# Overlapping Computations¶

Some array operations require communication of borders between neighboring blocks. Example operations include the following:

• Convolve a filter across an image
• Sliding sum/mean/max, …
• Search for image motifs like a Gaussian blob that might span the border of a block
• Evaluate a partial derivative
• Play the game of Life

Dask array supports these operations by creating a new array where each block is slightly expanded by the borders of its neighbors. This costs an excess copy and the communication of many small chunks but allows localized functions to evaluate in an embarrassing manner. We call this process ghosting.

## Ghosting¶

Consider two neighboring blocks in a Dask array.

We extend each block by trading thin nearby slices between arrays

We do this in all directions, including also diagonal interactions with the ghost function:

>>> import dask.array as da
>>> import numpy as np

>>> x = np.arange(64).reshape((8, 8))
>>> d = da.from_array(x, chunks=(4, 4))
>>> d.chunks
((4, 4), (4, 4))

>>> g = da.ghost.ghost(d, depth={0: 2, 1: 1},
...                       boundary={0: 100, 1: 'reflect'})
>>> g.chunks
((8, 8), (6, 6))

>>> np.array(g)
array([[100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],
[100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],
[  0,   0,   1,   2,   3,   4,   3,   4,   5,   6,   7,   7],
[  8,   8,   9,  10,  11,  12,  11,  12,  13,  14,  15,  15],
[ 16,  16,  17,  18,  19,  20,  19,  20,  21,  22,  23,  23],
[ 24,  24,  25,  26,  27,  28,  27,  28,  29,  30,  31,  31],
[ 32,  32,  33,  34,  35,  36,  35,  36,  37,  38,  39,  39],
[ 40,  40,  41,  42,  43,  44,  43,  44,  45,  46,  47,  47],
[ 16,  16,  17,  18,  19,  20,  19,  20,  21,  22,  23,  23],
[ 24,  24,  25,  26,  27,  28,  27,  28,  29,  30,  31,  31],
[ 32,  32,  33,  34,  35,  36,  35,  36,  37,  38,  39,  39],
[ 40,  40,  41,  42,  43,  44,  43,  44,  45,  46,  47,  47],
[ 48,  48,  49,  50,  51,  52,  51,  52,  53,  54,  55,  55],
[ 56,  56,  57,  58,  59,  60,  59,  60,  61,  62,  63,  63],
[100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],
[100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]])


## Boundaries¶

While ghosting you can specify how to handle the boundaries. Current policies include the following:

• periodic - wrap borders around to the other side
• reflect - reflect each border outwards
• any-constant - pad the border with this value

So an example boundary kind argument might look like the following

{0: 'periodic',
1: 'reflect',
2: np.nan}


Alternatively you can use functions like da.fromfunction and da.concatenate to pad arbitrarily.

## Map a function across blocks¶

Ghosting goes hand-in-hand with mapping a function across blocks. This function can now use the additional information copied over from the neighbors that is not stored locally in each block

>>> from scipy.ndimage.filters import gaussian_filter
>>> def func(block):
...    return gaussian_filter(block, sigma=1)

>>> filt = g.map_blocks(func)


While in this case we used a SciPy function above this could have been any arbitrary function. This is a good interaction point with Numba.

If your function does not preserve the shape of the block then you will need to provide a chunks keyword argument. If your block sizes are regular then this can be a blockshape, such as (1000, 1000) or if your blocks are irregular then this must be a full chunks tuple, for example ((1000, 700, 1000), (200, 300)).

>>> g.map_blocks(myfunc, chunks=(5, 5))


If your function needs to know the location of the block on which it operates you can give your function a keyword argument block_id

def func(block, block_id=None):
...


This extra keyword argument will be given a tuple that provides the block location like (0, 0) for the upper right block or (0, 1) for the block just to the right of that block.

## Trim Excess¶

After mapping a blocked function you may want to trim off the borders from each block by the same amount by which they were expanded. The function trim_internal is useful here and takes the same depth argument given to ghost.

>>> x.chunks
((10, 10, 10, 10), (10, 10, 10, 10))

>>> y = da.ghost.trim_internal(x, {0: 2, 1: 1})
>>> y.chunks
((6, 6, 6, 6), (8, 8, 8, 8))


## Full Workflow¶

And so a pretty typical ghosting workflow includes ghost, map_blocks, and trim_internal

>>> x = ...
>>> g = da.ghost.ghost(x, depth={0: 2, 1: 2},
...                       boundary={0: 'periodic', 1: 'periodic'})
>>> g2 = g.map_blocks(myfunc)
>>> result = da.ghost.trim_internal(g2, {0: 2, 1: 2})