Source code for dask.array.blockwise

import numbers
import warnings

import tlz as toolz

from .. import base, utils
from ..blockwise import blockwise as core_blockwise
from ..delayed import unpack_collections
from ..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 Sequence like (x, 'ij', y, 'jk', z, 'i') **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 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 += ... 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 .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.numblocks arrays.append(arg) arg = 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 .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 .core import new_da_object