from __future__ import division, print_function, absolute_import import inspect import math import warnings from functools import wraps, partial from numbers import Real, Integral import numpy as np from toolz import concat, sliding_window, interleave from ..compatibility import Iterable from ..core import flatten from ..base import tokenize from ..highlevelgraph import HighLevelGraph from ..utils import funcname from . import chunk from .creation import arange, diag, empty, indices from .utils import safe_wraps, validate_axis from .wrap import ones from .ufunc import multiply, sqrt from .core import (Array, map_blocks, elemwise, from_array, asarray, asanyarray, concatenate, stack, blockwise, broadcast_shapes, is_scalar_for_elemwise, broadcast_to, tensordot_lookup) from .einsumfuncs import einsum # noqa @wraps(np.array) def array(x, dtype=None, ndmin=None): while ndmin is not None and x.ndim < ndmin: x = x[None, :] if dtype is not None and x.dtype != dtype: x = x.astype(dtype) return x @wraps(np.result_type) def result_type(*args): args = [a if is_scalar_for_elemwise(a) else a.dtype for a in args] return np.result_type(*args) @wraps(np.atleast_3d) def atleast_3d(*arys): new_arys = [] for x in arys: x = asanyarray(x) if x.ndim == 0: x = x[None, None, None] elif x.ndim == 1: x = x[None, :, None] elif x.ndim == 2: x = x[:, :, None] new_arys.append(x) if len(new_arys) == 1: return new_arys[0] else: return new_arys @wraps(np.atleast_2d) def atleast_2d(*arys): new_arys = [] for x in arys: x = asanyarray(x) if x.ndim == 0: x = x[None, None] elif x.ndim == 1: x = x[None, :] new_arys.append(x) if len(new_arys) == 1: return new_arys[0] else: return new_arys @wraps(np.atleast_1d) def atleast_1d(*arys): new_arys = [] for x in arys: x = asanyarray(x) if x.ndim == 0: x = x[None] new_arys.append(x) if len(new_arys) == 1: return new_arys[0] else: return new_arys @wraps(np.vstack) def vstack(tup, allow_unknown_chunksizes=False): tup = tuple(atleast_2d(x) for x in tup) return concatenate(tup, axis=0, allow_unknown_chunksizes=allow_unknown_chunksizes) @wraps(np.hstack) def hstack(tup, allow_unknown_chunksizes=False): if all(x.ndim == 1 for x in tup): return concatenate(tup, axis=0, allow_unknown_chunksizes=allow_unknown_chunksizes) else: return concatenate(tup, axis=1, allow_unknown_chunksizes=allow_unknown_chunksizes) @wraps(np.dstack) def dstack(tup, allow_unknown_chunksizes=False): tup = tuple(atleast_3d(x) for x in tup) return concatenate(tup, axis=2, allow_unknown_chunksizes=allow_unknown_chunksizes) @wraps(np.swapaxes) def swapaxes(a, axis1, axis2): if axis1 == axis2: return a if axis1 < 0: axis1 = axis1 + a.ndim if axis2 < 0: axis2 = axis2 + a.ndim ind = list(range(a.ndim)) out = list(ind) out[axis1], out[axis2] = axis2, axis1 return blockwise(np.swapaxes, out, a, ind, axis1=axis1, axis2=axis2, dtype=a.dtype) @wraps(np.transpose) def transpose(a, axes=None): if axes: if len(axes) != a.ndim: raise ValueError("axes don't match array") else: axes = tuple(range(a.ndim))[::-1] axes = tuple(d + a.ndim if d < 0 else d for d in axes) return blockwise(np.transpose, axes, a, tuple(range(a.ndim)), dtype=a.dtype, axes=axes) def flip(m, axis): """ Reverse element order along axis. Parameters ---------- axis : int Axis to reverse element order of. Returns ------- reversed array : ndarray """ m = asanyarray(m) sl = m.ndim * [slice(None)] try: sl[axis] = slice(None, None, -1) except IndexError: raise ValueError( "`axis` of %s invalid for %s-D array" % (str(axis), str(m.ndim)) ) sl = tuple(sl) return m[sl] @wraps(np.flipud) def flipud(m): return flip(m, 0) @wraps(np.fliplr) def fliplr(m): return flip(m, 1) alphabet = 'abcdefghijklmnopqrstuvwxyz' ALPHABET = alphabet.upper() def _tensordot(a, b, axes): x = max([a, b], key=lambda x: x.__array_priority__) tensordot = tensordot_lookup.dispatch(type(x)) # workaround may be removed when numpy version (currently 1.13.0) is bumped a_dims = np.array([a.shape[i] for i in axes[0]]) b_dims = np.array([b.shape[i] for i in axes[1]]) if len(a_dims) > 0 and (a_dims == b_dims).all() and a_dims.min() == 0: x = np.zeros(tuple([s for i, s in enumerate(a.shape) if i not in axes[0]] + [s for i, s in enumerate(b.shape) if i not in axes[1]])) else: x = tensordot(a, b, axes=axes) ind = [slice(None, None)] * x.ndim for a in sorted(axes[0]): ind.insert(a, None) x = x[tuple(ind)] return x @wraps(np.tensordot) def tensordot(lhs, rhs, axes=2): if isinstance(axes, Iterable): left_axes, right_axes = axes else: left_axes = tuple(range(lhs.ndim - 1, lhs.ndim - axes - 1, -1)) right_axes = tuple(range(0, axes)) if isinstance(left_axes, Integral): left_axes = (left_axes,) if isinstance(right_axes, Integral): right_axes = (right_axes,) if isinstance(left_axes, list): left_axes = tuple(left_axes) if isinstance(right_axes, list): right_axes = tuple(right_axes) dt = np.promote_types(lhs.dtype, rhs.dtype) left_index = list(range(lhs.ndim)) right_index = list(range(lhs.ndim, lhs.ndim + rhs.ndim)) out_index = left_index + right_index for l, r in zip(left_axes, right_axes): out_index.remove(right_index[r]) right_index[r] = left_index[l] intermediate = blockwise(_tensordot, out_index, lhs, left_index, rhs, right_index, dtype=dt, axes=(left_axes, right_axes)) result = intermediate.sum(axis=left_axes) return result @wraps(np.dot) def dot(a, b): return tensordot(a, b, axes=((a.ndim - 1,), (b.ndim - 2,))) @wraps(np.vdot) def vdot(a, b): return dot(a.conj().ravel(), b.ravel()) @safe_wraps(np.matmul) def matmul(a, b): a = asanyarray(a) b = asanyarray(b) if a.ndim == 0 or b.ndim == 0: raise ValueError("`matmul` does not support scalars.") a_is_1d = False if a.ndim == 1: a_is_1d = True a = a[np.newaxis, :] b_is_1d = False if b.ndim == 1: b_is_1d = True b = b[:, np.newaxis] if a.ndim < b.ndim: a = a[(b.ndim - a.ndim) * (np.newaxis,)] elif a.ndim > b.ndim: b = b[(a.ndim - b.ndim) * (np.newaxis,)] out = blockwise( np.matmul, tuple(range(1, a.ndim + 1)), a, tuple(range(1, a.ndim - 1)) + (a.ndim - 1, 0,), b, tuple(range(1, a.ndim - 1)) + (0, a.ndim,), dtype=result_type(a, b), concatenate=True ) if a_is_1d: out = out[..., 0, :] if b_is_1d: out = out[..., 0] return out @wraps(np.outer) def outer(a, b): a = a.flatten() b = b.flatten() dtype = np.outer(a.dtype.type(), b.dtype.type()).dtype return blockwise(np.outer, "ij", a, "i", b, "j", dtype=dtype) def _inner_apply_along_axis(arr, func1d, func1d_axis, func1d_args, func1d_kwargs): return np.apply_along_axis( func1d, func1d_axis, arr, *func1d_args, **func1d_kwargs ) @wraps(np.apply_along_axis) def apply_along_axis(func1d, axis, arr, *args, **kwargs): arr = asarray(arr) # Validate and normalize axis. arr.shape[axis] axis = len(arr.shape[:axis]) # Test out some data with the function. test_data = np.ones((1,), dtype=arr.dtype) test_result = np.array(func1d(test_data, *args, **kwargs)) # Rechunk so that func1d is applied over the full axis. arr = arr.rechunk( arr.chunks[:axis] + (arr.shape[axis:axis + 1],) + arr.chunks[axis + 1:] ) # Map func1d over the data to get the result # Adds other axes as needed. result = arr.map_blocks( _inner_apply_along_axis, name=funcname(func1d) + '-along-axis', dtype=test_result.dtype, chunks=(arr.chunks[:axis] + test_result.shape + arr.chunks[axis + 1:]), drop_axis=axis, new_axis=list(range(axis, axis + test_result.ndim, 1)), func1d=func1d, func1d_axis=axis, func1d_args=args, func1d_kwargs=kwargs, ) return result @wraps(np.apply_over_axes) def apply_over_axes(func, a, axes): # Validate arguments a = asarray(a) try: axes = tuple(axes) except TypeError: axes = (axes,) sl = a.ndim * (slice(None),) # Compute using `apply_along_axis`. result = a for i in axes: result = apply_along_axis(func, i, result, 0) # Restore original dimensionality or error. if result.ndim == (a.ndim - 1): result = result[sl[:i] + (None,)] elif result.ndim != a.ndim: raise ValueError( "func must either preserve dimensionality of the input" " or reduce it by one." ) return result @wraps(np.ptp) def ptp(a, axis=None): return a.max(axis=axis) - a.min(axis=axis) @wraps(np.diff) def diff(a, n=1, axis=-1): a = asarray(a) n = int(n) axis = int(axis) sl_1 = a.ndim * [slice(None)] sl_2 = a.ndim * [slice(None)] sl_1[axis] = slice(1, None) sl_2[axis] = slice(None, -1) sl_1 = tuple(sl_1) sl_2 = tuple(sl_2) r = a for i in range(n): r = r[sl_1] - r[sl_2] return r @wraps(np.ediff1d) def ediff1d(ary, to_end=None, to_begin=None): ary = asarray(ary) aryf = ary.flatten() r = aryf[1:] - aryf[:-1] r = [r] if to_begin is not None: r = [asarray(to_begin).flatten()] + r if to_end is not None: r = r + [asarray(to_end).flatten()] r = concatenate(r) return r def _gradient_kernel(x, block_id, coord, axis, array_locs, grad_kwargs): """ x: nd-array array of one block coord: 1d-array or scalar coordinate along which the gradient is computed. axis: int axis along which the gradient is computed array_locs: actual location along axis. None if coordinate is scalar grad_kwargs: keyword to be passed to np.gradient """ block_loc = block_id[axis] if array_locs is not None: coord = coord[array_locs[0][block_loc]:array_locs[1][block_loc]] grad = np.gradient(x, coord, axis=axis, **grad_kwargs) return grad @wraps(np.gradient) def gradient(f, *varargs, **kwargs): f = asarray(f) kwargs["edge_order"] = math.ceil(kwargs.get("edge_order", 1)) if kwargs["edge_order"] > 2: raise ValueError("edge_order must be less than or equal to 2.") drop_result_list = False axis = kwargs.pop("axis", None) if axis is None: axis = tuple(range(f.ndim)) elif isinstance(axis, Integral): drop_result_list = True axis = (axis,) axis = validate_axis(axis, f.ndim) if len(axis) != len(set(axis)): raise ValueError("duplicate axes not allowed") axis = tuple(ax % f.ndim for ax in axis) if varargs == (): varargs = (1,) if len(varargs) == 1: varargs = len(axis) * varargs if len(varargs) != len(axis): raise TypeError( "Spacing must either be a single scalar, or a scalar / 1d-array " "per axis" ) if issubclass(f.dtype.type, (np.bool8, Integral)): f = f.astype(float) elif issubclass(f.dtype.type, Real) and f.dtype.itemsize < 4: f = f.astype(float) results = [] for i, ax in enumerate(axis): for c in f.chunks[ax]: if np.min(c) < kwargs["edge_order"] + 1: raise ValueError( 'Chunk size must be larger than edge_order + 1. ' 'Minimum chunk for aixs {} is {}. Rechunk to ' 'proceed.'.format(np.min(c), ax)) if np.isscalar(varargs[i]): array_locs = None else: if isinstance(varargs[i], Array): raise NotImplementedError( 'dask array coordinated is not supported.') # coordinate position for each block taking overlap into account chunk = np.array(f.chunks[ax]) array_loc_stop = np.cumsum(chunk) + 1 array_loc_start = array_loc_stop - chunk - 2 array_loc_stop[-1] -= 1 array_loc_start[0] = 0 array_locs = (array_loc_start, array_loc_stop) results.append(f.map_overlap( _gradient_kernel, dtype=f.dtype, depth={j: 1 if j == ax else 0 for j in range(f.ndim)}, boundary="none", coord=varargs[i], axis=ax, array_locs=array_locs, grad_kwargs=kwargs, )) if drop_result_list: results = results[0] return results def _bincount_sum(bincounts, dtype=int): n = max(map(len, bincounts)) out = np.zeros(n, dtype=dtype) for b in bincounts: out[:len(b)] += b return out @wraps(np.bincount) def bincount(x, weights=None, minlength=0): if x.ndim != 1: raise ValueError('Input array must be one dimensional. ' 'Try using x.ravel()') if weights is not None: if weights.chunks != x.chunks: raise ValueError('Chunks of input array x and weights must match.') token = tokenize(x, weights, minlength) name = 'bincount-' + token final_name = 'bincount-sum' + token # Call np.bincount on each block, possibly with weights if weights is not None: dsk = {(name, i): (np.bincount, (x.name, i), (weights.name, i), minlength) for i, _ in enumerate(x.__dask_keys__())} dtype = np.bincount([1], weights=[1]).dtype else: dsk = {(name, i): (np.bincount, (x.name, i), None, minlength) for i, _ in enumerate(x.__dask_keys__())} dtype = np.bincount([]).dtype dsk[(final_name, 0)] = (_bincount_sum, list(dsk), dtype) graph = HighLevelGraph.from_collections(final_name, dsk, dependencies=[x] if weights is None else [x, weights]) if minlength == 0: chunks = ((np.nan,),) else: chunks = ((minlength,),) return Array(graph, final_name, chunks, dtype) @wraps(np.digitize) def digitize(a, bins, right=False): bins = np.asarray(bins) dtype = np.digitize([0], bins, right=False).dtype return a.map_blocks(np.digitize, dtype=dtype, bins=bins, right=right) def histogram(a, bins=None, range=None, normed=False, weights=None, density=None): """ Blocked variant of :func:`numpy.histogram`. Follows the signature of :func:`numpy.histogram` exactly with the following exceptions: - Either an iterable specifying the ``bins`` or the number of ``bins`` and a ``range`` argument is required as computing ``min`` and ``max`` over blocked arrays is an expensive operation that must be performed explicitly. - ``weights`` must be a dask.array.Array with the same block structure as ``a``. Examples -------- Using number of bins and range: >>> import dask.array as da >>> import numpy as np >>> x = da.from_array(np.arange(10000), chunks=10) >>> h, bins = da.histogram(x, bins=10, range=[0, 10000]) >>> bins array([ 0., 1000., 2000., 3000., 4000., 5000., 6000., 7000., 8000., 9000., 10000.]) >>> h.compute() array([1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]) Explicitly specifying the bins: >>> h, bins = da.histogram(x, bins=np.array([0, 5000, 10000])) >>> bins array([ 0, 5000, 10000]) >>> h.compute() array([5000, 5000]) """ if not np.iterable(bins) and (range is None or bins is None): raise ValueError('dask.array.histogram requires either specifying ' 'bins as an iterable or specifying both a range and ' 'the number of bins') if weights is not None and weights.chunks != a.chunks: raise ValueError('Input array and weights must have the same ' 'chunked structure') if normed is not False: raise ValueError( "The normed= keyword argument has been deprecated. " "Please use density instead. " "See the numpy.histogram docstring for more information." ) if not np.iterable(bins): bin_token = bins mn, mx = range if mn == mx: mn -= 0.5 mx += 0.5 bins = np.linspace(mn, mx, bins + 1, endpoint=True) else: bin_token = bins token = tokenize(a, bin_token, range, weights, density) nchunks = len(list(flatten(a.__dask_keys__()))) chunks = ((1,) * nchunks, (len(bins) - 1,)) name = 'histogram-sum-' + token # Map the histogram to all bins def block_hist(x, range=None, weights=None): return np.histogram(x, bins, range=range, weights=weights)[0][np.newaxis] if weights is None: dsk = {(name, i, 0): (block_hist, k, range) for i, k in enumerate(flatten(a.__dask_keys__()))} dtype = np.histogram([])[0].dtype else: a_keys = flatten(a.__dask_keys__()) w_keys = flatten(weights.__dask_keys__()) dsk = {(name, i, 0): (block_hist, k, range, w) for i, (k, w) in enumerate(zip(a_keys, w_keys))} dtype = weights.dtype graph = HighLevelGraph.from_collections(name, dsk, dependencies=[a] if weights is None else [a, weights]) mapped = Array(graph, name, chunks, dtype=dtype) n = mapped.sum(axis=0) # We need to replicate normed and density options from numpy if density is not None: if density: db = from_array(np.diff(bins).astype(float), chunks=n.chunks) return n / db / n.sum(), bins else: return n, bins else: return n, bins @wraps(np.cov) def cov(m, y=None, rowvar=1, bias=0, ddof=None): # This was copied almost verbatim from np.cov # See numpy license at https://github.com/numpy/numpy/blob/master/LICENSE.txt # or NUMPY_LICENSE.txt within this directory if ddof is not None and ddof != int(ddof): raise ValueError( "ddof must be integer") # Handles complex arrays too m = asarray(m) if y is None: dtype = np.result_type(m, np.float64) else: y = asarray(y) dtype = np.result_type(m, y, np.float64) X = array(m, ndmin=2, dtype=dtype) if X.shape[0] == 1: rowvar = 1 if rowvar: N = X.shape[1] axis = 0 else: N = X.shape[0] axis = 1 # check ddof if ddof is None: if bias == 0: ddof = 1 else: ddof = 0 fact = float(N - ddof) if fact <= 0: warnings.warn("Degrees of freedom <= 0 for slice", RuntimeWarning) fact = 0.0 if y is not None: y = array(y, ndmin=2, dtype=dtype) X = concatenate((X, y), axis) X = X - X.mean(axis=1 - axis, keepdims=True) if not rowvar: return (dot(X.T, X.conj()) / fact).squeeze() else: return (dot(X, X.T.conj()) / fact).squeeze() @wraps(np.corrcoef) def corrcoef(x, y=None, rowvar=1): c = cov(x, y, rowvar) if c.shape == (): return c / c d = diag(c) d = d.reshape((d.shape[0], 1)) sqr_d = sqrt(d) return (c / sqr_d) / sqr_d.T @wraps(np.round) def round(a, decimals=0): return a.map_blocks(np.round, decimals=decimals, dtype=a.dtype) def _unique_internal(ar, indices, counts, return_inverse=False): """ Helper/wrapper function for :func:`numpy.unique`. Uses :func:`numpy.unique` to find the unique values for the array chunk. Given this chunk may not represent the whole array, also take the ``indices`` and ``counts`` that are in 1-to-1 correspondence to ``ar`` and reduce them in the same fashion as ``ar`` is reduced. Namely sum any counts that correspond to the same value and take the smallest index that corresponds to the same value. To handle the inverse mapping from the unique values to the original array, simply return a NumPy array created with ``arange`` with enough values to correspond 1-to-1 to the unique values. While there is more work needed to be done to create the full inverse mapping for the original array, this provides enough information to generate the inverse mapping in Dask. Given Dask likes to have one array returned from functions like ``blockwise``, some formatting is done to stuff all of the resulting arrays into one big NumPy structured array. Dask is then able to handle this object and can split it apart into the separate results on the Dask side, which then can be passed back to this function in concatenated chunks for further reduction or can be return to the user to perform other forms of analysis. By handling the problem in this way, it does not matter where a chunk is in a larger array or how big it is. The chunk can still be computed on the same way. Also it does not matter if the chunk is the result of other chunks being run through this function multiple times. The end result will still be just as accurate using this strategy. """ return_index = (indices is not None) return_counts = (counts is not None) u = np.unique(ar) dt = [("values", u.dtype)] if return_index: dt.append(("indices", np.intp)) if return_inverse: dt.append(("inverse", np.intp)) if return_counts: dt.append(("counts", np.intp)) r = np.empty(u.shape, dtype=dt) r["values"] = u if return_inverse: r["inverse"] = np.arange(len(r), dtype=np.intp) if return_index or return_counts: for i, v in enumerate(r["values"]): m = (ar == v) if return_index: indices[m].min(keepdims=True, out=r["indices"][i:i + 1]) if return_counts: counts[m].sum(keepdims=True, out=r["counts"][i:i + 1]) return r @wraps(np.unique) def unique(ar, return_index=False, return_inverse=False, return_counts=False): ar = ar.ravel() # Run unique on each chunk and collect results in a Dask Array of # unknown size. args = [ar, "i"] out_dtype = [("values", ar.dtype)] if return_index: args.extend([ arange(ar.shape[0], dtype=np.intp, chunks=ar.chunks[0]), "i" ]) out_dtype.append(("indices", np.intp)) else: args.extend([None, None]) if return_counts: args.extend([ ones((ar.shape[0],), dtype=np.intp, chunks=ar.chunks[0]), "i" ]) out_dtype.append(("counts", np.intp)) else: args.extend([None, None]) out = blockwise( _unique_internal, "i", *args, dtype=out_dtype, return_inverse=False ) out._chunks = tuple((np.nan,) * len(c) for c in out.chunks) # Take the results from the unique chunks and do the following. # # 1. Collect all results as arguments. # 2. Concatenate each result into one big array. # 3. Pass all results as arguments to the internal unique again. # # TODO: This should be replaced with a tree reduction using this strategy. # xref: https://github.com/dask/dask/issues/2851 out_parts = [out["values"]] if return_index: out_parts.append(out["indices"]) else: out_parts.append(None) if return_counts: out_parts.append(out["counts"]) else: out_parts.append(None) name = 'unique-aggregate-' + out.name dsk = { (name, 0): ( (_unique_internal,) + tuple( (np.concatenate, o. __dask_keys__()) if hasattr(o, "__dask_keys__") else o for o in out_parts ) + (return_inverse,) ) } out_dtype = [("values", ar.dtype)] if return_index: out_dtype.append(("indices", np.intp)) if return_inverse: out_dtype.append(("inverse", np.intp)) if return_counts: out_dtype.append(("counts", np.intp)) dependencies = [o for o in out_parts if hasattr(o, '__dask_keys__')] graph = HighLevelGraph.from_collections(name, dsk, dependencies=dependencies) chunks = ((np.nan,),) out = Array(graph, name, chunks, out_dtype) # Split out all results to return to the user. result = [out["values"]] if return_index: result.append(out["indices"]) if return_inverse: # Using the returned unique values and arange of unknown length, find # each value matching a unique value and replace it with its # corresponding index or `0`. There should be only one entry for this # index in axis `1` (the one of unknown length). Reduce axis `1` # through summing to get an array with known dimensionality and the # mapping of the original values. mtches = (ar[:, None] == out["values"][None, :]).astype(np.intp) result.append((mtches * out["inverse"]).sum(axis=1)) if return_counts: result.append(out["counts"]) if len(result) == 1: result = result[0] else: result = tuple(result) return result def _isin_kernel(element, test_elements, assume_unique=False): values = np.in1d(element.ravel(), test_elements, assume_unique=assume_unique) return values.reshape(element.shape + (1,) * test_elements.ndim) @safe_wraps(getattr(np, 'isin', None)) def isin(element, test_elements, assume_unique=False, invert=False): element = asarray(element) test_elements = asarray(test_elements) element_axes = tuple(range(element.ndim)) test_axes = tuple(i + element.ndim for i in range(test_elements.ndim)) mapped = blockwise( _isin_kernel, element_axes + test_axes, element, element_axes, test_elements, test_axes, adjust_chunks={axis: lambda _: 1 for axis in test_axes}, dtype=bool, assume_unique=assume_unique ) result = mapped.any(axis=test_axes) if invert: result = ~result return result @wraps(np.roll) def roll(array, shift, axis=None): result = array if axis is None: result = ravel(result) if not isinstance(shift, Integral): raise TypeError( "Expect `shift` to be an instance of Integral" " when `axis` is None." ) shift = (shift,) axis = (0,) else: try: len(shift) except TypeError: shift = (shift,) try: len(axis) except TypeError: axis = (axis,) if len(shift) != len(axis): raise ValueError("Must have the same number of shifts as axes.") for i, s in zip(axis, shift): s = -s s %= result.shape[i] sl1 = result.ndim * [slice(None)] sl2 = result.ndim * [slice(None)] sl1[i] = slice(s, None) sl2[i] = slice(None, s) sl1 = tuple(sl1) sl2 = tuple(sl2) result = concatenate([result[sl1], result[sl2]], axis=i) result = result.reshape(array.shape) return result @wraps(np.ravel) def ravel(array): return array.reshape((-1,)) @wraps(np.squeeze) def squeeze(a, axis=None): if axis is None: axis = tuple(i for i, d in enumerate(a.shape) if d == 1) elif not isinstance(axis, tuple): axis = (axis,) if any(a.shape[i] != 1 for i in axis): raise ValueError("cannot squeeze axis with size other than one") axis = validate_axis(axis, a.ndim) sl = tuple(0 if i in axis else slice(None) for i, s in enumerate(a.shape)) return a[sl] @wraps(np.compress) def compress(condition, a, axis=None): condition = asarray(condition).astype(bool) a = asarray(a) if condition.ndim != 1: raise ValueError("Condition must be one dimensional") if axis is None: a = a.ravel() axis = 0 axis = validate_axis(axis, a.ndim) # Treat `condition` as filled with `False` (if it is too short) a = a[tuple(slice(None, len(condition)) if i == axis else slice(None) for i in range(a.ndim))] # Use `condition` to select along 1 dimension a = a[tuple(condition if i == axis else slice(None) for i in range(a.ndim))] return a @wraps(np.extract) def extract(condition, arr): condition = asarray(condition).astype(bool) arr = asarray(arr) return compress(condition.ravel(), arr.ravel()) @wraps(np.take) def take(a, indices, axis=0): axis = validate_axis(axis, a.ndim) if isinstance(a, np.ndarray) and isinstance(indices, Array): return _take_dask_array_from_numpy(a, indices, axis) else: return a[(slice(None),) * axis + (indices,)] def _take_dask_array_from_numpy(a, indices, axis): assert isinstance(a, np.ndarray) assert isinstance(indices, Array) return indices.map_blocks(lambda block: np.take(a, block, axis), chunks=indices.chunks, dtype=a.dtype) @wraps(np.around) def around(x, decimals=0): return map_blocks(partial(np.around, decimals=decimals), x, dtype=x.dtype) def _asarray_isnull(values): import pandas as pd return np.asarray(pd.isnull(values)) def isnull(values): """ pandas.isnull for dask arrays """ # eagerly raise ImportError, if pandas isn't available import pandas as pd # noqa return elemwise(_asarray_isnull, values, dtype='bool') def notnull(values): """ pandas.notnull for dask arrays """ return ~isnull(values) @wraps(np.isclose) def isclose(arr1, arr2, rtol=1e-5, atol=1e-8, equal_nan=False): func = partial(np.isclose, rtol=rtol, atol=atol, equal_nan=equal_nan) return elemwise(func, arr1, arr2, dtype='bool') @wraps(np.allclose) def allclose(arr1, arr2, rtol=1e-5, atol=1e-8, equal_nan=False): return isclose(arr1, arr2, rtol=rtol, atol=atol, equal_nan=equal_nan).all() def variadic_choose(a, *choices): return np.choose(a, choices) @wraps(np.choose) def choose(a, choices): return elemwise(variadic_choose, a, *choices) def _isnonzero_vec(v): return bool(np.count_nonzero(v)) _isnonzero_vec = np.vectorize(_isnonzero_vec, otypes=[bool]) def isnonzero(a): try: np.zeros(tuple(), dtype=a.dtype).astype(bool) except ValueError: ###################################################### # Handle special cases where conversion to bool does # # not work correctly. # # # # xref: https://github.com/numpy/numpy/issues/9479 # ###################################################### return a.map_blocks(_isnonzero_vec, dtype=bool) else: return a.astype(bool) @wraps(np.argwhere) def argwhere(a): a = asarray(a) nz = isnonzero(a).flatten() ind = indices(a.shape, dtype=np.intp, chunks=a.chunks) if ind.ndim > 1: ind = stack([ind[i].ravel() for i in range(len(ind))], axis=1) ind = compress(nz, ind, axis=0) return ind @wraps(np.where) def where(condition, x=None, y=None): if (x is None) != (y is None): raise ValueError("either both or neither of x and y should be given") if (x is None) and (y is None): return nonzero(condition) if np.isscalar(condition): dtype = result_type(x, y) x = asarray(x) y = asarray(y) shape = broadcast_shapes(x.shape, y.shape) out = x if condition else y return broadcast_to(out, shape).astype(dtype) else: return elemwise(np.where, condition, x, y) @wraps(np.count_nonzero) def count_nonzero(a, axis=None): return isnonzero(asarray(a)).astype(np.intp).sum(axis=axis) @wraps(np.flatnonzero) def flatnonzero(a): return argwhere(asarray(a).ravel())[:, 0] @wraps(np.nonzero) def nonzero(a): ind = argwhere(a) if ind.ndim > 1: return tuple(ind[:, i] for i in range(ind.shape[1])) else: return (ind,) def _int_piecewise(x, *condlist, **kwargs): return np.piecewise( x, list(condlist), kwargs["funclist"], *kwargs["func_args"], **kwargs["func_kw"] ) def _unravel_index_kernel(indices, func_kwargs): return np.stack(np.unravel_index(indices, **func_kwargs)) @wraps(np.unravel_index) def unravel_index(indices, dims, order='C'): if dims and indices.size: unraveled_indices = tuple(indices.map_blocks( _unravel_index_kernel, dtype=np.intp, chunks=(((len(dims),),) + indices.chunks), new_axis=0, func_kwargs={"dims": dims, "order": order} )) else: unraveled_indices = tuple( empty((0,), dtype=np.intp, chunks=1) for i in dims ) return unraveled_indices @wraps(np.piecewise) def piecewise(x, condlist, funclist, *args, **kw): return map_blocks( _int_piecewise, x, *condlist, dtype=x.dtype, name="piecewise", funclist=funclist, func_args=args, func_kw=kw ) @wraps(chunk.coarsen) def coarsen(reduction, x, axes, trim_excess=False): if (not trim_excess and not all(bd % div == 0 for i, div in axes.items() for bd in x.chunks[i])): msg = "Coarsening factor does not align with block dimensions" raise ValueError(msg) if 'dask' in inspect.getfile(reduction): reduction = getattr(np, reduction.__name__) name = 'coarsen-' + tokenize(reduction, x, axes, trim_excess) dsk = {(name,) + key[1:]: (chunk.coarsen, reduction, key, axes, trim_excess) for key in flatten(x.__dask_keys__())} chunks = tuple(tuple(int(bd // axes.get(i, 1)) for bd in bds) for i, bds in enumerate(x.chunks)) dt = reduction(np.empty((1,) * x.ndim, dtype=x.dtype)).dtype graph = HighLevelGraph.from_collections(name, dsk, dependencies=[x]) return Array(graph, name, chunks, dtype=dt) def split_at_breaks(array, breaks, axis=0): """ Split an array into a list of arrays (using slices) at the given breaks >>> split_at_breaks(np.arange(6), [3, 5]) [array([0, 1, 2]), array([3, 4]), array([5])] """ padded_breaks = concat([[None], breaks, [None]]) slices = [slice(i, j) for i, j in sliding_window(2, padded_breaks)] preslice = (slice(None),) * axis split_array = [array[preslice + (s,)] for s in slices] return split_array @wraps(np.insert) def insert(arr, obj, values, axis): # axis is a required argument here to avoid needing to deal with the numpy # default case (which reshapes the array to make it flat) axis = validate_axis(axis,arr.ndim) if isinstance(obj, slice): obj = np.arange(*obj.indices(arr.shape[axis])) obj = np.asarray(obj) scalar_obj = obj.ndim == 0 if scalar_obj: obj = np.atleast_1d(obj) obj = np.where(obj < 0, obj + arr.shape[axis], obj) if (np.diff(obj) < 0).any(): raise NotImplementedError( 'da.insert only implemented for monotonic ``obj`` argument') split_arr = split_at_breaks(arr, np.unique(obj), axis) if getattr(values, 'ndim', 0) == 0: # we need to turn values into a dask array name = 'values-' + tokenize(values) dtype = getattr(values, 'dtype', type(values)) values = Array({(name,): values}, name, chunks=(), dtype=dtype) values_shape = tuple(len(obj) if axis == n else s for n, s in enumerate(arr.shape)) values = broadcast_to(values, values_shape) elif scalar_obj: values = values[(slice(None),) * axis + (None,)] values_chunks = tuple(values_bd if axis == n else arr_bd for n, (arr_bd, values_bd) in enumerate(zip(arr.chunks, values.chunks))) values = values.rechunk(values_chunks) counts = np.bincount(obj)[:-1] values_breaks = np.cumsum(counts[counts > 0]) split_values = split_at_breaks(values, values_breaks, axis) interleaved = list(interleave([split_arr, split_values])) interleaved = [i for i in interleaved if i.nbytes] return concatenate(interleaved, axis=axis) def _average(a, axis=None, weights=None, returned=False, is_masked=False): # This was minimally modified from numpy.average # See numpy license at https://github.com/numpy/numpy/blob/master/LICENSE.txt # or NUMPY_LICENSE.txt within this directory # Wrapper used by da.average or da.ma.average. a = asanyarray(a) if weights is None: avg = a.mean(axis) scl = avg.dtype.type(a.size / avg.size) else: wgt = asanyarray(weights) if issubclass(a.dtype.type, (np.integer, np.bool_)): result_dtype = result_type(a.dtype, wgt.dtype, 'f8') else: result_dtype = result_type(a.dtype, wgt.dtype) # Sanity checks if a.shape != wgt.shape: if axis is None: raise TypeError( "Axis must be specified when shapes of a and weights " "differ.") if wgt.ndim != 1: raise TypeError( "1D weights expected when shapes of a and weights differ.") if wgt.shape[0] != a.shape[axis]: raise ValueError( "Length of weights not compatible with specified axis.") # setup wgt to broadcast along axis wgt = broadcast_to(wgt, (a.ndim - 1) * (1,) + wgt.shape) wgt = wgt.swapaxes(-1, axis) if is_masked: from .ma import getmaskarray wgt = wgt * (~getmaskarray(a)) scl = wgt.sum(axis=axis, dtype=result_dtype) avg = multiply(a, wgt, dtype=result_dtype).sum(axis) / scl if returned: if scl.shape != avg.shape: scl = broadcast_to(scl, avg.shape).copy() return avg, scl else: return avg @wraps(np.average) def average(a, axis=None, weights=None, returned=False): return _average(a, axis, weights, returned, is_masked=False)