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15.1 Convolution functions

# 15.1 Convolution functions

 boxcar( data, boxshape, output=None, mode='nearest', cval=0.0)
boxcar computes a 1-D or 2-D boxcar filter on every 1-D or 2-D subarray of data. boxshape is a tuple of integers specifying the dimensions of the filter, e.g. `(3,3)`. If output is specified, it should be the same shape as data and the result will be stored in it. In that case None will be returned.

mode can be any of the following values:

nearest
: Elements beyond boundary come from nearest edge pixel.
wrap
: Elements beyond boundary come from the opposite array edge.
reflect
: Elements beyond boundary come from reflection on same array edge.
constant
: Elements beyond boundary are set to what is specified in cval, an optional numerical parameter; the default value is `0.0`.
```>>> print a
[1 5 4 7 2 9 3 6]
>>> print conv.boxcar(a,(3,))
[ 2.33333333  3.33333333  5.33333333  4.33333333  6.          4.66666667
6.          5.        ]
# for even number box size, it will take the extra point from the lower end
>>> print conv.boxcar(a,(2,))
[ 1.   3.   4.5  5.5  4.5  5.5  6.   4.5]
```

 convolve( data, kernel, mode=FULL)
Returns the discrete, linear convolution of 1-D sequences data and kernel; mode can be VALID, SAME, or `FULL` to specify the size of the resulting sequence. See section 15.2.

 convolve2d( data, kernel, output=None, fft=0, mode='nearest', cval=0.0)
Return the 2-dimensional convolution of data and kernel. If output is not None, the result is stored in output and None is returned. fft is used to switch between FFT-based convolution and the naive algorithm, defaulting to naive. Using fft mode becomes more beneficial as the size of the kernel grows; for small kernels, the naive algorithm is more efficient. mode has the same choices as those of boxcar. A number of storage considerations come into play with large arrays: (1) boundary modes are implemented by making an oversized temporary copy of the data array which has a shape equal to the sum of the data and kernel shapes. (2) likewise, the kernel is copied into an array with the same shape as the oversized data array. (3) In FFT mode, the fourier transforms of the data and kernel arrays are stored in double precision complex temporaries. The aggregate effect is that storage roughly equal to a factor of eight (x2 from 2 and x4 from 3) times the size of the data is required to compute the convolution of a Float32 data array.

 correlate( data, kernel, mode=FULL)
Return the cross-correlation of data and kernel; mode can be VALID, SAME, or `FULL` to specify the size of the resulting sequence. correlate is very closely related to convolve in implementation. See section 15.2.

 correlate2d( data, kernel, output=None, fft=0, mode='nearest', cval=0.0)
Return the 2-dimensional convolution of data and kernel. If output is not None, the result is stored in output and None is returned. fft is used to switch between FFT-based convolution and the naive algorithm, defaulting to naive. Using fft mode becomes more beneficial as the size of the kernel grows; for small kernels, the naive algorithm is more efficient. mode has the same choices as those of boxcar. See also convolve2d for notes regarding storage consumption.

Note: cross_correlate is deprecated and should not be used.

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