid |= plane
result += plane
result = scale * np.sqrt(result)
result[~valid] = np.nan
return result
def _slice1(cube, axis, scale, moment0, moment1):
"""
1st moment along an axis, calculated slicewise
Parameters
----------
cube : SpectralCube
axis : int
scale : float
moment0 : 0th moment
moment1 : 1st moment
Returns
-------
moment1_error : array
"""
shp = _moment_shp(cube, axis)
result = np.zeros(shp)
view = [slice(None)] * 3
pix_cen = cube._pix_cen()[axis]
for i in range(cube.shape[axis]):
view[axis] = i
result += np.power((pix_cen[view] - moment1), 2)
return (scale / moment0) * np.sqrt(result)
def moment_raywise(cube, order, axis):
"""
Compute moments by accumulating the answer one ray at a time
"""
shp = _moment_shp(cube, axis)
out = np.zeros(shp) * np.nan
pix_cen = cube._pix_cen()[axis]
pix_size = cube._pix_size()[axis]
for x, y, slc in cube._iter_rays(axis):
# the intensity, i.e. the weights
include = cube._mask.include(data=cube._data, wcs=cube._wcs,
view=slc)
if not include.any():
continue
data = cube.flattened(slc).value * pix_size[slc][include]
if order == 0:
out[x, y] = data.sum()
continue
order1 = (data * pix_cen[slc][include]).sum() / data.sum()
if order == 1:
out[x, y] = order1
continue
ordern = (data * (pix_cen[slc][include] - order1) ** order).sum()
ordern /= data.sum()
out[x, y] = ordern
return out
def _slice1(cube, axis, scale, moment0, moment1):
"""
1st moment along an axis, calculated slicewise
Parameters
----------
cube : SpectralCube
axis : int
scale : float or SpectralCube
moment0 : 0th moment
moment1 : 1st moment
Returns
-------
moment1_error : array
"""
if isinstance(scale, SpectralCube):
# scale should then have the same shape as the cube.
if cube.shape != scale.shape:
raise IndexError("When scale is a SpectralCube, it must have the"
" same shape as the cube.")
_scale_cube = True
else:
_scale_cube = False
# I don't think there is a way to do this with one pass.
# The first 2 moments always have to be pre-computed.
# Divide moment0 by the pixel size in the given axis so it represents the
# sum.
spec_unit = cube.spectral_axis.unit
axis_sum = u.Quantity(moment0 /
(cube._pix_size_slice(axis) * spec_unit))
shp = _moment_shp(cube, axis)
result = np.zeros(shp) * spec_unit ** 2
view = [slice(None)] * 3
pix_cen = u.Quantity(cube._pix_cen()[axis] * spec_unit)
# term2 does not depend on the plane.
term2 = moment1 / axis_sum
for i in range(cube.shape[axis]):
view[axis] = i
term1 = pix_cen[view] / axis_sum
if _scale_cube:
noise_plane = \
np.nan_to_num(scale.filled_data[view])
else:
noise_plane = scale
result += np.power((term1 - term2) * noise_plane, 2)
return np.sqrt(result)
def _slice1(cube, axis, scale, moment0, moment1):
"""
1st moment along an axis, calculated slicewise
Parameters
----------
cube : SpectralCube
axis : int
scale : float or SpectralCube
moment0 : 0th moment
moment1 : 1st moment
Returns
-------
moment1_error : array
"""
if isinstance(scale, SpectralCube):
# scale should then have the same shape as the cube.
if cube.shape != scale.shape:
raise IndexError("When scale is a SpectralCube, it must have the"
" same shape as the cube.")
_scale_cube = True
else:
_scale_cube = False
# I don't think there is a way to do this with one pass.
# The first 2 moments always have to be pre-computed.
# Divide moment0 by the pixel size in the given axis so it represents the
# sum.
spec_unit = cube.spectral_axis.unit
axis_sum = u.Quantity(moment0 /
(cube._pix_size_slice(axis) * spec_unit))
shp = _moment_shp(cube, axis)
result = np.zeros(shp) * spec_unit ** 2
view = [slice(None)] * 3
pix_cen = u.Quantity(cube._pix_cen()[axis] * spec_unit)
# term2 does not depend on the plane.
term2 = moment1 / axis_sum
for i in range(cube.shape[axis]):
view[axis] = i
term1 = pix_cen[view] / axis_sum
if _scale_cube:
noise_plane = \
np.nan_to_num(scale.filled_data[view])
else:
noise_plane = scale
result += np.power((term1 - term2) * noise_plane, 2)
return np.sqrt(result)
def _slice0(cube, axis, scale):
"""
0th moment along an axis, calculated slicewise
Parameters
----------
cube : SpectralCube
axis : int
scale : float
Returns
-------
moment0_error : array
"""
if isinstance(scale, SpectralCube):
# scale should then have the same shape as the cube.
if cube.shape != scale.shape:
raise IndexError("When scale is a SpectralCube, it must have the"
" same shape as the cube.")
_scale_cube = True
else:
_scale_cube = False
shp = _moment_shp(cube, axis)
result = np.zeros(shp) * cube.unit ** 2
view = [slice(None)] * 3
valid = np.zeros(shp, dtype=np.bool)
for i in range(cube.shape[axis]):
view[axis] = i
plane = cube._mask.include(data=cube._data, wcs=cube._wcs, view=view)
valid |= plane
if _scale_cube:
noise_plane = np.nan_to_num(scale.filled_data[view])
else:
noise_plane = scale
result += plane * np.power(noise_plane, 2)
out_result = np.sqrt(result) * cube._pix_size_slice(axis)
out_result[~valid] = np.nan
return out_result
def _slice0(cube, axis, scale):
"""
0th moment along an axis, calculated slicewise
Parameters
----------
cube : SpectralCube
axis : int
scale : float
Returns
-------
moment0_error : array
"""
if isinstance(scale, SpectralCube):
# scale should then have the same shape as the cube.
if cube.shape != scale.shape:
raise IndexError("When scale is a SpectralCube, it must have the"
" same shape as the cube.")
_scale_cube = True
else:
_scale_cube = False
shp = _moment_shp(cube, axis)
result = np.zeros(shp) * cube.unit ** 2
view = [slice(None)] * 3
valid = np.zeros(shp, dtype=np.bool)
for i in range(cube.shape[axis]):
view[axis] = i
plane = cube._mask.include(data=cube._data, wcs=cube._wcs, view=view)
valid |= plane
if _scale_cube:
noise_plane = np.nan_to_num(scale.filled_data[view])
else:
noise_plane = scale
result += plane * np.power(noise_plane, 2)
out_result = np.sqrt(result) * cube._pix_size_slice(axis)
out_result[~valid] = np.nan
return out_result
def _cube1(cube, axis, scale, moment0, moment1):
'''
Moment 1 error computed cube-wise.
'''
if isinstance(scale, SpectralCube):
# scale should then have the same shape as the cube.
if cube.shape != scale.shape:
raise IndexError("When scale is a SpectralCube, it must have the"
" same shape as the cube.")
noise_plane = scale.filled_data[:]
else:
noise_plane = scale
# I don't think there is a way to do this with one pass.
# The first 2 moments always have to be pre-computed.
# Divide moment0 by the pixel size in the given axis so it represents the
# sum.
spec_unit = cube.spectral_axis.unit
axis_sum = u.Quantity(moment0 /
(cube._pix_size_slice(axis) * spec_unit))
shp = _moment_shp(cube, axis)
result = np.zeros(shp) * spec_unit
pix_cen = cube._pix_cen()[axis] * spec_unit
term1 = pix_cen / axis_sum
term2 = moment1 / axis_sum
result = np.sqrt(np.sum(np.power((term1 - term2) *
np.nan_to_num(noise_plane), 2),
axis=axis))
good_pix = np.isfinite(moment0) + np.isfinite(moment1)
result[~good_pix] = np.NaN
return result
def _cube1(cube, axis, scale, moment0, moment1):
'''
Moment 1 error computed cube-wise.
'''
if isinstance(scale, SpectralCube):
# scale should then have the same shape as the cube.
if cube.shape != scale.shape:
raise IndexError("When scale is a SpectralCube, it must have the"
" same shape as the cube.")
noise_plane = scale.filled_data[:]
else:
noise_plane = scale
# I don't think there is a way to do this with one pass.
# The first 2 moments always have to be pre-computed.
# Divide moment0 by the pixel size in the given axis so it represents the
# sum.
spec_unit = cube.spectral_axis.unit
axis_sum = u.Quantity(moment0 /
(cube._pix_size_slice(axis) * spec_unit))
shp = _moment_shp(cube, axis)
result = np.zeros(shp) * spec_unit
pix_cen = cube._pix_cen()[axis] * spec_unit
term1 = pix_cen / axis_sum
term2 = moment1 / axis_sum
result = np.sqrt(np.sum(np.power((term1 - term2) *
np.nan_to_num(noise_plane), 2),
axis=axis))
good_pix = np.isfinite(moment0) + np.isfinite(moment1)
result[~good_pix] = np.NaN
return result
def _slice2(cube, axis, scale, moment0, moment1, moment2,
moment1_err):
"""
2nd moment error along an axis, calculated slicewise
Parameters
----------
cube : SpectralCube
axis : int
scale : float
moment0 : 0th moment
moment1 : 1st moment
moment2 : 2nd moment
moment1_err : 1st moment error
Returns
-------
moment1_error : array
"""
shp = _moment_shp(cube, axis)
term1 = np.zeros(shp)
term2 = np.zeros(shp)
view = [slice(None)] * 3
pix_cen = cube._pix_cen()[axis]
pix_size = cube._pix_size()[axis]
for i in range(cube.shape[axis]):
view[axis] = i
plane = cube._get_filled_data(fill=0, view=view)
term1 += scale**2 * \
np.power((np.power((pix_cen[view] - moment1), 2) -
moment2), 2)
term2 += (plane*pix_size[view]) * (pix_cen[view] - moment1)
return (1/moment0) * np.sqrt(term1 + 4*np.power(moment1_err*term2, 2))
def _slice2(cube, axis, scale, moment0, moment1, moment2,
moment1_err):
"""
2nd moment error along an axis, calculated slicewise
Parameters
----------
cube : SpectralCube
axis : int
scale : float or SpectralCube
moment0 : 0th moment
moment1 : 1st moment
moment2 : 2nd moment
moment1_err : 1st moment error
Returns
-------
moment1_error : array
"""
if isinstance(scale, SpectralCube):
# scale should then have the same shape as the cube.
if cube.shape != scale.shape:
raise IndexError("When scale is a SpectralCube, it must have the"
" same shape as the cube.")
_scale_cube = True
else:
_scale_cube = False
# Divide moment0 by the pixel size in the given axis so it represents the
# sum.
spec_unit = cube.spectral_axis.unit
axis_sum = u.Quantity(moment0 /
(cube._pix_size_slice(axis) * spec_unit))
shp = _moment_shp(cube, axis)
term1 = np.zeros(shp) * spec_unit ** 4
term2 = np.zeros(shp) * spec_unit * cube.unit
view = [slice(None)] * 3
pix_cen = cube._pix_cen()[axis] * spec_unit
# term12 does not depend on plane.
term12 = moment2 / axis_sum
for i in range(cube.shape[axis]):
view[axis] = i
plane = np.nan_to_num(cube.filled_data[view])
term11 = np.power((pix_cen[view] - moment1), 2) / axis_sum
if _scale_cube:
noise_plane = \
np.nan_to_num(scale.filled_data[view])
else:
noise_plane = scale
term1 += np.power((term11 - term12) * noise_plane, 2)
term2 += np.nan_to_num(plane) * (pix_cen[view] - moment1)
term2 = 4 * np.power((moment1_err * term2) / (axis_sum), 2)
return np.sqrt(term1 + term2)
def _slice2(cube, axis, scale, moment0, moment1, moment2,
moment1_err):
"""
2nd moment error along an axis, calculated slicewise
Parameters
----------
cube : SpectralCube
axis : int
scale : float or SpectralCube
moment0 : 0th moment
moment1 : 1st moment
moment2 : 2nd moment
moment1_err : 1st moment error
Returns
-------
moment1_error : array
"""
if isinstance(scale, SpectralCube):
# scale should then have the same shape as the cube.
if cube.shape != scale.shape:
raise IndexError("When scale is a SpectralCube, it must have the"
" same shape as the cube.")
_scale_cube = True
else:
_scale_cube = False
# Divide moment0 by the pixel size in the given axis so it represents the
# sum.
spec_unit = cube.spectral_axis.unit
axis_sum = u.Quantity(moment0 /
(cube._pix_size_slice(axis) * spec_unit))
shp = _moment_shp(cube, axis)
term1 = np.zeros(shp) * spec_unit ** 4
term2 = np.zeros(shp) * spec_unit * cube.unit
view = [slice(None)] * 3
pix_cen = cube._pix_cen()[axis] * spec_unit
# term12 does not depend on plane.
term12 = moment2 / axis_sum
for i in range(cube.shape[axis]):
view[axis] = i
plane = np.nan_to_num(cube.filled_data[view])
term11 = np.power((pix_cen[view] - moment1), 2) / axis_sum
if _scale_cube:
noise_plane = \
np.nan_to_num(scale.filled_data[view])
else:
noise_plane = scale
term1 += np.power((term11 - term12) * noise_plane, 2)
term2 += np.nan_to_num(plane) * (pix_cen[view] - moment1)
term2 = 4 * np.power((moment1_err * term2) / (axis_sum), 2)
return np.sqrt(term1 + term2)
