Source code for dask.array.reductions

import builtins
import contextlib
import operator
from collections.abc import Iterable
from functools import partial
from itertools import product, repeat
from math import ceil, factorial, log, log2
from numbers import Integral, Number

import numpy as np
from tlz import accumulate, compose, drop, get, partition_all, pluck

from .. import config
from ..base import tokenize
from ..blockwise import lol_tuples
from ..highlevelgraph import HighLevelGraph
from ..utils import deepmap, derived_from, funcname, getargspec, is_series_like
from . import chunk
from .blockwise import blockwise
from .core import Array, _concatenate2, handle_out, implements
from .creation import arange, diagonal

# Keep empty_lookup here for backwards compatibility
from .dispatch import divide_lookup, empty_lookup  # noqa: F401
from .utils import (
    asarray_safe,
    compute_meta,
    is_arraylike,
    meta_from_array,
    validate_axis,
)
from .wrap import ones, zeros


def divide(a, b, dtype=None):
    key = lambda x: getattr(x, "__array_priority__", float("-inf"))
    f = divide_lookup.dispatch(type(builtins.max(a, b, key=key)))
    return f(a, b, dtype=dtype)


[docs]def reduction( x, chunk, aggregate, axis=None, keepdims=False, dtype=None, split_every=None, combine=None, name=None, out=None, concatenate=True, output_size=1, meta=None, ): """General version of reductions Parameters ---------- x: Array Data being reduced along one or more axes chunk: callable(x_chunk, axis, keepdims) First function to be executed when resolving the dask graph. This function is applied in parallel to all original chunks of x. See below for function parameters. combine: callable(x_chunk, axis, keepdims), optional Function used for intermediate recursive aggregation (see split_every below). If omitted, it defaults to aggregate. If the reduction can be performed in less than 3 steps, it will not be invoked at all. aggregate: callable(x_chunk, axis, keepdims) Last function to be executed when resolving the dask graph, producing the final output. It is always invoked, even when the reduced Array counts a single chunk along the reduced axes. axis: int or sequence of ints, optional Axis or axes to aggregate upon. If omitted, aggregate along all axes. keepdims: boolean, optional Whether the reduction function should preserve the reduced axes, leaving them at size ``output_size``, or remove them. dtype: np.dtype data type of output. This argument was previously optional, but leaving as ``None`` will now raise an exception. split_every: int >= 2 or dict(axis: int), optional Determines the depth of the recursive aggregation. If set to or more than the number of input chunks, the aggregation will be performed in two steps, one ``chunk`` function per input chunk and a single ``aggregate`` function at the end. If set to less than that, an intermediate ``combine`` function will be used, so that any one ``combine`` or ``aggregate`` function has no more than ``split_every`` inputs. The depth of the aggregation graph will be :math:`log_{split_every}(input chunks along reduced axes)`. Setting to a low value can reduce cache size and network transfers, at the cost of more CPU and a larger dask graph. Omit to let dask heuristically decide a good default. A default can also be set globally with the ``split_every`` key in :mod:`dask.config`. name: str, optional Prefix of the keys of the intermediate and output nodes. If omitted it defaults to the function names. out: Array, optional Another dask array whose contents will be replaced. Omit to create a new one. Note that, unlike in numpy, this setting gives no performance benefits whatsoever, but can still be useful if one needs to preserve the references to a previously existing Array. concatenate: bool, optional If True (the default), the outputs of the ``chunk``/``combine`` functions are concatenated into a single np.array before being passed to the ``combine``/``aggregate`` functions. If False, the input of ``combine`` and ``aggregate`` will be either a list of the raw outputs of the previous step or a single output, and the function will have to concatenate it itself. It can be useful to set this to False if the chunk and/or combine steps do not produce np.arrays. output_size: int >= 1, optional Size of the output of the ``aggregate`` function along the reduced axes. Ignored if keepdims is False. Returns ------- dask array **Function Parameters** x_chunk: numpy.ndarray Individual input chunk. For ``chunk`` functions, it is one of the original chunks of x. For ``combine`` and ``aggregate`` functions, it's the concatenation of the outputs produced by the previous ``chunk`` or ``combine`` functions. If concatenate=False, it's a list of the raw outputs from the previous functions. axis: tuple Normalized list of axes to reduce upon, e.g. ``(0, )`` Scalar, negative, and None axes have been normalized away. Note that some numpy reduction functions cannot reduce along multiple axes at once and strictly require an int in input. Such functions have to be wrapped to cope. keepdims: bool Whether the reduction function should preserve the reduced axes or remove them. """ if axis is None: axis = tuple(range(x.ndim)) if isinstance(axis, Integral): axis = (axis,) axis = validate_axis(axis, x.ndim) if dtype is None: raise ValueError("Must specify dtype") if "dtype" in getargspec(chunk).args: chunk = partial(chunk, dtype=dtype) if "dtype" in getargspec(aggregate).args: aggregate = partial(aggregate, dtype=dtype) if is_series_like(x): x = x.values # Map chunk across all blocks inds = tuple(range(x.ndim)) # The dtype of `tmp` doesn't actually matter, and may be incorrect. tmp = blockwise( chunk, inds, x, inds, axis=axis, keepdims=True, token=name, dtype=dtype or float ) tmp._chunks = tuple( (output_size,) * len(c) if i in axis else c for i, c in enumerate(tmp.chunks) ) if meta is None and hasattr(x, "_meta"): try: reduced_meta = compute_meta( chunk, x.dtype, x._meta, axis=axis, keepdims=True, computing_meta=True ) except TypeError: reduced_meta = compute_meta( chunk, x.dtype, x._meta, axis=axis, keepdims=True ) except ValueError: pass else: reduced_meta = None result = _tree_reduce( tmp, aggregate, axis, keepdims, dtype, split_every, combine, name=name, concatenate=concatenate, reduced_meta=reduced_meta, ) if keepdims and output_size != 1: result._chunks = tuple( (output_size,) if i in axis else c for i, c in enumerate(tmp.chunks) ) if meta is not None: result._meta = meta return handle_out(out, result)
def _tree_reduce( x, aggregate, axis, keepdims, dtype, split_every=None, combine=None, name=None, concatenate=True, reduced_meta=None, ): """Perform the tree reduction step of a reduction. Lower level, users should use ``reduction`` or ``arg_reduction`` directly. """ # Normalize split_every split_every = split_every or config.get("split_every", 4) if isinstance(split_every, dict): split_every = {k: split_every.get(k, 2) for k in axis} elif isinstance(split_every, Integral): n = builtins.max(int(split_every ** (1 / (len(axis) or 1))), 2) split_every = dict.fromkeys(axis, n) else: raise ValueError("split_every must be a int or a dict") # Reduce across intermediates depth = 1 for i, n in enumerate(x.numblocks): if i in split_every and split_every[i] != 1: depth = int(builtins.max(depth, ceil(log(n, split_every[i])))) func = partial(combine or aggregate, axis=axis, keepdims=True) if concatenate: func = compose(func, partial(_concatenate2, axes=axis)) for i in range(depth - 1): x = partial_reduce( func, x, split_every, True, dtype=dtype, name=(name or funcname(combine or aggregate)) + "-partial", reduced_meta=reduced_meta, ) func = partial(aggregate, axis=axis, keepdims=keepdims) if concatenate: func = compose(func, partial(_concatenate2, axes=axis)) return partial_reduce( func, x, split_every, keepdims=keepdims, dtype=dtype, name=(name or funcname(aggregate)) + "-aggregate", reduced_meta=reduced_meta, ) def partial_reduce( func, x, split_every, keepdims=False, dtype=None, name=None, reduced_meta=None ): """Partial reduction across multiple axes. Parameters ---------- func : function x : Array split_every : dict Maximum reduction block sizes in each dimension. Examples -------- Reduce across axis 0 and 2, merging a maximum of 1 block in the 0th dimension, and 3 blocks in the 2nd dimension: >>> partial_reduce(np.min, x, {0: 1, 2: 3}) # doctest: +SKIP """ name = ( (name or funcname(func)) + "-" + tokenize(func, x, split_every, keepdims, dtype) ) parts = [ list(partition_all(split_every.get(i, 1), range(n))) for (i, n) in enumerate(x.numblocks) ] keys = product(*map(range, map(len, parts))) out_chunks = [ tuple(1 for p in partition_all(split_every[i], c)) if i in split_every else c for (i, c) in enumerate(x.chunks) ] if not keepdims: out_axis = [i for i in range(x.ndim) if i not in split_every] getter = lambda k: get(out_axis, k) keys = map(getter, keys) out_chunks = list(getter(out_chunks)) dsk = {} for k, p in zip(keys, product(*parts)): decided = {i: j[0] for (i, j) in enumerate(p) if len(j) == 1} dummy = dict(i for i in enumerate(p) if i[0] not in decided) g = lol_tuples((x.name,), range(x.ndim), decided, dummy) dsk[(name,) + k] = (func, g) graph = HighLevelGraph.from_collections(name, dsk, dependencies=[x]) meta = x._meta if reduced_meta is not None: try: meta = func(reduced_meta, computing_meta=True) # no meta keyword argument exists for func, and it isn't required except TypeError: try: meta = func(reduced_meta) except ValueError as e: # min/max functions have no identity, don't apply function to meta if "zero-size array to reduction operation" in str(e): meta = reduced_meta # when no work can be computed on the empty array (e.g., func is a ufunc) except ValueError: pass # some functions can't compute empty arrays (those for which reduced_meta # fall into the ValueError exception) and we have to rely on reshaping # the array according to len(out_chunks) if is_arraylike(meta) and meta.ndim != len(out_chunks): if len(out_chunks) == 0: meta = meta.sum() else: meta = meta.reshape((0,) * len(out_chunks)) if np.isscalar(meta): return Array(graph, name, out_chunks, dtype=dtype) else: with contextlib.suppress(AttributeError): meta = meta.astype(dtype) return Array(graph, name, out_chunks, meta=meta)
[docs]@derived_from(np) def sum(a, axis=None, dtype=None, keepdims=False, split_every=None, out=None): if dtype is None: dtype = getattr(np.zeros(1, dtype=a.dtype).sum(), "dtype", object) result = reduction( a, chunk.sum, chunk.sum, axis=axis, keepdims=keepdims, dtype=dtype, split_every=split_every, out=out, ) return result
[docs]@derived_from(np) def prod(a, axis=None, dtype=None, keepdims=False, split_every=None, out=None): if dtype is not None: dt = dtype else: dt = getattr(np.empty((1,), dtype=a.dtype).prod(), "dtype", object) return reduction( a, chunk.prod, chunk.prod, axis=axis, keepdims=keepdims, dtype=dt, split_every=split_every, out=out, )
[docs]@implements(np.min, np.amin) @derived_from(np) def min(a, axis=None, keepdims=False, split_every=None, out=None): return reduction( a, chunk.min, chunk.min, axis=axis, keepdims=keepdims, dtype=a.dtype, split_every=split_every, out=out, )
[docs]@implements(np.max, np.amax) @derived_from(np) def max(a, axis=None, keepdims=False, split_every=None, out=None): return reduction( a, chunk.max, chunk.max, axis=axis, keepdims=keepdims, dtype=a.dtype, split_every=split_every, out=out, )
[docs]@derived_from(np) def any(a, axis=None, keepdims=False, split_every=None, out=None): return reduction( a, chunk.any, chunk.any, axis=axis, keepdims=keepdims, dtype="bool", split_every=split_every, out=out, )
[docs]@derived_from(np) def all(a, axis=None, keepdims=False, split_every=None, out=None): return reduction( a, chunk.all, chunk.all, axis=axis, keepdims=keepdims, dtype="bool", split_every=split_every, out=out, )
[docs]@derived_from(np) def nansum(a, axis=None, dtype=None, keepdims=False, split_every=None, out=None): if dtype is not None: dt = dtype else: dt = getattr(chunk.nansum(np.empty((1,), dtype=a.dtype)), "dtype", object) return reduction( a, chunk.nansum, chunk.sum, axis=axis, keepdims=keepdims, dtype=dt, split_every=split_every, out=out, )
[docs]@derived_from(np) def nanprod(a, axis=None, dtype=None, keepdims=False, split_every=None, out=None): if dtype is not None: dt = dtype else: dt = getattr(chunk.nansum(np.empty((1,), dtype=a.dtype)), "dtype", object) return reduction( a, chunk.nanprod, chunk.prod, axis=axis, keepdims=keepdims, dtype=dt, split_every=split_every, out=out, )
[docs]@derived_from(np) def nancumsum(x, axis, dtype=None, out=None, *, method="sequential"): """Dask added an additional keyword-only argument ``method``. method : {'sequential', 'blelloch'}, optional Choose which method to use to perform the cumsum. Default is 'sequential'. * 'sequential' performs the cumsum of each prior block before the current block. * 'blelloch' is a work-efficient parallel cumsum. It exposes parallelism by first taking the sum of each block and combines the sums via a binary tree. This method may be faster or more memory efficient depending on workload, scheduler, and hardware. More benchmarking is necessary. """ return cumreduction( chunk.nancumsum, operator.add, 0, x, axis, dtype, out=out, method=method, preop=np.nansum, )
[docs]@derived_from(np) def nancumprod(x, axis, dtype=None, out=None, *, method="sequential"): """Dask added an additional keyword-only argument ``method``. method : {'sequential', 'blelloch'}, optional Choose which method to use to perform the cumprod. Default is 'sequential'. * 'sequential' performs the cumprod of each prior block before the current block. * 'blelloch' is a work-efficient parallel cumprod. It exposes parallelism by first taking the product of each block and combines the products via a binary tree. This method may be faster or more memory efficient depending on workload, scheduler, and hardware. More benchmarking is necessary. """ return cumreduction( chunk.nancumprod, operator.mul, 1, x, axis, dtype, out=out, method=method, preop=np.nanprod, )
[docs]@derived_from(np) def nanmin(a, axis=None, keepdims=False, split_every=None, out=None): return reduction( a, chunk.nanmin, chunk.nanmin, axis=axis, keepdims=keepdims, dtype=a.dtype, split_every=split_every, out=out, )
[docs]@derived_from(np) def nanmax(a, axis=None, keepdims=False, split_every=None, out=None): return reduction( a, chunk.nanmax, chunk.nanmax, axis=axis, keepdims=keepdims, dtype=a.dtype, split_every=split_every, out=out, )
def numel(x, **kwargs): """A reduction to count the number of elements""" if hasattr(x, "mask"): return chunk.sum(np.ones_like(x), **kwargs) shape = x.shape keepdims = kwargs.get("keepdims", False) axis = kwargs.get("axis", None) dtype = kwargs.get("dtype", np.float64) if axis is None: prod = np.prod(shape, dtype=dtype) return ( np.full_like(x, prod, shape=(1,) * len(shape), dtype=dtype) if keepdims is True else prod ) if not isinstance(axis, tuple or list): axis = [axis] prod = np.prod([shape[dim] for dim in axis]) if keepdims is True: new_shape = tuple( shape[dim] if dim not in axis else 1 for dim in range(len(shape)) ) else: new_shape = tuple(shape[dim] for dim in range(len(shape)) if dim not in axis) return np.full_like(x, prod, shape=new_shape, dtype=dtype) def nannumel(x, **kwargs): """A reduction to count the number of elements""" return chunk.sum(~(np.isnan(x)), **kwargs) def mean_chunk( x, sum=chunk.sum, numel=numel, dtype="f8", computing_meta=False, **kwargs ): if computing_meta: return x n = numel(x, dtype=dtype, **kwargs) total = sum(x, dtype=dtype, **kwargs) return {"n": n, "total": total} def mean_combine( pairs, sum=chunk.sum, numel=numel, dtype="f8", axis=None, computing_meta=False, **kwargs, ): if not isinstance(pairs, list): pairs = [pairs] ns = deepmap(lambda pair: pair["n"], pairs) if not computing_meta else pairs n = _concatenate2(ns, axes=axis).sum(axis=axis, **kwargs) if computing_meta: return n totals = deepmap(lambda pair: pair["total"], pairs) total = _concatenate2(totals, axes=axis).sum(axis=axis, **kwargs) return {"n": n, "total": total} def mean_agg(pairs, dtype="f8", axis=None, computing_meta=False, **kwargs): ns = deepmap(lambda pair: pair["n"], pairs) if not computing_meta else pairs n = _concatenate2(ns, axes=axis) n = np.sum(n, axis=axis, dtype=dtype, **kwargs) if computing_meta: return n totals = deepmap(lambda pair: pair["total"], pairs) total = _concatenate2(totals, axes=axis).sum(axis=axis, dtype=dtype, **kwargs) with np.errstate(divide="ignore", invalid="ignore"): return divide(total, n, dtype=dtype)
[docs]@derived_from(np) def mean(a, axis=None, dtype=None, keepdims=False, split_every=None, out=None): if dtype is not None: dt = dtype elif a.dtype == object: dt = object else: dt = getattr(np.mean(np.zeros(shape=(1,), dtype=a.dtype)), "dtype", object) return reduction( a, mean_chunk, mean_agg, axis=axis, keepdims=keepdims, dtype=dt, split_every=split_every, combine=mean_combine, out=out, concatenate=False, )
[docs]@derived_from(np) def nanmean(a, axis=None, dtype=None, keepdims=False, split_every=None, out=None): if dtype is not None: dt = dtype else: dt = getattr(np.mean(np.empty(shape=(1,), dtype=a.dtype)), "dtype", object) return reduction( a, partial(mean_chunk, sum=chunk.nansum, numel=nannumel), mean_agg, axis=axis, keepdims=keepdims, dtype=dt, split_every=split_every, out=out, concatenate=False, combine=partial(mean_combine, sum=chunk.nansum, numel=nannumel), )
def moment_chunk( A, order=2, sum=chunk.sum, numel=numel, dtype="f8", computing_meta=False, **kwargs ): if computing_meta: return A n = numel(A, **kwargs) n = n.astype(np.int64) total = sum(A, dtype=dtype, **kwargs) with np.errstate(divide="ignore", invalid="ignore"): u = total / n xs = [sum((A - u) ** i, dtype=dtype, **kwargs) for i in range(2, order + 1)] M = np.stack(xs, axis=-1) return {"total": total, "n": n, "M": M} def _moment_helper(Ms, ns, inner_term, order, sum, axis, kwargs): M = Ms[..., order - 2].sum(axis=axis, **kwargs) + sum( ns * inner_term ** order, axis=axis, **kwargs ) for k in range(1, order - 1): coeff = factorial(order) / (factorial(k) * factorial(order - k)) M += coeff * sum(Ms[..., order - k - 2] * inner_term ** k, axis=axis, **kwargs) return M def moment_combine( pairs, order=2, ddof=0, dtype="f8", sum=np.sum, axis=None, computing_meta=False, **kwargs, ): if not isinstance(pairs, list): pairs = [pairs] kwargs["dtype"] = dtype kwargs["keepdims"] = True ns = deepmap(lambda pair: pair["n"], pairs) if not computing_meta else pairs ns = _concatenate2(ns, axes=axis) n = ns.sum(axis=axis, **kwargs) if computing_meta: return n totals = _concatenate2(deepmap(lambda pair: pair["total"], pairs), axes=axis) Ms = _concatenate2(deepmap(lambda pair: pair["M"], pairs), axes=axis) total = totals.sum(axis=axis, **kwargs) with np.errstate(divide="ignore", invalid="ignore"): mu = divide(total, n, dtype=dtype) inner_term = divide(totals, ns, dtype=dtype) - mu xs = [ _moment_helper(Ms, ns, inner_term, o, sum, axis, kwargs) for o in range(2, order + 1) ] M = np.stack(xs, axis=-1) return {"total": total, "n": n, "M": M} def moment_agg( pairs, order=2, ddof=0, dtype="f8", sum=np.sum, axis=None, computing_meta=False, **kwargs, ): if not isinstance(pairs, list): pairs = [pairs] kwargs["dtype"] = dtype # To properly handle ndarrays, the original dimensions need to be kept for # part of the calculation. keepdim_kw = kwargs.copy() keepdim_kw["keepdims"] = True ns = deepmap(lambda pair: pair["n"], pairs) if not computing_meta else pairs ns = _concatenate2(ns, axes=axis) n = ns.sum(axis=axis, **keepdim_kw) if computing_meta: return n totals = _concatenate2(deepmap(lambda pair: pair["total"], pairs), axes=axis) Ms = _concatenate2(deepmap(lambda pair: pair["M"], pairs), axes=axis) mu = divide(totals.sum(axis=axis, **keepdim_kw), n, dtype=dtype) with np.errstate(divide="ignore", invalid="ignore"): inner_term = divide(totals, ns, dtype=dtype) - mu M = _moment_helper(Ms, ns, inner_term, order, sum, axis, kwargs) denominator = n.sum(axis=axis, **kwargs) - ddof # taking care of the edge case with empty or all-nans array with ddof > 0 if isinstance(denominator, Number): if denominator < 0: denominator = np.nan elif denominator is not np.ma.masked: denominator[denominator < 0] = np.nan return divide(M, denominator, dtype=dtype)
[docs]def moment( a, order, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None, out=None ): if not isinstance(order, Integral) or order < 0: raise ValueError("Order must be an integer >= 0") if order < 2: reduced = a.sum(axis=axis) # get reduced shape and chunks if order == 0: # When order equals 0, the result is 1, by definition. return ones( reduced.shape, chunks=reduced.chunks, dtype="f8", meta=reduced._meta ) # By definition the first order about the mean is 0. return zeros( reduced.shape, chunks=reduced.chunks, dtype="f8", meta=reduced._meta ) if dtype is not None: dt = dtype else: dt = getattr(np.var(np.ones(shape=(1,), dtype=a.dtype)), "dtype", object) return reduction( a, partial(moment_chunk, order=order), partial(moment_agg, order=order, ddof=ddof), axis=axis, keepdims=keepdims, dtype=dt, split_every=split_every, out=out, concatenate=False, combine=partial(moment_combine, order=order), )
[docs]@derived_from(np) def var(a, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None, out=None): if dtype is not None: dt = dtype else: dt = getattr(np.var(np.ones(shape=(1,), dtype=a.dtype)), "dtype", object) return reduction( a, moment_chunk, partial(moment_agg, ddof=ddof), axis=axis, keepdims=keepdims, dtype=dt, split_every=split_every, combine=moment_combine, name="var", out=out, concatenate=False, )
[docs]@derived_from(np) def nanvar( a, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None, out=None ): if dtype is not None: dt = dtype else: dt = getattr(np.var(np.ones(shape=(1,), dtype=a.dtype)), "dtype", object) return reduction( a, partial(moment_chunk, sum=chunk.nansum, numel=nannumel), partial(moment_agg, sum=np.nansum, ddof=ddof), axis=axis, keepdims=keepdims, dtype=dt, split_every=split_every, combine=partial(moment_combine, sum=np.nansum), out=out, concatenate=False, )
def _sqrt(a): o = np.sqrt(a) if isinstance(o, np.ma.masked_array) and not o.shape and o.mask.all(): return np.ma.masked return o def safe_sqrt(a): """A version of sqrt that properly handles scalar masked arrays. To mimic ``np.ma`` reductions, we need to convert scalar masked arrays that have an active mask to the ``np.ma.masked`` singleton. This is properly handled automatically for reduction code, but not for ufuncs. We implement a simple version here, since calling `np.ma.sqrt` everywhere is significantly more expensive. """ if hasattr(a, "_elemwise"): return a._elemwise(_sqrt, a) return _sqrt(a)
[docs]@derived_from(np) def std(a, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None, out=None): result = safe_sqrt( var( a, axis=axis, dtype=dtype, keepdims=keepdims, ddof=ddof, split_every=split_every, out=out, ) ) if dtype and dtype != result.dtype: result = result.astype(dtype) return result
[docs]@derived_from(np) def nanstd( a, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None, out=None ): result = safe_sqrt( nanvar( a, axis=axis, dtype=dtype, keepdims=keepdims, ddof=ddof, split_every=split_every, out=out, ) ) if dtype and dtype != result.dtype: result = result.astype(dtype) return result
def _arg_combine(data, axis, argfunc, keepdims=False): """Merge intermediate results from ``arg_*`` functions""" if isinstance(data, dict): # Array type doesn't support structured arrays (e.g., CuPy), # therefore `data` is stored in a `dict`. assert data["vals"].ndim == data["arg"].ndim axis = ( None if len(axis) == data["vals"].ndim or data["vals"].ndim == 1 else axis[0] ) else: axis = None if len(axis) == data.ndim or data.ndim == 1 else axis[0] vals = data["vals"] arg = data["arg"] if axis is None: local_args = argfunc(vals, axis=axis, keepdims=keepdims) vals = vals.ravel()[local_args] arg = arg.ravel()[local_args] else: local_args = argfunc(vals, axis=axis) inds = np.ogrid[tuple(map(slice, local_args.shape))] inds.insert(axis, local_args) inds = tuple(inds) vals = vals[inds] arg = arg[inds] if keepdims: vals = np.expand_dims(vals, axis) arg = np.expand_dims(arg, axis) return arg, vals def arg_chunk(func, argfunc, x, axis, offset_info): arg_axis = None if len(axis) == x.ndim or x.ndim == 1 else axis[0] vals = func(x, axis=arg_axis, keepdims=True) arg = argfunc(x, axis=arg_axis, keepdims=True) if arg_axis is None: offset, total_shape = offset_info ind = np.unravel_index(arg.ravel()[0], x.shape) total_ind = tuple(o + i for (o, i) in zip(offset, ind)) arg[:] = np.ravel_multi_index(total_ind, total_shape) else: arg += offset_info if isinstance(vals, np.ma.masked_array): if "min" in argfunc.__name__: fill_value = np.ma.minimum_fill_value(vals) else: fill_value = np.ma.maximum_fill_value(vals) vals = np.ma.filled(vals, fill_value) try: result = np.empty_like( vals, shape=vals.shape, dtype=[("vals", vals.dtype), ("arg", arg.dtype)] ) except TypeError: # Array type doesn't support structured arrays (e.g., CuPy) result = dict() result["vals"] = vals result["arg"] = arg return result def arg_combine(func, argfunc, data, axis=None, **kwargs): arg, vals = _arg_combine(data, axis, argfunc, keepdims=True) try: result = np.empty_like( vals, shape=vals.shape, dtype=[("vals", vals.dtype), ("arg", arg.dtype)] ) except TypeError: # Array type doesn't support structured arrays (e.g., CuPy). result = dict() result["vals"] = vals result["arg"] = arg return result def arg_agg(func, argfunc, data, axis=None, **kwargs): return _arg_combine(data, axis, argfunc, keepdims=False)[0] def nanarg_agg(func, argfunc, data, axis=None, **kwargs): arg, vals = _arg_combine(data, axis, argfunc, keepdims=False) if np.any(np.isnan(vals)): raise ValueError("All NaN slice encountered") return arg def arg_reduction(x, chunk, combine, agg, axis=None, split_every=None, out=None): """Generic function for argreduction. Parameters ---------- x : Array chunk : callable Partialed ``arg_chunk``. combine : callable Partialed ``arg_combine``. agg : callable Partialed ``arg_agg``. axis : int, optional split_every : int or dict, optional """ if axis is None: axis = tuple(range(x.ndim)) ravel = True elif isinstance(axis, Integral): axis = validate_axis(axis, x.ndim) axis = (axis,) ravel = x.ndim == 1 else: raise TypeError(f"axis must be either `None` or int, got '{axis}'") for ax in axis: chunks = x.chunks[ax] if len(chunks) > 1 and np.isnan(chunks).any(): raise ValueError( "Arg-reductions do not work with arrays that have " "unknown chunksizes. At some point in your computation " "this array lost chunking information.\n\n" "A possible solution is with \n" " x.compute_chunk_sizes()" ) # Map chunk across all blocks name = f"arg-reduce-{tokenize(axis, x, chunk, combine, split_every)}" old = x.name keys = list(product(*map(range, x.numblocks))) offsets = list(product(*(accumulate(operator.add, bd[:-1], 0) for bd in x.chunks))) if ravel: offset_info = zip(offsets, repeat(x.shape)) else: offset_info = pluck(axis[0], offsets) chunks = tuple((1,) * len(c) if i in axis else c for (i, c) in enumerate(x.chunks)) dsk = { (name,) + k: (chunk, (old,) + k, axis, off) for (k, off) in zip(keys, offset_info) } dtype = np.argmin(asarray_safe([1], like=meta_from_array(x))) meta = None if is_arraylike(dtype): # This case occurs on non-NumPy types (e.g., CuPy), where the returned # value is an ndarray rather than a scalar. meta = dtype dtype = meta.dtype graph = HighLevelGraph.from_collections(name, dsk, dependencies=[x]) tmp = Array(graph, name, chunks, dtype=dtype, meta=meta) result = _tree_reduce(tmp, agg, axis, False, dtype, split_every, combine) return handle_out(out, result) def make_arg_reduction(func, argfunc, is_nan_func=False): """Create an argreduction callable Parameters ---------- func : callable The reduction (e.g. ``min``) argfunc : callable The argreduction (e.g. ``argmin``) """ chunk = partial(arg_chunk, func, argfunc) combine = partial(arg_combine, func, argfunc) if is_nan_func: agg = partial(nanarg_agg, func, argfunc) else: agg = partial(arg_agg, func, argfunc) def wrapped(x, axis=None, split_every=None, out=None): return arg_reduction( x, chunk, combine, agg, axis, split_every=split_every, out=out ) wrapped.__name__ = func.__name__ return derived_from(np)(wrapped) def _nanargmin(x, axis, **kwargs): try: return chunk.nanargmin(x, axis, **kwargs) except ValueError: return chunk.nanargmin(np.where(np.isnan(x), np.inf, x), axis, **kwargs) def _nanargmax(x, axis, **kwargs): try: return chunk.nanargmax(x, axis, **kwargs) except ValueError: return chunk.nanargmax(np.where(np.isnan(x), -np.inf, x), axis, **kwargs) argmin = make_arg_reduction(chunk.min, chunk.argmin) argmax = make_arg_reduction(chunk.max, chunk.argmax) nanargmin = make_arg_reduction(chunk.nanmin, _nanargmin, True) nanargmax = make_arg_reduction(chunk.nanmax, _nanargmax, True) def _prefixscan_combine(func, binop, pre, x, axis, dtype): """Combine results of a parallel prefix scan such as cumsum Parameters ---------- func : callable Cumulative function (e.g. ``np.cumsum``) binop : callable Associative function (e.g. ``add``) pre : np.array The value calculated in parallel from ``preop``. For example, the sum of all the previous blocks. x : np.array Current block axis : int dtype : dtype Returns ------- np.array """ # We could compute this in two tasks. # This would allow us to do useful work (i.e., func), while waiting on `pre`. # Using one task may guide the scheduler to do better and reduce scheduling overhead. return binop(pre, func(x, axis=axis, dtype=dtype)) def _prefixscan_first(func, x, axis, dtype): """Compute the prefix scan (e.g., cumsum) on the first block Parameters ---------- func : callable Cumulative function (e.g. ``np.cumsum``) x : np.array Current block axis : int dtype : dtype Returns ------- np.array """ return func(x, axis=axis, dtype=dtype) def prefixscan_blelloch(func, preop, binop, x, axis=None, dtype=None, out=None): """Generic function to perform parallel cumulative scan (a.k.a prefix scan) The Blelloch prefix scan is work-efficient and exposes parallelism. A parallel cumsum works by first taking the sum of each block, then do a binary tree merge followed by a fan-out (i.e., the Brent-Kung pattern). We then take the cumsum of each block and add the sum of the previous blocks. When performing a cumsum across N chunks, this method has 2 * lg(N) levels of dependencies. In contrast, the sequential method has N levels of dependencies. Floating point operations should be more accurate with this method compared to sequential. Parameters ---------- func : callable Cumulative function (e.g. ``np.cumsum``) preop : callable Function to get the final value of a cumulative function (e.g., ``np.sum``) binop : callable Associative function (e.g. ``add``) x : dask array axis : int dtype : dtype Returns ------- dask array """ if axis is None: x = x.flatten().rechunk(chunks=x.npartitions) axis = 0 if dtype is None: dtype = getattr(func(np.empty((0,), dtype=x.dtype)), "dtype", object) assert isinstance(axis, Integral) axis = validate_axis(axis, x.ndim) name = f"{func.__name__}-{tokenize(func, axis, preop, binop, x, dtype)}" base_key = (name,) # Right now, the metadata for batches is incorrect, but this should be okay batches = x.map_blocks(preop, axis=axis, keepdims=True, dtype=dtype) # We don't need the last index until the end *indices, last_index = full_indices = [ list( product( *[range(nb) if j != axis else [i] for j, nb in enumerate(x.numblocks)] ) ) for i in range(x.numblocks[axis]) ] prefix_vals = [[(batches.name,) + index for index in vals] for vals in indices] dsk = {} n_vals = len(prefix_vals) level = 0 if n_vals >= 2: # Upsweep stride = 1 stride2 = 2 while stride2 <= n_vals: for i in range(stride2 - 1, n_vals, stride2): new_vals = [] for index, left_val, right_val in zip( indices[i], prefix_vals[i - stride], prefix_vals[i] ): key = base_key + index + (level, i) dsk[key] = (binop, left_val, right_val) new_vals.append(key) prefix_vals[i] = new_vals stride = stride2 stride2 *= 2 level += 1 # Downsweep # With `n_vals == 3`, we would have `stride = 1` and `stride = 0`, but we need # to do a downsweep iteration, so make sure stride2 is at least 2. stride2 = builtins.max(2, 2 ** ceil(log2(n_vals // 2))) stride = stride2 // 2 while stride > 0: for i in range(stride2 + stride - 1, n_vals, stride2): new_vals = [] for index, left_val, right_val in zip( indices[i], prefix_vals[i - stride], prefix_vals[i] ): key = base_key + index + (level, i) dsk[key] = (binop, left_val, right_val) new_vals.append(key) prefix_vals[i] = new_vals stride2 = stride stride //= 2 level += 1 if full_indices: for index in full_indices[0]: dsk[base_key + index] = ( _prefixscan_first, func, (x.name,) + index, axis, dtype, ) for indexes, vals in zip(drop(1, full_indices), prefix_vals): for index, val in zip(indexes, vals): dsk[base_key + index] = ( _prefixscan_combine, func, binop, val, (x.name,) + index, axis, dtype, ) if len(full_indices) < 2: deps = [x] else: deps = [x, batches] graph = HighLevelGraph.from_collections(name, dsk, dependencies=deps) result = Array(graph, name, x.chunks, batches.dtype) return handle_out(out, result) def cumreduction( func, binop, ident, x, axis=None, dtype=None, out=None, method="sequential", preop=None, ): """Generic function for cumulative reduction Parameters ---------- func: callable Cumulative function like np.cumsum or np.cumprod binop: callable Associated binary operator like ``np.cumsum->add`` or ``np.cumprod->mul`` ident: Number Associated identity like ``np.cumsum->0`` or ``np.cumprod->1`` x: dask Array axis: int dtype: dtype method : {'sequential', 'blelloch'}, optional Choose which method to use to perform the cumsum. Default is 'sequential'. * 'sequential' performs the scan of each prior block before the current block. * 'blelloch' is a work-efficient parallel scan. It exposes parallelism by first calling ``preop`` on each block and combines the values via a binary tree. This method may be faster or more memory efficient depending on workload, scheduler, and hardware. More benchmarking is necessary. preop: callable, optional Function used by 'blelloch' method like `np.cumsum->np.sum`` or ``np.cumprod->np.prod`` Returns ------- dask array See also -------- cumsum cumprod """ if method == "blelloch": if preop is None: raise TypeError( 'cumreduction with "blelloch" method required `preop=` argument' ) return prefixscan_blelloch(func, preop, binop, x, axis, dtype, out=out) elif method != "sequential": raise ValueError( f'Invalid method for cumreduction. Expected "sequential" or "blelloch". Got: {method!r}' ) if axis is None: x = x.flatten().rechunk(chunks=x.npartitions) axis = 0 if dtype is None: dtype = getattr(func(np.empty((0,), dtype=x.dtype)), "dtype", object) assert isinstance(axis, Integral) axis = validate_axis(axis, x.ndim) m = x.map_blocks(func, axis=axis, dtype=dtype) name = f"{func.__name__}-{tokenize(func, axis, binop, ident, x, dtype)}" n = x.numblocks[axis] full = slice(None, None, None) slc = (full,) * axis + (slice(-1, None),) + (full,) * (x.ndim - axis - 1) indices = list( product(*[range(nb) if i != axis else [0] for i, nb in enumerate(x.numblocks)]) ) dsk = dict() for ind in indices: shape = tuple(x.chunks[i][ii] if i != axis else 1 for i, ii in enumerate(ind)) dsk[(name, "extra") + ind] = (np.full, shape, ident, m.dtype) dsk[(name,) + ind] = (m.name,) + ind for i in range(1, n): last_indices = indices indices = list( product( *[range(nb) if ii != axis else [i] for ii, nb in enumerate(x.numblocks)] ) ) for old, ind in zip(last_indices, indices): this_slice = (name, "extra") + ind dsk[this_slice] = ( binop, (name, "extra") + old, (operator.getitem, (m.name,) + old, slc), ) dsk[(name,) + ind] = (binop, this_slice, (m.name,) + ind) graph = HighLevelGraph.from_collections(name, dsk, dependencies=[m]) result = Array(graph, name, x.chunks, m.dtype) return handle_out(out, result) def _cumsum_merge(a, b): if isinstance(a, np.ma.masked_array) or isinstance(b, np.ma.masked_array): values = np.ma.getdata(a) + np.ma.getdata(b) return np.ma.masked_array(values, mask=np.ma.getmaskarray(b)) return a + b def _cumprod_merge(a, b): if isinstance(a, np.ma.masked_array) or isinstance(b, np.ma.masked_array): values = np.ma.getdata(a) * np.ma.getdata(b) return np.ma.masked_array(values, mask=np.ma.getmaskarray(b)) return a * b
[docs]@derived_from(np) def cumsum(x, axis=None, dtype=None, out=None, method="sequential"): """Dask added an additional keyword-only argument ``method``. method : {'sequential', 'blelloch'}, optional Choose which method to use to perform the cumsum. Default is 'sequential'. * 'sequential' performs the cumsum of each prior block before the current block. * 'blelloch' is a work-efficient parallel cumsum. It exposes parallelism by first taking the sum of each block and combines the sums via a binary tree. This method may be faster or more memory efficient depending on workload, scheduler, and hardware. More benchmarking is necessary. """ return cumreduction( np.cumsum, _cumsum_merge, 0, x, axis, dtype, out=out, method=method, preop=np.sum, )
[docs]@derived_from(np) def cumprod(x, axis=None, dtype=None, out=None, method="sequential"): """Dask added an additional keyword-only argument ``method``. method : {'sequential', 'blelloch'}, optional Choose which method to use to perform the cumprod. Default is 'sequential'. * 'sequential' performs the cumprod of each prior block before the current block. * 'blelloch' is a work-efficient parallel cumprod. It exposes parallelism by first taking the product of each block and combines the products via a binary tree. This method may be faster or more memory efficient depending on workload, scheduler, and hardware. More benchmarking is necessary. """ return cumreduction( np.cumprod, _cumprod_merge, 1, x, axis, dtype, out=out, method=method, preop=np.prod, )
[docs]def topk(a, k, axis=-1, split_every=None): """Extract the k largest elements from a on the given axis, and return them sorted from largest to smallest. If k is negative, extract the -k smallest elements instead, and return them sorted from smallest to largest. This performs best when ``k`` is much smaller than the chunk size. All results will be returned in a single chunk along the given axis. Parameters ---------- x: Array Data being sorted k: int axis: int, optional split_every: int >=2, optional See :func:`reduce`. This parameter becomes very important when k is on the same order of magnitude of the chunk size or more, as it prevents getting the whole or a significant portion of the input array in memory all at once, with a negative impact on network transfer too when running on distributed. Returns ------- Selection of x with size abs(k) along the given axis. Examples -------- >>> import dask.array as da >>> x = np.array([5, 1, 3, 6]) >>> d = da.from_array(x, chunks=2) >>> d.topk(2).compute() array([6, 5]) >>> d.topk(-2).compute() array([1, 3]) """ axis = validate_axis(axis, a.ndim) # chunk and combine steps of the reduction, which recursively invoke # np.partition to pick the top/bottom k elements from the previous step. # The selection is not sorted internally. chunk_combine = partial(chunk.topk, k=k) # aggregate step of the reduction. Internally invokes the chunk/combine # function, then sorts the results internally. aggregate = partial(chunk.topk_aggregate, k=k) return reduction( a, chunk=chunk_combine, combine=chunk_combine, aggregate=aggregate, axis=axis, keepdims=True, dtype=a.dtype, split_every=split_every, output_size=abs(k), )
[docs]def argtopk(a, k, axis=-1, split_every=None): """Extract the indices of the k largest elements from a on the given axis, and return them sorted from largest to smallest. If k is negative, extract the indices of the -k smallest elements instead, and return them sorted from smallest to largest. This performs best when ``k`` is much smaller than the chunk size. All results will be returned in a single chunk along the given axis. Parameters ---------- x: Array Data being sorted k: int axis: int, optional split_every: int >=2, optional See :func:`topk`. The performance considerations for topk also apply here. Returns ------- Selection of np.intp indices of x with size abs(k) along the given axis. Examples -------- >>> import dask.array as da >>> x = np.array([5, 1, 3, 6]) >>> d = da.from_array(x, chunks=2) >>> d.argtopk(2).compute() array([3, 0]) >>> d.argtopk(-2).compute() array([1, 2]) """ axis = validate_axis(axis, a.ndim) # Generate nodes where every chunk is a tuple of (a, original index of a) idx = arange(a.shape[axis], chunks=(a.chunks[axis],), dtype=np.intp) idx = idx[tuple(slice(None) if i == axis else np.newaxis for i in range(a.ndim))] a_plus_idx = a.map_blocks(chunk.argtopk_preprocess, idx, dtype=object) # chunk and combine steps of the reduction. They acquire in input a tuple # of (a, original indices of a) and return another tuple containing the top # k elements of a and the matching original indices. The selection is not # sorted internally, as in np.argpartition. chunk_combine = partial(chunk.argtopk, k=k) # aggregate step of the reduction. Internally invokes the chunk/combine # function, then sorts the results internally, drops a and returns the # index only. aggregate = partial(chunk.argtopk_aggregate, k=k) if isinstance(axis, Number): naxis = 1 else: naxis = len(axis) meta = a._meta.astype(np.intp).reshape((0,) * (a.ndim - naxis + 1)) return reduction( a_plus_idx, chunk=chunk_combine, combine=chunk_combine, aggregate=aggregate, axis=axis, keepdims=True, dtype=np.intp, split_every=split_every, concatenate=False, output_size=abs(k), meta=meta, )
[docs]@derived_from(np) def trace(a, offset=0, axis1=0, axis2=1, dtype=None): return diagonal(a, offset=offset, axis1=axis1, axis2=axis2).sum(-1, dtype=dtype)
[docs]@derived_from(np) def median(a, axis=None, keepdims=False, out=None): """ This works by automatically chunking the reduced axes to a single chunk if necessary and then calling ``numpy.median`` function across the remaining dimensions """ if axis is None: raise NotImplementedError( "The da.median function only works along an axis. " "The full algorithm is difficult to do in parallel" ) if not isinstance(axis, Iterable): axis = (axis,) axis = [ax + a.ndim if ax < 0 else ax for ax in axis] # rechunk if reduced axes are not contained in a single chunk if builtins.any(a.numblocks[ax] > 1 for ax in axis): a = a.rechunk({ax: -1 if ax in axis else "auto" for ax in range(a.ndim)}) result = a.map_blocks( np.median, axis=axis, keepdims=keepdims, drop_axis=axis if not keepdims else None, chunks=[1 if ax in axis else c for ax, c in enumerate(a.chunks)] if keepdims else None, ) result = handle_out(out, result) return result
[docs]@derived_from(np) def nanmedian(a, axis=None, keepdims=False, out=None): """ This works by automatically chunking the reduced axes to a single chunk and then calling ``numpy.nanmedian`` function across the remaining dimensions """ if axis is None: raise NotImplementedError( "The da.nanmedian function only works along an axis or a subset of axes. " "The full algorithm is difficult to do in parallel" ) if not isinstance(axis, Iterable): axis = (axis,) axis = [ax + a.ndim if ax < 0 else ax for ax in axis] # rechunk if reduced axes are not contained in a single chunk if builtins.any(a.numblocks[ax] > 1 for ax in axis): a = a.rechunk({ax: -1 if ax in axis else "auto" for ax in range(a.ndim)}) result = a.map_blocks( np.nanmedian, axis=axis, keepdims=keepdims, drop_axis=axis if not keepdims else None, chunks=[1 if ax in axis else c for ax, c in enumerate(a.chunks)] if keepdims else None, ) result = handle_out(out, result) return result