# 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)
>>> result = convolve_fft(image, kernel)


convolve() is implemented as a direct convolution algorithm, while 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 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)


### Examples¶

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])
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')
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')
array([1.6 , 3.6 , 5.  , 5.75, 6.5 , 7.25, 7.8 ])


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)


A 2D array as a list:

>>> kernel = [[0, 1, 0],
...           [1, 2, 1],
...           [0, 1, 0]]
>>> result = convolve(image, kernel)


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)


## Kernels¶

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