*****************************
Slicing Multidimensional Data
*****************************

WCSAxes can either plot one or two dimensional data. If we have a dataset with
higher dimensionality than the plot we want to make, we have to select which
dimensions to use for the x or x and y axes of the plot. This example will show
how to slice a FITS data cube and plot an image from it.

Slicing the WCS object
**********************

Like the example introduced in :ref:`initialization`, we will read in the
data using `astropy.io.fits
<https://docs.astropy.org/en/stable/io/fits/index.html>`_ and parse the WCS
information. The original FITS file can be downloaded from `here
<http://www.astropy.org/astropy-data/l1448/l1448_13co.fits>`_.

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    import matplotlib.pyplot as plt
    from astropy.wcs import WCS
    from astropy.io import fits
    from astropy.utils.data import get_pkg_data_filename
    filename = get_pkg_data_filename('l1448/l1448_13co.fits')
    hdu = fits.open(filename)[0]
    wcs = WCS(hdu.header)
    image_data = hdu.data

This is a three-dimensional dataset which you can check by looking at the
header information by::

    >>> hdu.header  # doctest: +SKIP
    ...
    NAXIS = 3 /number of axes
    CTYPE1  = 'RA---SFL'           /
    CTYPE2  = 'DEC--SFL'           /
    CTYPE3  = 'VELO-LSR'           /
    ...

The header keyword 'NAXIS' gives the number of dimensions of the dataset. The keywords 'CTYPE1', 'CTYPE2' and 'CTYPE3' give the data type of these dimensions to be right ascension, declination and velocity respectively.

We then instantiate the `~astropy.visualization.wcsaxes.WCSAxes` using the
:class:`~astropy.wcs.WCS` object and select the slices we want to plot:

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    import matplotlib.pyplot as plt
    fig, ax = plt.subplots(subplot_kw=dict(projection=wcs, slices=(50, 'y', 'x')))

By setting ``slices=(50, 'y', 'x')``, we have chosen to plot the second
dimension on the y-axis and the third dimension on the x-axis. Even though we
are not plotting the all the dimensions, we have to specify which slices to
select for the dimensions that are not shown. In this example, we are not
plotting the first dimension so we have selected the slice 50 to display. You
can experiment with this by changing the selected slice and looking at how the
plotted image changes.

Plotting the image
******************

We then add the axes to the image and plot it using the method
:meth:`~matplotlib.axes.Axes.imshow`.

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    ax.coords[2].set_ticklabel(exclude_overlapping=True)
    ax.imshow(image_data[:, :, 50].transpose())

Here, ``image_data`` is an :class:`~numpy.ndarray` object. In Numpy, the order
of the axes is reversed so the first dimension in the FITS file appears last,
the last dimension appears first and so on. Therefore the index passed to
:meth:`~matplotlib.axes.Axes.imshow` should be the same as passed to
``slices`` but in reversed order. We also need to
:meth:`~numpy.ndarray.transpose` ``image_data`` as we have reversed the
dimensions plotted on the x and y axes in the slice.

If we don't want to reverse the dimensions plotted, we can simply do:

.. plot::
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    import astropy.units as u
    from astropy.wcs import WCS
    from astropy.io import fits
    from astropy.utils.data import get_pkg_data_filename
    filename = get_pkg_data_filename('l1448/l1448_13co.fits')
    hdu = fits.open(filename)[0]
    wcs = WCS(hdu.header)
    image_data = hdu.data

.. plot::
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    import matplotlib.pyplot as plt
    fig, ax = plt.subplots(subplot_kw=dict(projection=wcs, slices=(50, 'x', 'y')))
    ax.imshow(image_data[:, :, 50])


Plotting one dimensional data
*****************************

If we wanted to plot the spectral axes for one pixel we can do this by slicing
down to one dimension.

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    import matplotlib.pyplot as plt
    fig, ax = plt.subplots(subplot_kw=dict(projection=wcs, slices=(50, 50, 'x')))


Here we have selected the 50 pixel in the first and second dimensions and will
use the third dimension as our x axis.

We can now plot the spectral axis for this pixel. Note that we are plotting
against pixel coordinates in the call to ``ax.plot``, ``WCSAxes`` will display
the world coordinates for us.

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   ax.plot(image_data[:, 50, 50])

As this is still a ``WCSAxes`` plot, we can set the display units for the x-axis

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   ra, dec, vel = ax.coords
   vel.set_format_unit(u.km/u.s)


If we wanted to plot a one dimensional plot along a spatial dimension, i.e.
intensity along a row in the image, ``WCSAxes`` defaults to displaying both the
world coordinates for this plot. We can customise the colors and add grid lines
for each of the spatial axes.

.. plot::
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    import matplotlib.pyplot as plot
    fig, ax = plt.subplots(subplot_kw=dict(projection=wcs, slices=(50, 'x', 0)))

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   ax.plot(image_data[0, :, 50])

   ra, dec, wave = ax.coords
   ra.set_ticks(color="red")
   ra.set_ticklabel(color="red")
   ra.grid(color="red")

   dec.set_ticks(color="blue")
   dec.set_ticklabel(color="blue")
   dec.grid(color="blue")
