Commit 4944fbae by Kruyff,D.L.W. (Dylan)

### Make prototype compatible for larger data size

parent 12614e4f
 import warnings from operator import getitem from itertools import product from numbers import Integral from tlz import merge, pipe, concat, partial, get from tlz.curried import map from . import chunk, wrap from .core import ( Array, map_blocks, concatenate, concatenate3, reshapelist, unify_chunks, ) from ..highlevelgraph import HighLevelGraph from ..base import tokenize from ..core import flatten from ..utils import concrete def fractional_slice(task, axes): """ >>> fractional_slice(('x', 5.1), {0: 2}) # doctest: +SKIP (getitem, ('x', 6), (slice(0, 2),)) >>> fractional_slice(('x', 3, 5.1), {0: 2, 1: 3}) # doctest: +SKIP (getitem, ('x', 3, 5), (slice(None, None, None), slice(-3, None))) >>> fractional_slice(('x', 2.9, 5.1), {0: 2, 1: 3}) # doctest: +SKIP (getitem, ('x', 3, 5), (slice(0, 2), slice(-3, None))) """ rounded = (task[0],) + tuple(int(round(i)) for i in task[1:]) index = [] for i, (t, r) in enumerate(zip(task[1:], rounded[1:])): depth = axes.get(i, 0) if isinstance(depth, tuple): left_depth = depth[0] right_depth = depth[1] else: left_depth = depth right_depth = depth if t == r: index.append(slice(None, None, None)) elif t < r and right_depth: index.append(slice(0, right_depth)) elif t > r and left_depth: index.append(slice(-left_depth, None)) else: index.append(slice(0, 0)) index = tuple(index) if all(ind == slice(None, None, None) for ind in index): return task else: return (getitem, rounded, index) def expand_key(k, dims, name=None, axes=None): """ Get all neighboring keys around center Parameters ---------- k: tuple They key around which to generate new keys dims: Sequence[int] The number of chunks in each dimension name: Option[str] The name to include in the output keys, or none to include no name axes: Dict[int, int] The axes active in the expansion. We don't expand on non-active axes Examples -------- >>> expand_key(('x', 2, 3), dims=[5, 5], name='y', axes={0: 1, 1: 1}) # doctest: +NORMALIZE_WHITESPACE [[('y', 1.1, 2.1), ('y', 1.1, 3), ('y', 1.1, 3.9)], [('y', 2, 2.1), ('y', 2, 3), ('y', 2, 3.9)], [('y', 2.9, 2.1), ('y', 2.9, 3), ('y', 2.9, 3.9)]] >>> expand_key(('x', 0, 4), dims=[5, 5], name='y', axes={0: 1, 1: 1}) # doctest: +NORMALIZE_WHITESPACE [[('y', 0, 3.1), ('y', 0, 4)], [('y', 0.9, 3.1), ('y', 0.9, 4)]] """ def inds(i, ind): rv = [] if ind - 0.9 > 0: rv.append(ind - 0.9) rv.append(ind) if ind + 0.9 < dims[i] - 1: rv.append(ind + 0.9) return rv shape = [] for i, ind in enumerate(k[1:]): num = 1 if ind > 0: num += 1 if ind < dims[i] - 1: num += 1 shape.append(num) args = [ inds(i, ind) if any((axes.get(i, 0),)) else [ind] for i, ind in enumerate(k[1:]) ] if name is not None: args = [[name]] + args seq = list(product(*args)) shape2 = [d if any((axes.get(i, 0),)) else 1 for i, d in enumerate(shape)] result = reshapelist(shape2, seq) return result def overlap_internal(x, axes): """ Share boundaries between neighboring blocks Parameters ---------- x: da.Array A dask array axes: dict The size of the shared boundary per axis The axes input informs how many cells to overlap between neighboring blocks {0: 2, 2: 5} means share two cells in 0 axis, 5 cells in 2 axis """ dims = list(map(len, x.chunks)) expand_key2 = partial(expand_key, dims=dims, axes=axes) # Make keys for each of the surrounding sub-arrays interior_keys = pipe( x.__dask_keys__(), flatten, map(expand_key2), map(flatten), concat, list ) name = "overlap-" + tokenize(x, axes) getitem_name = "getitem-" + tokenize(x, axes) interior_slices = {} overlap_blocks = {} for k in interior_keys: frac_slice = fractional_slice((x.name,) + k, axes) if (x.name,) + k != frac_slice: interior_slices[(getitem_name,) + k] = frac_slice else: interior_slices[(getitem_name,) + k] = (x.name,) + k overlap_blocks[(name,) + k] = ( concatenate3, (concrete, expand_key2((None,) + k, name=getitem_name)), ) chunks = [] for i, bds in enumerate(x.chunks): depth = axes.get(i, 0) if isinstance(depth, tuple): left_depth = depth[0] right_depth = depth[1] else: left_depth = depth right_depth = depth if len(bds) == 1: chunks.append(bds) else: left = [bds[0] + right_depth] right = [bds[-1] + left_depth] mid = [] for bd in bds[1:-1]: mid.append(bd + left_depth + right_depth) chunks.append(left + mid + right) dsk = merge(interior_slices, overlap_blocks) graph = HighLevelGraph.from_collections(name, dsk, dependencies=[x]) return Array(graph, name, chunks, meta=x) def trim_overlap(x, depth, boundary=None): """Trim sides from each block. This couples well with the ``map_overlap`` operation which may leave excess data on each block. See also -------- dask.array.overlap.map_overlap """ # parameter to be passed to trim_internal axes = coerce_depth(x.ndim, depth) boundary2 = coerce_boundary(x.ndim, boundary) return trim_internal(x, axes=axes, boundary=boundary2) def trim_internal(x, axes, boundary=None): """ Trim sides from each block This couples well with the overlap operation, which may leave excess data on each block See also -------- dask.array.chunk.trim dask.array.map_blocks """ boundary = coerce_boundary(x.ndim, boundary) olist = [] for i, bd in enumerate(x.chunks): bdy = boundary.get(i, "none") overlap = axes.get(i, 0) ilist = [] for j, d in enumerate(bd): if bdy != "none": if isinstance(overlap, tuple): d = d - sum(overlap) else: d = d - overlap * 2 else: if isinstance(overlap, tuple): d = d - overlap[0] if j != 0 else d d = d - overlap[1] if j != len(bd) - 1 else d else: d = d - overlap if j != 0 else d d = d - overlap if j != len(bd) - 1 else d ilist.append(d) olist.append(tuple(ilist)) chunks = tuple(olist) return map_blocks( partial(_trim, axes=axes, boundary=boundary), x, chunks=chunks, dtype=x.dtype ) def _trim(x, axes, boundary, block_info): """Similar to dask.array.chunk.trim but requires one to specificy the boundary condition. ``axes``, and ``boundary`` are assumed to have been coerced. """ axes = [axes.get(i, 0) for i in range(x.ndim)] axes_front = (ax[0] if isinstance(ax, tuple) else ax for ax in axes) axes_back = ( -ax[1] if isinstance(ax, tuple) and ax[1] else -ax if isinstance(ax, Integral) and ax else None for ax in axes ) trim_front = ( 0 if (chunk_location == 0 and boundary.get(i, "none") == "none") else ax for i, (chunk_location, ax) in enumerate( zip(block_info[0]["chunk-location"], axes_front) ) ) trim_back = ( None if (chunk_location == chunks - 1 and boundary.get(i, "none") == "none") else ax for i, (chunks, chunk_location, ax) in enumerate( zip(block_info[0]["num-chunks"], block_info[0]["chunk-location"], axes_back) ) ) ind = tuple(slice(front, back) for front, back in zip(trim_front, trim_back)) return x[ind] def periodic(x, axis, depth): """ Copy a slice of an array around to its other side Useful to create periodic boundary conditions for overlap """ left = ( (slice(None, None, None),) * axis + (slice(0, depth),) + (slice(None, None, None),) * (x.ndim - axis - 1) ) right = ( (slice(None, None, None),) * axis + (slice(-depth, None),) + (slice(None, None, None),) * (x.ndim - axis - 1) ) l = x[left] r = x[right] l, r = _remove_overlap_boundaries(l, r, axis, depth) return concatenate([r, x, l], axis=axis) def reflect(x, axis, depth): """ Reflect boundaries of array on the same side This is the converse of ``periodic`` """ if depth == 1: left = ( (slice(None, None, None),) * axis + (slice(0, 1),) + (slice(None, None, None),) * (x.ndim - axis - 1) ) else: left = ( (slice(None, None, None),) * axis + (slice(depth - 1, None, -1),) + (slice(None, None, None),) * (x.ndim - axis - 1) ) right = ( (slice(None, None, None),) * axis + (slice(-1, -depth - 1, -1),) + (slice(None, None, None),) * (x.ndim - axis - 1) ) l = x[left] r = x[right] l, r = _remove_overlap_boundaries(l, r, axis, depth) return concatenate([l, x, r], axis=axis) def nearest(x, axis, depth): """ Each reflect each boundary value outwards This mimics what the skimage.filters.gaussian_filter(... mode="nearest") does. """ left = ( (slice(None, None, None),) * axis + (slice(0, 1),) + (slice(None, None, None),) * (x.ndim - axis - 1) ) right = ( (slice(None, None, None),) * axis + (slice(-1, -2, -1),) + (slice(None, None, None),) * (x.ndim - axis - 1) ) l = concatenate([x[left]] * depth, axis=axis) r = concatenate([x[right]] * depth, axis=axis) l, r = _remove_overlap_boundaries(l, r, axis, depth) return concatenate([l, x, r], axis=axis) def constant(x, axis, depth, value): """ Add constant slice to either side of array """ chunks = list(x.chunks) chunks[axis] = (depth,) try: c = wrap.full_like( getattr(x, "_meta", x), value, shape=tuple(map(sum, chunks)), chunks=tuple(chunks), dtype=x.dtype, ) except TypeError: c = wrap.full( tuple(map(sum, chunks)), value, chunks=tuple(chunks), dtype=x.dtype ) return concatenate([c, x, c], axis=axis) def _remove_overlap_boundaries(l, r, axis, depth): lchunks = list(l.chunks) lchunks[axis] = (depth,) rchunks = list(r.chunks) rchunks[axis] = (depth,) l = l.rechunk(tuple(lchunks)) r = r.rechunk(tuple(rchunks)) return l, r def boundaries(x, depth=None, kind=None): """ Add boundary conditions to an array before overlaping See Also -------- periodic constant """ if not isinstance(kind, dict): kind = dict((i, kind) for i in range(x.ndim)) if not isinstance(depth, dict): depth = dict((i, depth) for i in range(x.ndim)) for i in range(x.ndim): d = depth.get(i, 0) if d == 0: continue this_kind = kind.get(i, "none") if this_kind == "none": continue elif this_kind == "periodic": x = periodic(x, i, d) elif this_kind == "reflect": x = reflect(x, i, d) elif this_kind == "nearest": x = nearest(x, i, d) elif i in kind: x = constant(x, i, d, kind[i]) return x def overlap(x, depth, boundary): """ Share boundaries between neighboring blocks Parameters ---------- x: da.Array A dask array depth: dict The size of the shared boundary per axis boundary: dict The boundary condition on each axis. Options are 'reflect', 'periodic', 'nearest', 'none', or an array value. Such a value will fill the boundary with that value. The depth input informs how many cells to overlap between neighboring blocks ``{0: 2, 2: 5}`` means share two cells in 0 axis, 5 cells in 2 axis. Axes missing from this input will not be overlapped. Examples -------- >>> import numpy as np >>> import dask.array as da >>> 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]]) """ depth2 = coerce_depth(x.ndim, depth) boundary2 = coerce_boundary(x.ndim, boundary) # is depth larger than chunk size? depth_values = [depth2.get(i, 0) for i in range(x.ndim)] for d, c in zip(depth_values, x.chunks): maxd = max(d) if isinstance(d, tuple) else d if maxd > min(c): raise ValueError( "The overlapping depth %d is larger than your\n" "smallest chunk size %d. Rechunk your array\n" "with a larger chunk size or a chunk size that\n" "more evenly divides the shape of your array." % (d, min(c)) ) x2 = boundaries(x, depth2, boundary2) x3 = overlap_internal(x2, depth2) trim = dict( (k, v * 2 if boundary2.get(k, "none") != "none" else 0) for k, v in depth2.items() ) x4 = chunk.trim(x3, trim) return x4 def add_dummy_padding(x, depth, boundary): """ Pads an array which has 'none' as the boundary type. Used to simplify trimming arrays which use 'none'. >>> import dask.array as da >>> x = da.arange(6, chunks=3) >>> add_dummy_padding(x, {0: 1}, {0: 'none'}).compute() # doctest: +NORMALIZE_WHITESPACE array([..., 0, 1, 2, 3, 4, 5, ...]) """ for k, v in boundary.items(): d = depth.get(k, 0) if v == "none" and d > 0: empty_shape = list(x.shape) empty_shape[k] = d empty_chunks = list(x.chunks) empty_chunks[k] = (d,) try: empty = wrap.empty_like( getattr(x, "_meta", x), shape=empty_shape, chunks=empty_chunks, dtype=x.dtype, ) except TypeError: empty = wrap.empty(empty_shape, chunks=empty_chunks, dtype=x.dtype) out_chunks = list(x.chunks) ax_chunks = list(out_chunks[k]) ax_chunks[0] += d ax_chunks[-1] += d out_chunks[k] = tuple(ax_chunks) x = concatenate([empty, x, empty], axis=k) x = x.rechunk(out_chunks) return x def map_overlap( func, *args, depth=None, boundary=None, trim=True, align_arrays=True, **kwargs ): """ 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. 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. args : dask 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 --------