# Source code for dask.array.overlap

    from __future__ import annotations

    import warnings
    from functools import reduce
    from numbers import Integral, Number
    from operator import mul

    import numpy as np
    from tlz import concat, get, partial
    from tlz.curried import map

    from dask._compatibility import import_optional_dependency
    from dask.array import chunk
    from dask.array._shuffle import _calculate_new_chunksizes
    from dask.array.core import Array, broadcast_to, concatenate, map_blocks, unify_chunks
    from dask.array.creation import arange, empty_like, full_like, repeat
    from dask.array.numpy_compat import normalize_axis_tuple
    from dask.array.reductions import cumreduction
    from dask.array.routines import notnull, where
    from dask.base import tokenize
    from dask.highlevelgraph import HighLevelGraph
    from dask.layers import ArrayOverlapLayer
    from dask.utils import derived_from

    def _overlap_internal_chunks(original_chunks, axes):
        """Get new chunks for array with overlap."""
        chunks = []
        for i, bds in enumerate(original_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)
        return chunks

    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
        """
        token = tokenize(x, axes)
        name = "overlap-" + token

        graph = ArrayOverlapLayer(
            name=x.name,
            axes=axes,
            chunks=x.chunks,
            numblocks=x.numblocks,
            token=token,
        )
        graph = HighLevelGraph.from_collections(name, graph, dependencies=[x])
        chunks = _overlap_internal_chunks(x.chunks, axes)

        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)
        return trim_internal(x, axes=axes, boundary=boundary)

    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,
            meta=x._meta,
        )

    def _trim(x, axes, boundary, _overlap_trim_info):
        """Similar to dask.array.chunk.trim but requires one to specify the
        boundary condition.

        ``axes``, and ``boundary`` are assumed to have been coerced.

        """
        chunk_location = _overlap_trim_info[0]
        num_chunks = _overlap_trim_info[1]
        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(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(num_chunks, 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 = repeat(x[left], depth, axis=axis)
        r = repeat(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,)

        c = full_like(
            x,
            value,
            shape=tuple(map(sum, chunks)),
            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 overlapping

        See Also
        --------
        periodic
        constant
        """
        if not isinstance(kind, dict):
            kind = {i: kind for i in range(x.ndim)}
        if not isinstance(depth, dict):
            depth = {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 ensure_minimum_chunksize(size, chunks):
        """Determine new chunks to ensure that every chunk >= size

        Parameters
        ----------
        size: int
            The maximum size of any chunk.
        chunks: tuple
            Chunks along one axis, e.g. ``(3, 3, 2)``

        Examples
        --------
        >>> ensure_minimum_chunksize(10, (20, 20, 1))
        (20, 11, 10)
        >>> ensure_minimum_chunksize(3, (1, 1, 3))
        (5,)

        See Also
        --------
        overlap
        """
        if size <= min(chunks):
            return chunks

        # add too-small chunks to chunks before them
        output = []
        new = 0
        for c in chunks:
            if c < size:
                if new > size + (size - c):
                    output.append(new - (size - c))
                    new = size
                else:
                    new += c
            if new >= size:
                output.append(new)
                new = 0
            if c >= size:
                new += c
        if new >= size:
            output.append(new)
        elif len(output) >= 1:
            output[-1] += new
        else:
            raise ValueError(
                f"The overlapping depth {size} is larger than your array {sum(chunks)}."
            )

        return tuple(output)

    def _get_overlap_rechunked_chunks(x, depth2):
        depths = [max(d) if isinstance(d, tuple) else d for d in depth2.values()]
        # rechunk if new chunks are needed to fit depth in every chunk
        return tuple(ensure_minimum_chunksize(size, c) for size, c in zip(depths, x.chunks))

    def overlap(x, depth, boundary, *, allow_rechunk=True):
        """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.
        allow_rechunk: bool, keyword only
            Allows rechunking, otherwise chunk sizes need to match and core
            dimensions are to consist only of one chunk.

        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.

        Any axis containing chunks smaller than depth will be rechunked if
        possible, provided the keyword ``allow_rechunk`` is True (recommended).

        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)

        depths = [max(d) if isinstance(d, tuple) else d for d in depth2.values()]
        if allow_rechunk:
            # rechunk if new chunks are needed to fit depth in every chunk
            x1 = x.rechunk(
                _get_overlap_rechunked_chunks(x, depth2)
            )  # this is a no-op if x.chunks == new_chunks

        else:
            original_chunks_too_small = any([min(c) < d for d, c in zip(depths, x.chunks)])
            if original_chunks_too_small:
                raise ValueError(
                    "Overlap depth is larger than smallest chunksize.\n"
                    "Please set allow_rechunk=True to rechunk automatically.\n"
                    f"Overlap depths required: {depths}\n"
                    f"Input chunks: {x.chunks}\n"
                )
            x1 = x

        x2 = boundaries(x1, depth2, boundary2)
        x3 = overlap_internal(x2, depth2)
        trim = {
            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,)

                empty = empty_like(
                    getattr(x, "_meta", x),
                    shape=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,
        allow_rechunk=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. If depth is
        larger than any chunk along a particular axis, then the array is
        rechunked.

        Note that this function will attempt to automatically determine the output
        array type before computing it, please refer to the ``meta`` keyword argument
        in ``map_blocks`` if you expect that the function will not succeed when
        operating on 0-d arrays.

        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, keyword only
            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, keyword only
            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, keyword only
            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, keyword only
            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.
        allow_rechunk: bool, keyword only
            Allows rechunking, otherwise chunk sizes need to match and core
            dimensions are to consist only of one chunk.
        **kwargs:
            Other keyword arguments valid in ``map_blocks``

        Examples
        --------
        >>> import numpy as np
        >>> import dask.array as da

        >>> x = np.array([1, 1, 2, 3, 3, 3, 2, 1, 1])
        >>> x = da.from_array(x, chunks=5)
        >>> def derivative(x):
        ...     return x - np.roll(x, 1)

        >>> y = x.map_overlap(derivative, depth=1, boundary=0)
        >>> y.compute()
        array([ 1,  0,  1,  1,  0,  0, -1, -1,  0])

        >>> x = np.arange(16).reshape((4, 4))
        >>> d = da.from_array(x, chunks=(2, 2))
        >>> d.map_overlap(lambda x: x + x.size, depth=1, boundary='reflect').compute()
        array([[16, 17, 18, 19],
               [20, 21, 22, 23],
               [24, 25, 26, 27],
               [28, 29, 30, 31]])

        >>> func = lambda x: x + x.size
        >>> depth = {0: 1, 1: 1}
        >>> boundary = {0: 'reflect', 1: 'none'}
        >>> d.map_overlap(func, depth, boundary).compute()  # doctest: +NORMALIZE_WHITESPACE
        array([[12,  13,  14,  15],
               [16,  17,  18,  19],
               [20,  21,  22,  23],
               [24,  25,  26,  27]])

        The ``da.map_overlap`` function can also accept multiple arrays.

        >>> func = lambda x, y: x + y
        >>> x = da.arange(8).reshape(2, 4).rechunk((1, 2))
        >>> y = da.arange(4).rechunk(2)
        >>> da.map_overlap(func, x, y, depth=1, boundary='reflect').compute() # doctest: +NORMALIZE_WHITESPACE
        array([[ 0,  2,  4,  6],
               [ 4,  6,  8,  10]])

        When multiple arrays are given, they do not need to have the
        same number of dimensions but they must broadcast together.
        Arrays are aligned block by block (just as in ``da.map_blocks``)
        so the blocks must have a common chunk size.  This common chunking
        is determined automatically as long as ``align_arrays`` is True.

        >>> x = da.arange(8, chunks=4)
        >>> y = da.arange(8, chunks=2)
        >>> r = da.map_overlap(func, x, y, depth=1, boundary='reflect', align_arrays=True)
        >>> len(r.to_delayed())
        4

        >>> da.map_overlap(func, x, y, depth=1, boundary='reflect', align_arrays=False).compute()
        Traceback (most recent call last):
            ...
        ValueError: Shapes do not align {'.0': {2, 4}}

        Note also that this function is equivalent to ``map_blocks``
        by default.  A non-zero ``depth`` must be defined for any
        overlap to appear in the arrays provided to ``func``.

        >>> func = lambda x: x.sum()
        >>> x = da.ones(10, dtype='int')
        >>> block_args = dict(chunks=(), drop_axis=0)
        >>> da.map_blocks(func, x, **block_args).compute()
        np.int64(10)
        >>> da.map_overlap(func, x, **block_args, boundary='reflect').compute()
        np.int64(10)
        >>> da.map_overlap(func, x, **block_args, depth=1, boundary='reflect').compute()
        np.int64(12)

        For functions that may not handle 0-d arrays, it's also possible to specify
        ``meta`` with an empty array matching the type of the expected result. In
        the example below, ``func`` will result in an ``IndexError`` when computing
        ``meta``:

        >>> x = np.arange(16).reshape((4, 4))
        >>> d = da.from_array(x, chunks=(2, 2))
        >>> y = d.map_overlap(lambda x: x + x[2], depth=1, boundary='reflect', meta=np.array(()))
        >>> y
        dask.array<_trim, shape=(4, 4), dtype=float64, chunksize=(2, 2), chunktype=numpy.ndarray>
        >>> y.compute()
        array([[ 4,  6,  8, 10],
               [ 8, 10, 12, 14],
               [20, 22, 24, 26],
               [24, 26, 28, 30]])

        Similarly, it's possible to specify a non-NumPy array to ``meta``:

        >>> import cupy  # doctest: +SKIP
        >>> x = cupy.arange(16).reshape((4, 4))  # doctest: +SKIP
        >>> d = da.from_array(x, chunks=(2, 2))  # doctest: +SKIP
        >>> y = d.map_overlap(lambda x: x + x[2], depth=1, boundary='reflect', meta=cupy.array(()))  # doctest: +SKIP
        >>> y  # doctest: +SKIP
        dask.array<_trim, shape=(4, 4), dtype=float64, chunksize=(2, 2), chunktype=cupy.ndarray>
        >>> y.compute()  # doctest: +SKIP
        array([[ 4,  6,  8, 10],
               [ 8, 10, 12, 14],
               [20, 22, 24, 26],
               [24, 26, 28, 30]])
        """
        # Look for invocation using deprecated single-array signature
        # map_overlap(x, func, depth, boundary=None, trim=True, **kwargs)
        if isinstance(func, Array) and callable(args[0]):
            warnings.warn(
                "The use of map_overlap(array, func, **kwargs) is deprecated since dask 2.17.0 "
                "and will be an error in a future release. To silence this warning, use the syntax "
                "map_overlap(func, array0,[ array1, ...,] **kwargs) instead.",
                FutureWarning,
            )
            sig = ["func", "depth", "boundary", "trim"]
            depth = get(sig.index("depth"), args, depth)
            boundary = get(sig.index("boundary"), args, boundary)
            trim = get(sig.index("trim"), args, trim)
            func, args = args[0], [func]

        if not callable(func):
            raise TypeError(
                "First argument must be callable function, not {}\n"
                "Usage:   da.map_overlap(function, x)\n"
                "   or:   da.map_overlap(function, x, y, z)".format(type(func).__name__)
            )
        if not all(isinstance(x, Array) for x in args):
            raise TypeError(
                "All variadic arguments must be arrays, not {}\n"
                "Usage:   da.map_overlap(function, x)\n"
                "   or:   da.map_overlap(function, x, y, z)".format(
                    [type(x).__name__ for x in args]
                )
            )

        # Coerce depth and boundary arguments to lists of individual
        # specifications for each array argument
        def coerce(xs, arg, fn):
            if not isinstance(arg, list):
                arg = [arg] * len(xs)
            return [fn(x.ndim, a) for x, a in zip(xs, arg)]

        depth = coerce(args, depth, coerce_depth)
        boundary = coerce(args, boundary, coerce_boundary)

        # Align chunks in each array to a common size
        if align_arrays:
            # Reverse unification order to allow block broadcasting
            inds = [list(reversed(range(x.ndim))) for x in args]
            _, args = unify_chunks(*list(concat(zip(args, inds))), warn=False)

        # Escape to map_blocks if depth is zero (a more efficient computation)
        if all([all(depth_val == 0 for depth_val in d.values()) for d in depth]):
            return map_blocks(func, *args, **kwargs)

        for i, x in enumerate(args):
            for j in range(x.ndim):
                if isinstance(depth[i][j], tuple) and boundary[i][j] != "none":
                    raise NotImplementedError(
                        "Asymmetric overlap is currently only implemented "
                        "for boundary='none', however boundary for dimension "
                        "{} in array argument {} is {}".format(j, i, boundary[i][j])
                    )

        def assert_int_chunksize(xs):
            assert all(type(c) is int for x in xs for cc in x.chunks for c in cc)

        assert_int_chunksize(args)
        if not trim and "chunks" not in kwargs:
            if allow_rechunk:
                # Adjust chunks based on the rechunking result
                kwargs["chunks"] = _get_overlap_rechunked_chunks(
                    args[0], coerce_depth(args[0].ndim, depth[0])
                )
            else:
                kwargs["chunks"] = args[0].chunks
        args = [
            overlap(x, depth=d, boundary=b, allow_rechunk=allow_rechunk)
            for x, d, b in zip(args, depth, boundary)
        ]
        assert_int_chunksize(args)
        x = map_blocks(func, *args, **kwargs)
        assert_int_chunksize([x])
        if trim:
            # Find index of array argument with maximum rank and break ties by choosing first provided
            i = sorted(enumerate(args), key=lambda v: (v[1].ndim, -v[0]))[-1][0]
            # Trim using depth/boundary setting for array of highest rank
            depth = depth[i]
            boundary = boundary[i]
            # remove any dropped axes from depth and boundary variables
            drop_axis = kwargs.pop("drop_axis", None)
            if drop_axis is not None:
                if isinstance(drop_axis, Number):
                    drop_axis = [drop_axis]

                # convert negative drop_axis to equivalent positive value
                ndim_out = max(a.ndim for a in args if isinstance(a, Array))
                drop_axis = [d % ndim_out for d in drop_axis]

                kept_axes = tuple(ax for ax in range(args[i].ndim) if ax not in drop_axis)
                # note that keys are relabeled to match values in range(x.ndim)
                depth = {n: depth[ax] for n, ax in enumerate(kept_axes)}
                boundary = {n: boundary[ax] for n, ax in enumerate(kept_axes)}

            # add any new axes to depth and boundary variables
            new_axis = kwargs.pop("new_axis", None)
            if new_axis is not None:
                if isinstance(new_axis, Number):
                    new_axis = [new_axis]

                # convert negative new_axis to equivalent positive value
                ndim_out = max(a.ndim for a in args if isinstance(a, Array))
                new_axis = [d % ndim_out for d in new_axis]

                for axis in new_axis:
                    for existing_axis in list(depth.keys()):
                        if existing_axis >= axis:
                            # Shuffle existing axis forward to give room to insert new_axis
                            depth[existing_axis + 1] = depth[existing_axis]
                            boundary[existing_axis + 1] = boundary[existing_axis]

                    depth[axis] = 0
                    boundary[axis] = "none"

            return trim_internal(x, depth, boundary)
        else:
            return x

    def coerce_depth(ndim, depth):
        default = 0
        if depth is None:
            depth = default
        if isinstance(depth, Integral):
            depth = (depth,) * ndim
        if isinstance(depth, tuple):
            depth = dict(zip(range(ndim), depth))
        if isinstance(depth, dict):
            depth = {ax: depth.get(ax, default) for ax in range(ndim)}
        return coerce_depth_type(ndim, depth)

    def coerce_depth_type(ndim, depth):
        for i in range(ndim):
            if isinstance(depth[i], tuple):
                depth[i] = tuple(int(d) for d in depth[i])
            else:
                depth[i] = int(depth[i])
        return depth

    def coerce_boundary(ndim, boundary):
        default = "none"
        if boundary is None:
            boundary = default
        if not isinstance(boundary, (tuple, dict)):
            boundary = (boundary,) * ndim
        if isinstance(boundary, tuple):
            boundary = dict(zip(range(ndim), boundary))
        if isinstance(boundary, dict):
            boundary = {ax: boundary.get(ax, default) for ax in range(ndim)}
        return boundary

    @derived_from(np.lib.stride_tricks)
    def sliding_window_view(x, window_shape, axis=None, automatic_rechunk=True):
        window_shape = tuple(window_shape) if np.iterable(window_shape) else (window_shape,)

        window_shape_array = np.array(window_shape)
        if np.any(window_shape_array <= 0):
            raise ValueError("`window_shape` must contain values > 0")

        if axis is None:
            axis = tuple(range(x.ndim))
            if len(window_shape) != len(axis):
                raise ValueError(
                    f"Since axis is `None`, must provide "
                    f"window_shape for all dimensions of `x`; "
                    f"got {len(window_shape)} window_shape elements "
                    f"and `x.ndim` is {x.ndim}."
                )
        else:
            axis = normalize_axis_tuple(axis, x.ndim, allow_duplicate=True)
            if len(window_shape) != len(axis):
                raise ValueError(
                    f"Must provide matching length window_shape and "
                    f"axis; got {len(window_shape)} window_shape "
                    f"elements and {len(axis)} axes elements."
                )

        depths = [0] * x.ndim
        for ax, window in zip(axis, window_shape):
            depths[ax] += window - 1

        # Ensure that each chunk is big enough to leave at least a size-1 chunk
        # after windowing (this is only really necessary for the last chunk).
        safe_chunks = list(
            ensure_minimum_chunksize(d + 1, c) for d, c in zip(depths, x.chunks)
        )
        if automatic_rechunk:
            safe_chunks = [
                s if d != 0 else c for d, c, s in zip(depths, x.chunks, safe_chunks)
            ]
            # safe chunks is our output chunks, so add the new dimensions
            safe_chunks.extend([(w,) for w in window_shape])
            max_chunk = reduce(mul, map(max, x.chunks))
            new_chunks = _calculate_new_chunksizes(
                x.chunks,
                safe_chunks.copy(),
                {i for i, d in enumerate(depths) if d == 0},
                max_chunk,
            )
            x = x.rechunk(tuple(new_chunks))
        else:
            x = x.rechunk(tuple(safe_chunks))

        # result.shape = x_shape_trimmed + window_shape,
        # where x_shape_trimmed is x.shape with every entry
        # reduced by one less than the corresponding window size.
        # trim chunks to match x_shape_trimmed
        newchunks = tuple(c[:-1] + (c[-1] - d,) for d, c in zip(depths, x.chunks)) + tuple(
            (window,) for window in window_shape
        )

        return map_overlap(
            np.lib.stride_tricks.sliding_window_view,
            x,
            depth=tuple((0, d) for d in depths),  # Overlap on +ve side only
            boundary="none",
            meta=x._meta,
            new_axis=range(x.ndim, x.ndim + len(axis)),
            chunks=newchunks,
            trim=False,
            align_arrays=False,
            window_shape=window_shape,
            axis=axis,
        )

    def push(array, n, axis):
        """
        Dask-version of bottleneck.push

        .. note::

            Requires bottleneck to be installed.
        """
        import_optional_dependency("bottleneck", min_version="1.3.7")

        if n is not None and 0 < n < array.shape[axis] - 1:
            arr = broadcast_to(
                arange(
                    array.shape[axis], chunks=array.chunks[axis], dtype=array.dtype
                ).reshape(
                    tuple(size if i == axis else 1 for i, size in enumerate(array.shape))
                ),
                array.shape,
                array.chunks,
            )
            valid_arange = where(notnull(array), arr, np.nan)
            valid_limits = (arr - push(valid_arange, None, axis)) <= n
            # omit the forward fill that violate the limit
            return where(valid_limits, push(array, None, axis), np.nan)

        # The method parameter makes that the tests for python 3.7 fails.
        return cumreduction(
            func=_push,
            binop=_fill_with_last_one,
            ident=np.nan,
            x=array,
            axis=axis,
            dtype=array.dtype,
        )

    def _fill_with_last_one(a, b):
        # cumreduction apply the push func over all the blocks first so, the only missing part is filling
        # the missing values using the last data of the previous chunk
        return np.where(~np.isnan(b), b, a)

    def _push(array, n: int | None = None, axis: int = -1):
        # work around for bottleneck 178
        limit = n if n is not None else array.shape[axis]

        import bottleneck as bn

        return bn.push(array, limit, axis)