Tabular Coordinates

So far we have assumed that we are constructing an NDCube using a WCS that has been read from a file or explicitly created. However, in some cases we may have tables giving the coordinate values at each pixel and converting these into a WCS manually can be tedious. Therefore ndcube provides tools for constructing WCSes from such tables.

Tabular coordinates are useful when there is no mathematical description of the axis, or when it’s a natural fit for the data you have. It’s worth considering that tabular coordinates are generally not as polished as a functional transform in a WCS. Therefore, if possible, building a functional WCS for your coordinate system is highly recommended.

Tabular Coordinates and WCSes

All coordinate information in ndcube is represented as a WCS. Even the ExtraCoords class, which allows the user to add tabular data to axes, uses the gwcs library to store this information as a WCS. This enables ndcube’s coordinate transformation and plotting functions to leverage the same infrastructure, irrespective of whether the coordinates are functional or tabular.

The FITS WCS standard also supports tabular axes with the -TAB CTYPE. Support for reading files using this convention has (reasonably) recently been added to Astropy, so if you have a FITS file using this convention you should be able to load it into a WCS object. If you wish to be able to serialise your NDCube object to FITS files you will need to manually construct a WCS object using the -TAB convention.

The functionality provided by ndcube makes it easy to construct a gwcs.wcs.WCS object backed by lookup tables. At the time of writing there are some known issues with the support for generic lookup tables in gwcs.

Constructing a WCS from Lookup Tables

ndcube supports constructing lookup tables from SkyCoord, Time and Quantity objects. These objects are wrapped in BaseTableCoordinate objects which can be composed together into a multi-dimensional WCS.

Note

Only one dimensional tables are currently supported. It is possible to construct higher dimensional lookup tables by “meshing” the inputs, which is described below.

A simple example of constructing a WCS from a lookup table in a TimeTableCoordinate is the following temporal axis:

>>> from astropy.time import Time
>>> import astropy.units as u
>>> from ndcube.extra_coords import TimeTableCoordinate

>>> time_axis = Time("2021-01-01T00:00:00") + (list(range(10)) * u.hour)
>>> time_axis
<Time object: scale='utc' format='isot' value=['2021-01-01T00:00:00.000' '2021-01-01T01:00:00.000'
 '2021-01-01T02:00:00.000' '2021-01-01T03:00:00.000'
 '2021-01-01T04:00:00.000' '2021-01-01T05:00:00.000'
 '2021-01-01T06:00:00.000' '2021-01-01T07:00:00.000'
 '2021-01-01T08:00:00.000' '2021-01-01T09:00:00.000']>

>>> gwcs = TimeTableCoordinate(time_axis).wcs
>>> gwcs
<WCS(output_frame=TemporalFrame, input_frame=PixelFrame, forward_transform=Model: Tabular1D
N_inputs: 1
N_outputs: 1
Parameters:
  points: (<Quantity [0., 1., 2., 3., 4., 5., 6., 7., 8., 9.] pix>,)
  lookup_table: [    0.  3600.  7200. 10800. 14400. 18000. 21600. 25200. 28800. 32400.] s
  method: linear
  fill_value: nan
  bounds_error: False)>

This gwcs.WCS object can then be passed to the constructor of NDCube alongside your array and other parameters.

Combining Two Coordinates into a Single WCS

We can extend this example to be a space-space-time cube. In this example we are going to utilize the mesh= keyword argument for the first time. This keyword argument interprets the input to SkyCoordTableCoordinate in a similar way to numpy.meshgrid.

>>> from astropy.coordinates import SkyCoord
>>> from ndcube.extra_coords import SkyCoordTableCoordinate

>>> icrs_table = SkyCoord(range(10)*u.deg, range(10, 20)*u.deg)
>>> icrs_table
<SkyCoord (ICRS): (ra, dec) in deg
    [(0., 10.), (1., 11.), (2., 12.), (3., 13.), (4., 14.), (5., 15.),
     (6., 16.), (7., 17.), (8., 18.), (9., 19.)]>

>>> gwcs = (TimeTableCoordinate(time_axis) & SkyCoordTableCoordinate(icrs_table, mesh=True)).wcs
>>> gwcs
<WCS(output_frame=CompositeFrame, input_frame=PixelFrame, forward_transform=Model: CompoundModel
Inputs: ('x', 'x0', 'x1')
Outputs: ('y', 'y0', 'y1')
Model set size: 1
Expression: [0] & [1] & [2]
Components:
    [0]: <Tabular1D(points=(<Quantity [0., 1., 2., 3., 4., 5., 6., 7., 8., 9.] pix>,), lookup_table=[    0.  3600.  7200. 10800. 14400. 18000. 21600. 25200. 28800. 32400.] s)>

    [1]: <Tabular1D(points=(<Quantity [0., 1., 2., 3., 4., 5., 6., 7., 8., 9.] pix>,), lookup_table=[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.] deg)>

    [2]: <Tabular1D(points=(<Quantity [0., 1., 2., 3., 4., 5., 6., 7., 8., 9.] pix>,), lookup_table=[10. 11. 12. 13. 14. 15. 16. 17. 18. 19.] deg)>
Parameters:)>

As you can see the coordinate information is stored in memory efficient one dimensional tables, and then converted to a two dimensional coordinate when needed.

Note

Due to a limitation in gwcs only unit spherical (two dimensional) SkyCoords are supported at this time.