from __future__ import annotations
import numbers
import warnings
import tlz as toolz
from dask import base, utils
from dask.blockwise import blockwise as core_blockwise
from dask.delayed import unpack_collections
from dask.highlevelgraph import HighLevelGraph
[docs]def blockwise(
func,
out_ind,
*args,
name=None,
token=None,
dtype=None,
adjust_chunks=None,
new_axes=None,
align_arrays=True,
concatenate=None,
meta=None,
**kwargs,
):
"""Tensor operation: Generalized inner and outer products
A broad class of blocked algorithms and patterns can be specified with a
concise multi-index notation. The ``blockwise`` function applies an in-memory
function across multiple blocks of multiple inputs in a variety of ways.
Many dask.array operations are special cases of blockwise including
elementwise, broadcasting, reductions, tensordot, and transpose.
Parameters
----------
func : callable
Function to apply to individual tuples of blocks
out_ind : iterable
Block pattern of the output, something like 'ijk' or (1, 2, 3)
*args : sequence of Array, index pairs
You may also pass literal arguments, accompanied by None index
e.g. (x, 'ij', y, 'jk', z, 'i', some_literal, None)
**kwargs : dict
Extra keyword arguments to pass to function
dtype : np.dtype
Datatype of resulting array.
concatenate : bool, keyword only
If true concatenate arrays along dummy indices, else provide lists
adjust_chunks : dict
Dictionary mapping index to function to be applied to chunk sizes
new_axes : dict, keyword only
New indexes and their dimension lengths
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.
Examples
--------
2D embarrassingly parallel operation from two arrays, x, and y.
>>> import operator, numpy as np, dask.array as da
>>> x = da.from_array([[1, 2],
... [3, 4]], chunks=(1, 2))
>>> y = da.from_array([[10, 20],
... [0, 0]])
>>> z = blockwise(operator.add, 'ij', x, 'ij', y, 'ij', dtype='f8')
>>> z.compute()
array([[11, 22],
[ 3, 4]])
Outer product multiplying a by b, two 1-d vectors
>>> a = da.from_array([0, 1, 2], chunks=1)
>>> b = da.from_array([10, 50, 100], chunks=1)
>>> z = blockwise(np.outer, 'ij', a, 'i', b, 'j', dtype='f8')
>>> z.compute()
array([[ 0, 0, 0],
[ 10, 50, 100],
[ 20, 100, 200]])
z = x.T
>>> z = blockwise(np.transpose, 'ji', x, 'ij', dtype=x.dtype)
>>> z.compute()
array([[1, 3],
[2, 4]])
The transpose case above is illustrative because it does transposition
both on each in-memory block by calling ``np.transpose`` and on the order
of the blocks themselves, by switching the order of the index ``ij -> ji``.
We can compose these same patterns with more variables and more complex
in-memory functions
z = X + Y.T
>>> z = blockwise(lambda x, y: x + y.T, 'ij', x, 'ij', y, 'ji', dtype='f8')
>>> z.compute()
array([[11, 2],
[23, 4]])
Any index, like ``i`` missing from the output index is interpreted as a
contraction (note that this differs from Einstein convention; repeated
indices do not imply contraction.) In the case of a contraction the passed
function should expect an iterable of blocks on any array that holds that
index. To receive arrays concatenated along contracted dimensions instead
pass ``concatenate=True``.
Inner product multiplying a by b, two 1-d vectors
>>> def sequence_dot(a_blocks, b_blocks):
... result = 0
... for a, b in zip(a_blocks, b_blocks):
... result += a.dot(b)
... return result
>>> z = blockwise(sequence_dot, '', a, 'i', b, 'i', dtype='f8')
>>> z.compute()
250
Add new single-chunk dimensions with the ``new_axes=`` keyword, including
the length of the new dimension. New dimensions will always be in a single
chunk.
>>> def f(a):
... return a[:, None] * np.ones((1, 5))
>>> z = blockwise(f, 'az', a, 'a', new_axes={'z': 5}, dtype=a.dtype)
New dimensions can also be multi-chunk by specifying a tuple of chunk
sizes. This has limited utility as is (because the chunks are all the
same), but the resulting graph can be modified to achieve more useful
results (see ``da.map_blocks``).
>>> z = blockwise(f, 'az', a, 'a', new_axes={'z': (5, 5)}, dtype=x.dtype)
>>> z.chunks
((1, 1, 1), (5, 5))
If the applied function changes the size of each chunk you can specify this
with a ``adjust_chunks={...}`` dictionary holding a function for each index
that modifies the dimension size in that index.
>>> def double(x):
... return np.concatenate([x, x])
>>> y = blockwise(double, 'ij', x, 'ij',
... adjust_chunks={'i': lambda n: 2 * n}, dtype=x.dtype)
>>> y.chunks
((2, 2), (2,))
Include literals by indexing with None
>>> z = blockwise(operator.add, 'ij', x, 'ij', 1234, None, dtype=x.dtype)
>>> z.compute()
array([[1235, 1236],
[1237, 1238]])
"""
out = name
new_axes = new_axes or {}
# Input Validation
if len(set(out_ind)) != len(out_ind):
raise ValueError(
"Repeated elements not allowed in output index",
[k for k, v in toolz.frequencies(out_ind).items() if v > 1],
)
new = (
set(out_ind)
- {a for arg in args[1::2] if arg is not None for a in arg}
- set(new_axes or ())
)
if new:
raise ValueError("Unknown dimension", new)
from dask.array.core import normalize_arg, unify_chunks
if align_arrays:
chunkss, arrays = unify_chunks(*args)
else:
arginds = [(a, i) for (a, i) in toolz.partition(2, args) if i is not None]
chunkss = {}
# For each dimension, use the input chunking that has the most blocks;
# this will ensure that broadcasting works as expected, and in
# particular the number of blocks should be correct if the inputs are
# consistent.
for arg, ind in arginds:
for c, i in zip(arg.chunks, ind):
if i not in chunkss or len(c) > len(chunkss[i]):
chunkss[i] = c
arrays = args[::2]
for k, v in new_axes.items():
if not isinstance(v, tuple):
v = (v,)
chunkss[k] = v
arginds = zip(arrays, args[1::2])
numblocks = {}
dependencies = []
arrays = []
# Normalize arguments
argindsstr = []
for arg, ind in arginds:
if ind is None:
arg = normalize_arg(arg)
arg, collections = unpack_collections(arg)
dependencies.extend(collections)
else:
if (
hasattr(arg, "ndim")
and hasattr(ind, "__len__")
and arg.ndim != len(ind)
):
raise ValueError(
"Index string %s does not match array dimension %d"
% (ind, arg.ndim)
)
numblocks[arg.name] = arg.numblocks
arrays.append(arg)
arg = arg.name
argindsstr.extend((arg, ind))
# Normalize keyword arguments
kwargs2 = {}
for k, v in kwargs.items():
v = normalize_arg(v)
v, collections = unpack_collections(v)
dependencies.extend(collections)
kwargs2[k] = v
# Finish up the name
if not out:
out = "{}-{}".format(
token or utils.funcname(func).strip("_"),
base.tokenize(func, out_ind, argindsstr, dtype, **kwargs),
)
graph = core_blockwise(
func,
out,
out_ind,
*argindsstr,
numblocks=numblocks,
dependencies=dependencies,
new_axes=new_axes,
concatenate=concatenate,
**kwargs2,
)
graph = HighLevelGraph.from_collections(
out, graph, dependencies=arrays + dependencies
)
chunks = [chunkss[i] for i in out_ind]
if adjust_chunks:
for i, ind in enumerate(out_ind):
if ind in adjust_chunks:
if callable(adjust_chunks[ind]):
chunks[i] = tuple(map(adjust_chunks[ind], chunks[i]))
elif isinstance(adjust_chunks[ind], numbers.Integral):
chunks[i] = tuple(adjust_chunks[ind] for _ in chunks[i])
elif isinstance(adjust_chunks[ind], (tuple, list)):
if len(adjust_chunks[ind]) != len(chunks[i]):
raise ValueError(
f"Dimension {i} has {len(chunks[i])} blocks, adjust_chunks "
f"specified with {len(adjust_chunks[ind])} blocks"
)
chunks[i] = tuple(adjust_chunks[ind])
else:
raise NotImplementedError(
"adjust_chunks values must be callable, int, or tuple"
)
chunks = tuple(chunks)
if meta is None:
from dask.array.utils import compute_meta
meta = compute_meta(func, dtype, *args[::2], **kwargs)
return new_da_object(graph, out, chunks, meta=meta, dtype=dtype)
def atop(*args, **kwargs):
warnings.warn("The da.atop function has moved to da.blockwise")
return blockwise(*args, **kwargs)
from dask.array.core import new_da_object