Overlapping Computations
Contents
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:

Map a function over blocks of arrays with some overlap 
 dask.array.map_overlap(func, *args, depth=None, boundary=None, trim=True, align_arrays=True, **kwargs)[source]
Map a function over blocks of arrays with some overlap
We share neighboring zones between blocks of the array, map a function, and then trim away the neighboring strips. If depth is larger than any chunk along a particular axis, then the array is rechunked.
Note that this function will attempt to automatically determine the output array type before computing it, please refer to the
meta
keyword argument inmap_blocks
if you expect that the function will not succeed when operating on 0d arrays. Parameters
 func: function
The function to apply to each extended block. If multiple arrays are provided, then the function should expect to receive chunks of each array in the same order.
 argsdask arrays
 depth: int, tuple, dict or list
The number of elements that each block should share with its neighbors If a tuple or dict then this can be different per axis. If a list then each element of that list must be an int, tuple or dict defining depth for the corresponding array in args. Asymmetric depths may be specified using a dict value of (/+) tuples. Note that asymmetric depths are currently only supported when
boundary
is ‘none’. The default value is 0. boundary: str, tuple, dict or list
How to handle the boundaries. Values include ‘reflect’, ‘periodic’, ‘nearest’, ‘none’, or any constant value like 0 or np.nan. If a list then each element must be a str, tuple or dict defining the boundary for the corresponding array in args. The default value is ‘reflect’.
 trim: bool
Whether or not to trim
depth
elements from each block after calling the map function. Set this to False if your mapping function already does this for you align_arrays: bool
Whether or not to align chunks along equally sized dimensions when multiple arrays are provided. This allows for larger chunks in some arrays to be broken into smaller ones that match chunk sizes in other arrays such that they are compatible for block function mapping. If this is false, then an error will be thrown if arrays do not already have the same number of blocks in each dimension.
 **kwargs:
Other keyword arguments valid in
map_blocks
Examples
>>> import numpy as np >>> import dask.array as da
>>> x = np.array([1, 1, 2, 3, 3, 3, 2, 1, 1]) >>> x = da.from_array(x, chunks=5) >>> def derivative(x): ... return x  np.roll(x, 1)
>>> y = x.map_overlap(derivative, depth=1, boundary=0) >>> y.compute() array([ 1, 0, 1, 1, 0, 0, 1, 1, 0])
>>> x = np.arange(16).reshape((4, 4)) >>> d = da.from_array(x, chunks=(2, 2)) >>> d.map_overlap(lambda x: x + x.size, depth=1, boundary='reflect').compute() array([[16, 17, 18, 19], [20, 21, 22, 23], [24, 25, 26, 27], [28, 29, 30, 31]])
>>> func = lambda x: x + x.size >>> depth = {0: 1, 1: 1} >>> boundary = {0: 'reflect', 1: 'none'} >>> d.map_overlap(func, depth, boundary).compute() array([[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23], [24, 25, 26, 27]])
The
da.map_overlap
function can also accept multiple arrays.>>> func = lambda x, y: x + y >>> x = da.arange(8).reshape(2, 4).rechunk((1, 2)) >>> y = da.arange(4).rechunk(2) >>> da.map_overlap(func, x, y, depth=1, boundary='reflect').compute() array([[ 0, 2, 4, 6], [ 4, 6, 8, 10]])
When multiple arrays are given, they do not need to have the same number of dimensions but they must broadcast together. Arrays are aligned block by block (just as in
da.map_blocks
) so the blocks must have a common chunk size. This common chunking is determined automatically as long asalign_arrays
is True.>>> x = da.arange(8, chunks=4) >>> y = da.arange(8, chunks=2) >>> r = da.map_overlap(func, x, y, depth=1, boundary='reflect', align_arrays=True) >>> len(r.to_delayed()) 4
>>> da.map_overlap(func, x, y, depth=1, boundary='reflect', align_arrays=False).compute() Traceback (most recent call last): ... ValueError: Shapes do not align {'.0': {2, 4}}
Note also that this function is equivalent to
map_blocks
by default. A nonzerodepth
must be defined for any overlap to appear in the arrays provided tofunc
.>>> func = lambda x: x.sum() >>> x = da.ones(10, dtype='int') >>> block_args = dict(chunks=(), drop_axis=0) >>> da.map_blocks(func, x, **block_args).compute() 10 >>> da.map_overlap(func, x, **block_args, boundary='reflect').compute() 10 >>> da.map_overlap(func, x, **block_args, depth=1, boundary='reflect').compute() 12
For functions that may not handle 0d arrays, it’s also possible to specify
meta
with an empty array matching the type of the expected result. In the example below,func
will result in anIndexError
when computingmeta
:>>> x = np.arange(16).reshape((4, 4)) >>> d = da.from_array(x, chunks=(2, 2)) >>> y = d.map_overlap(lambda x: x + x[2], depth=1, boundary='reflect', meta=np.array(())) >>> y dask.array<_trim, shape=(4, 4), dtype=float64, chunksize=(2, 2), chunktype=numpy.ndarray> >>> y.compute() array([[ 4, 6, 8, 10], [ 8, 10, 12, 14], [20, 22, 24, 26], [24, 26, 28, 30]])
Similarly, it’s possible to specify a nonNumPy array to
meta
:>>> import cupy >>> x = cupy.arange(16).reshape((4, 4)) >>> d = da.from_array(x, chunks=(2, 2)) >>> y = d.map_overlap(lambda x: x + x[2], depth=1, boundary='reflect', meta=cupy.array(())) >>> y dask.array<_trim, shape=(4, 4), dtype=float64, chunksize=(2, 2), chunktype=cupy.ndarray> >>> y.compute() array([[ 4, 6, 8, 10], [ 8, 10, 12, 14], [20, 22, 24, 26], [24, 26, 28, 30]])
Explanation¶
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 overlap 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.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 sidereflect
 reflect each border outwardsanyconstant
 pad the border with this value
An example boundary kind argument might look like the following:
{0: 'periodic',
1: 'reflect',
2: np.nan}
Alternatively, you can use dask.array.pad()
for other types of
paddings.
Map a function across blocks¶
Overlapping goes handinhand 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 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))
.
>>> 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 upperleft 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
:
>>> 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
:
>>> 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})