Using the Convolution Functions
*******************************

Overview
========

Two convolution functions are provided. They are imported as::

    >>> from astropy.convolution import convolve, convolve_fft

and are both used as::

    >>> result = convolve(image, kernel)  # doctest: +SKIP
    >>> result = convolve_fft(image, kernel)  # doctest: +SKIP

:func:`~astropy.convolution.convolve` is implemented as a
direct convolution algorithm, while
:func:`~astropy.convolution.convolve_fft` uses a Fast Fourier
Transform (FFT). Thus, the former is better for small kernels, while the latter
is much more efficient for larger kernels.

The input images and kernels should be lists or ``numpy`` arrays with either 1,
2, or 3 dimensions (and the number of dimensions should be the same for the
image and kernel). The result is a ``numpy`` array with the same dimensions as
the input image. The convolution is always done as floating point.

The :func:`~astropy.convolution.convolve` function takes an
optional ``boundary=`` argument describing how to perform the convolution at
the edge of the array. The values for ``boundary`` can be:

* ``None``: set the result values to zero where the kernel extends beyond the
  edge of the array (default).

* ``'fill'``: set values outside the array boundary to a constant. If this
  option is specified, the constant should be specified using the
  ``fill_value=`` argument, which defaults to zero.

* ``'wrap'``: assume that the boundaries are periodic.

* ``'extend'`` : set values outside the array to the nearest array value.

By default, the kernel is not normalized. To normalize it prior to convolution,
use::

    >>> result = convolve(image, kernel, normalize_kernel=True)  # doctest: +SKIP

Examples
--------

..
  EXAMPLE START
  Smoothing Arrays with Custom Kernels

Smooth a 1D array with a custom kernel and no boundary treatment::

    >>> import numpy as np
    >>> convolve([1, 4, 5, 6, 5, 7, 8], [0.2, 0.6, 0.2])  # doctest: +FLOAT_CMP
    array([1.4, 3.6, 5. , 5.6, 5.6, 6.8, 6.2])

As above, but using the 'extend' algorithm for boundaries::

    >>> convolve([1, 4, 5, 6, 5, 7, 8], [0.2, 0.6, 0.2], boundary='extend')  # doctest: +FLOAT_CMP
    array([1.6, 3.6, 5. , 5.6, 5.6, 6.8, 7.8])

If a NaN value is present in the original array, it will be
interpolated using the kernel::

    >>> import numpy as np
    >>> convolve([1, 4, 5, 6, np.nan, 7, 8], [0.2, 0.6, 0.2], boundary='extend')  # doctest: +FLOAT_CMP
    array([1.6 , 3.6 , 5.  , 5.75, 6.5 , 7.25, 7.8 ])

..
  EXAMPLE END

..
  EXAMPLE START
  Constructing Kernels from Lists

Kernels and arrays can be specified either as lists or as ``numpy``
arrays. The following examples show how to construct a 1D array as a
list::

    >>> kernel = [0, 1, 0]
    >>> result = convolve(spectrum, kernel)  # doctest: +SKIP

A 2D array as a list::

    >>> kernel = [[0, 1, 0],
    ...           [1, 2, 1],
    ...           [0, 1, 0]]
    >>> result = convolve(image, kernel)  # doctest: +SKIP

And a 3D array as a list::

    >>> kernel = [[[0, 0, 0], [0, 2, 0], [0, 0, 0]],
    ...           [[0, 1, 0], [2, 3, 2], [0, 1, 0]],
    ...           [[0, 0, 0], [0, 2, 0], [0, 0, 0]]]
    >>> result = convolve(cube, kernel)  # doctest: +SKIP

..
  EXAMPLE END

Kernels
=======

The above examples use custom kernels, but `astropy.convolution` also
includes a number of built-in kernels, which are described in
:doc:`kernels`.