First commit of docs explaining arithmetic operations.

Author: DanRyanIrish

docs/explaining_ndcube/arithmetic_operations.rst

@@ -0,0 +1,138 @@
+.. _arithmetic:
+
+*********************
+Arithmetic Operations
+*********************
+
+Arithmetic operations are a crucial tool in n-dimensional data analysis.
+Applications include subtracting a background from a 1-D timeseries or spectrum, scaling an image by a vignetting function, any many others.
+To aid with such workflows, `~ndcube.NDCube` supports addition, subtraction, multiplication, and division with scalars, arrays, `~astropy.units.Quantity`.
+Raising an `~ndcube.NDCube` to a power is also supported.
+These operations return a new `~ndcube.NDCube` with the data array (and where appropriate, the uncertainties) altered in accordance with the arithmetic operation.
+Other attributes of the `~ndcube.NDCube` remain unchanged.
+
+In addition, combining `~ndcube.NDCube` with coordinate-less `~astropy.nddata.NDData` subclasses via these operations is important.
+Such operations can be more complicated.  Hence see the :ref:`arithmetic_nddata` section below for a discussion separate, more detailed discussion. 
+
+.. _arithmetic_standard:
+
+Standard Arithmetic Operations
+==============================
+
+Addition and Subtraction with Scalars, Arrays and Quantities
+------------------------------------------------------------
+
+Let's demonstrate how we can add and subtract scalars, arrays and `~astropy.units.Quantity` to/from an `~ndcube.NDCube` called ``cube``.
+Note that addition and subtraction only changes the data values of the `~ndcube.NDCube`.
+
+.. expanding-code-block:: python
+  :summary: Expand to see my_cube instantiated.
+
+  >>> import astropy.units as u
+  >>> import astropy.wcs
+  >>> import numpy as np
+  >>> from astropy.nddata import StdDevUncertainty
+
+  >>> from ndcube import NDCube
+
+  >>> # Define data array.
+  >>> data = np.arange(2*3).reshape((2, 3)) + 10
+
+  >>> # Define WCS transformations in an astropy WCS object.
+  >>> wcs = astropy.wcs.WCS(naxis=2)
+  >>> wcs.wcs.ctype = 'HPLT-TAN', 'HPLN-TAN'
+  >>> wcs.wcs.cunit = 'deg', 'deg'
+  >>> wcs.wcs.cdelt = 0.5, 0.4
+  >>> wcs.wcs.crpix = 2, 2
+  >>> wcs.wcs.crval = 0.5, 1
+
+  >>> # Define mask. Initially set all elements unmasked.
+  >>> mask = np.zeros_like(data, dtype=bool)
+  >>> mask[0, :] = True  # Now mask some values.
+  >>> # Define uncertainty, metadata and unit.
+  >>> uncertainty = StdDevUncertainty(np.sqrt(np.abs(data)))
+  >>> meta = {"Description": "This is example NDCube metadata."}
+  >>> unit = u.ct
+
+  >>> # Instantiate NDCube with supporting data.
+  >>> cube = NDCube(data, wcs=wcs, uncertainty=uncertainty, mask=mask, meta=meta)
+  
+.. code-block:: python
+
+  >>> cube.data
+  array([[10, 11, 12],
+         [13, 14, 15]])
+  >>> new_cube = cube + 1
+  >>> new_cube.data
+  array([[11, 12, 13],
+         [14, 15, 16]])
+
+Note that all the data values have been increased by 1.
+We can also add an array if we want to add a different number to each data element:
+
+.. code-block:: python
+
+  >>> import numpy as np
+  >>> arr = np.arange(cube.data.size).reshape(cube.data.shape)
+  >>> arr
+  array([[0, 1, 2],
+         [3, 4, 5]])
+  >>> new_cube = cube + arr
+  >>> new_cube.data
+  array([[10, 12, 14],
+         [16, 18, 20]])
+
+Subtraction works in the same way.
+
+.. code-block:: python
+
+  >>> new_cube = cube - 1
+  >>> new_cube.data
+  array([[ 9, 10, 11],
+         [12, 13, 14]])
+  >>> new_cube = cube - arr
+  >>> new_cube.data
+  array([[10, 10, 10],
+         [10, 10, 10]])
+         
+Note that ``cube`` has no unit, which is why we are able to add and subtract scalars and arrays.
+If, however, we have an `~ndcube.NDCube` with a unit assigned,
+
+.. code-block:: python
+
+  >>> cube_unitful = NDCube(cube, unit=u.ct)
+  
+then adding or subtracting an array or unitless scalar will raise an error.
+In such cases, we must use a `~astropy.unit.Quantity` with a compatible unit:
+
+.. code-block:: python
+
+  >>> cube.data
+  array([[10, 11, 12],
+         [13, 14, 15]])
+  >>> new_cube = cube_unitful + 1 * u.ct  # Adding a scalar quantity
+  >>> new_cube.data
+  array([[11, 12, 13],
+         [14, 15, 16]])
+  >>> new_cube = cube_unitful - 1 * u.ct  # Subtracting a scalar quantity
+  >>> new_cube.data
+  array([[ 9, 10, 11],
+         [12, 13, 14]])
+  >>> new_cube = cube_unitful + arr * u.ct  # Adding an array-like quantity
+  >>> new_cube.data
+  array([[10, 12, 14],
+         [16, 18, 20]])
+  >>> new_cube = cube_unitful - arr * u.ct  # Subtracting an array-like quantity
+  >>> new_cube.data
+  array([[10, 10, 10],
+         [10, 10, 10]])
+  
+Multiplying and Dividing with Scalars, Arrays and Quantities
+------------------------------------------------------------
+
+.. _arithmetic_nddata:
+
+Arithmetic Operations with Coordinate-less NDData
+=================================================
+
+

docs/explaining_ndcube/index.rst

@@ -14,3 +14,4 @@ Explaining ``ndcube``
    tabular_coordinates
    reproject
    visualization
+   arithmetic_operations