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 embarrassingly parallel manner.

The main API for these computations is the map_overlap method defined below:

.. currentmodule:: dask.array

.. autosummary:: map_overlap

.. autofunction:: map_overlap :noindex:

Explanation

Consider two neighboring blocks in a Dask array:

.. image:: images/unoverlapping-neighbors.svg :width: 30% :alt: Two neighboring blocks which do not overlap.

We extend each block by trading thin nearby slices between arrays:

.. image:: images/overlapping-neighbors.svg :width: 30% :alt: Two neighboring block with thin strips along their shared border representing data shared between them.

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

.. image:: images/overlapping-blocks.svg :width: 40% :alt: A two-dimensional grid of blocks where each one has thin strips around their borders representing data shared from their neighbors. They include small corner bits for data shared from diagonal neighbors as well.

.. code-block:: python

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.overlap.overlap(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

With respect to overlapping, 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

An example boundary kind argument might look like the following:

.. code-block:: python

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

Alternatively, you can use :py:func:dask.array.pad for other types of paddings.

Map a function across blocks

Overlapping 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:

.. code-block:: python

from scipy.ndimage 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, any arbitrary function could have been used instead. 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 size is regular, then this argument can take a block shape of, for example, (1000, 1000). In case of irregular block sizes, it must be a tuple with the full chunks shape like ((1000, 700, 1000), (200, 300)).

.. code-block:: python

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:

.. code-block:: python

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-left 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 overlap:

.. code-block:: python

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

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

Full Workflow

And so, a pretty typical overlapping workflow includes overlap, map_blocks and trim_internal:

.. code-block:: python

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

.. _Life: https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life .. _Numba: https://numba.pydata.org/