manyi/venv/Lib/site-packages/numpy/lib/arraypad.py

"""
The arraypad module contains a group of functions to pad values onto the edges
of an n-dimensional array.

"""
from __future__ import division, absolute_import, print_function

import numpy as np
from numpy.core.overrides import array_function_dispatch


__all__ = ['pad']


###############################################################################
# Private utility functions.


def _arange_ndarray(arr, shape, axis, reverse=False):
    """
    Create an ndarray of `shape` with increments along specified `axis`

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    shape : tuple of ints
        Shape of desired array. Should be equivalent to `arr.shape` except
        `shape[axis]` which may have any positive value.
    axis : int
        Axis to increment along.
    reverse : bool
        If False, increment in a positive fashion from 1 to `shape[axis]`,
        inclusive. If True, the bounds are the same but the order reversed.

    Returns
    -------
    padarr : ndarray
        Output array sized to pad `arr` along `axis`, with linear range from
        1 to `shape[axis]` along specified `axis`.

    Notes
    -----
    The range is deliberately 1-indexed for this specific use case. Think of
    this algorithm as broadcasting `np.arange` to a single `axis` of an
    arbitrarily shaped ndarray.

    """
    initshape = tuple(1 if i != axis else shape[axis]
                      for (i, x) in enumerate(arr.shape))
    if not reverse:
        padarr = np.arange(1, shape[axis] + 1)
    else:
        padarr = np.arange(shape[axis], 0, -1)
    padarr = padarr.reshape(initshape)
    for i, dim in enumerate(shape):
        if padarr.shape[i] != dim:
            padarr = padarr.repeat(dim, axis=i)
    return padarr


def _round_ifneeded(arr, dtype):
    """
    Rounds arr inplace if destination dtype is integer.

    Parameters
    ----------
    arr : ndarray
        Input array.
    dtype : dtype
        The dtype of the destination array.

    """
    if np.issubdtype(dtype, np.integer):
        arr.round(out=arr)


def _slice_at_axis(shape, sl, axis):
    """
    Construct a slice tuple the length of shape, with sl at the specified axis
    """
    slice_tup = (slice(None),)
    return slice_tup * axis + (sl,) + slice_tup * (len(shape) - axis - 1)


def _slice_first(shape, n, axis):
    """ Construct a slice tuple to take the first n elements along axis """
    return _slice_at_axis(shape, slice(0, n), axis=axis)


def _slice_last(shape, n, axis):
    """ Construct a slice tuple to take the last n elements along axis """
    dim = shape[axis]  # doing this explicitly makes n=0 work
    return _slice_at_axis(shape, slice(dim - n, dim), axis=axis)


def _do_prepend(arr, pad_chunk, axis):
    return np.concatenate(
        (pad_chunk.astype(arr.dtype, copy=False), arr), axis=axis)


def _do_append(arr, pad_chunk, axis):
    return np.concatenate(
        (arr, pad_chunk.astype(arr.dtype, copy=False)), axis=axis)


def _prepend_const(arr, pad_amt, val, axis=-1):
    """
    Prepend constant `val` along `axis` of `arr`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to prepend.
    val : scalar
        Constant value to use. For best results should be of type `arr.dtype`;
        if not `arr.dtype` will be cast to `arr.dtype`.
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` constant `val` prepended along `axis`.

    """
    if pad_amt == 0:
        return arr
    padshape = tuple(x if i != axis else pad_amt
                     for (i, x) in enumerate(arr.shape))
    return _do_prepend(arr, np.full(padshape, val, dtype=arr.dtype), axis)


def _append_const(arr, pad_amt, val, axis=-1):
    """
    Append constant `val` along `axis` of `arr`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to append.
    val : scalar
        Constant value to use. For best results should be of type `arr.dtype`;
        if not `arr.dtype` will be cast to `arr.dtype`.
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` constant `val` appended along `axis`.

    """
    if pad_amt == 0:
        return arr
    padshape = tuple(x if i != axis else pad_amt
                     for (i, x) in enumerate(arr.shape))
    return _do_append(arr, np.full(padshape, val, dtype=arr.dtype), axis)



def _prepend_edge(arr, pad_amt, axis=-1):
    """
    Prepend `pad_amt` to `arr` along `axis` by extending edge values.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to prepend.
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, extended by `pad_amt` edge values appended along `axis`.

    """
    if pad_amt == 0:
        return arr

    edge_slice = _slice_first(arr.shape, 1, axis=axis)
    edge_arr = arr[edge_slice]
    return _do_prepend(arr, edge_arr.repeat(pad_amt, axis=axis), axis)


def _append_edge(arr, pad_amt, axis=-1):
    """
    Append `pad_amt` to `arr` along `axis` by extending edge values.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to append.
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, extended by `pad_amt` edge values prepended along
        `axis`.

    """
    if pad_amt == 0:
        return arr

    edge_slice = _slice_last(arr.shape, 1, axis=axis)
    edge_arr = arr[edge_slice]
    return _do_append(arr, edge_arr.repeat(pad_amt, axis=axis), axis)


def _prepend_ramp(arr, pad_amt, end, axis=-1):
    """
    Prepend linear ramp along `axis`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to prepend.
    end : scalar
        Constal value to use. For best results should be of type `arr.dtype`;
        if not `arr.dtype` will be cast to `arr.dtype`.
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` values prepended along `axis`. The
        prepended region ramps linearly from the edge value to `end`.

    """
    if pad_amt == 0:
        return arr

    # Slice a chunk from the edge to calculate stats on and extract edge
    edge_slice = _slice_first(arr.shape, 1, axis=axis)
    edge = arr[edge_slice]

    ramp_arr = np.linspace(
        start=end,
        stop=edge.squeeze(axis),
        num=pad_amt,
        endpoint=False,
        dtype=arr.dtype,
        axis=axis
    )

    return _do_prepend(arr, ramp_arr, axis)


def _append_ramp(arr, pad_amt, end, axis=-1):
    """
    Append linear ramp along `axis`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to append.
    end : scalar
        Constal value to use. For best results should be of type `arr.dtype`;
        if not `arr.dtype` will be cast to `arr.dtype`.
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` values appended along `axis`. The
        appended region ramps linearly from the edge value to `end`.

    """
    if pad_amt == 0:
        return arr

    # Slice a chunk from the edge to calculate stats on and extract edge
    edge_slice = _slice_last(arr.shape, 1, axis=axis)
    edge = arr[edge_slice]

    ramp_arr = np.linspace(
        start=end,
        stop=edge.squeeze(axis),
        num=pad_amt,
        endpoint=False,
        dtype=arr.dtype,
        axis=axis
    )
    # Reverse linear space in appropriate dimension
    ramp_arr = ramp_arr[
        _slice_at_axis(ramp_arr.shape, slice(None, None, -1), axis)
    ]

    return _do_append(arr, ramp_arr, axis)


def _prepend_max(arr, pad_amt, num, axis=-1):
    """
    Prepend `pad_amt` maximum values along `axis`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to prepend.
    num : int
        Depth into `arr` along `axis` to calculate maximum.
        Range: [1, `arr.shape[axis]`] or None (entire axis)
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` values appended along `axis`. The
        prepended region is the maximum of the first `num` values along
        `axis`.

    """
    if pad_amt == 0:
        return arr

    # Equivalent to edge padding for single value, so do that instead
    if num == 1:
        return _prepend_edge(arr, pad_amt, axis)

    # Use entire array if `num` is too large
    if num is not None:
        if num >= arr.shape[axis]:
            num = None

    # Slice a chunk from the edge to calculate stats on
    max_slice = _slice_first(arr.shape, num, axis=axis)

    # Extract slice, calculate max
    max_chunk = arr[max_slice].max(axis=axis, keepdims=True)

    # Concatenate `arr` with `max_chunk`, extended along `axis` by `pad_amt`
    return _do_prepend(arr, max_chunk.repeat(pad_amt, axis=axis), axis)


def _append_max(arr, pad_amt, num, axis=-1):
    """
    Pad one `axis` of `arr` with the maximum of the last `num` elements.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to append.
    num : int
        Depth into `arr` along `axis` to calculate maximum.
        Range: [1, `arr.shape[axis]`] or None (entire axis)
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` values appended along `axis`. The
        appended region is the maximum of the final `num` values along `axis`.

    """
    if pad_amt == 0:
        return arr

    # Equivalent to edge padding for single value, so do that instead
    if num == 1:
        return _append_edge(arr, pad_amt, axis)

    # Use entire array if `num` is too large
    if num is not None:
        if num >= arr.shape[axis]:
            num = None

    # Slice a chunk from the edge to calculate stats on
    if num is not None:
        max_slice = _slice_last(arr.shape, num, axis=axis)
    else:
        max_slice = tuple(slice(None) for x in arr.shape)

    # Extract slice, calculate max
    max_chunk = arr[max_slice].max(axis=axis, keepdims=True)

    # Concatenate `arr` with `max_chunk`, extended along `axis` by `pad_amt`
    return _do_append(arr, max_chunk.repeat(pad_amt, axis=axis), axis)


def _prepend_mean(arr, pad_amt, num, axis=-1):
    """
    Prepend `pad_amt` mean values along `axis`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to prepend.
    num : int
        Depth into `arr` along `axis` to calculate mean.
        Range: [1, `arr.shape[axis]`] or None (entire axis)
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` values prepended along `axis`. The
        prepended region is the mean of the first `num` values along `axis`.

    """
    if pad_amt == 0:
        return arr

    # Equivalent to edge padding for single value, so do that instead
    if num == 1:
        return _prepend_edge(arr, pad_amt, axis)

    # Use entire array if `num` is too large
    if num is not None:
        if num >= arr.shape[axis]:
            num = None

    # Slice a chunk from the edge to calculate stats on
    mean_slice = _slice_first(arr.shape, num, axis=axis)

    # Extract slice, calculate mean
    mean_chunk = arr[mean_slice].mean(axis, keepdims=True)
    _round_ifneeded(mean_chunk, arr.dtype)

    # Concatenate `arr` with `mean_chunk`, extended along `axis` by `pad_amt`
    return _do_prepend(arr, mean_chunk.repeat(pad_amt, axis), axis=axis)


def _append_mean(arr, pad_amt, num, axis=-1):
    """
    Append `pad_amt` mean values along `axis`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to append.
    num : int
        Depth into `arr` along `axis` to calculate mean.
        Range: [1, `arr.shape[axis]`] or None (entire axis)
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` values appended along `axis`. The
        appended region is the maximum of the final `num` values along `axis`.

    """
    if pad_amt == 0:
        return arr

    # Equivalent to edge padding for single value, so do that instead
    if num == 1:
        return _append_edge(arr, pad_amt, axis)

    # Use entire array if `num` is too large
    if num is not None:
        if num >= arr.shape[axis]:
            num = None

    # Slice a chunk from the edge to calculate stats on
    if num is not None:
        mean_slice = _slice_last(arr.shape, num, axis=axis)
    else:
        mean_slice = tuple(slice(None) for x in arr.shape)

    # Extract slice, calculate mean
    mean_chunk = arr[mean_slice].mean(axis=axis, keepdims=True)
    _round_ifneeded(mean_chunk, arr.dtype)

    # Concatenate `arr` with `mean_chunk`, extended along `axis` by `pad_amt`
    return _do_append(arr, mean_chunk.repeat(pad_amt, axis), axis=axis)


def _prepend_med(arr, pad_amt, num, axis=-1):
    """
    Prepend `pad_amt` median values along `axis`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to prepend.
    num : int
        Depth into `arr` along `axis` to calculate median.
        Range: [1, `arr.shape[axis]`] or None (entire axis)
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` values prepended along `axis`. The
        prepended region is the median of the first `num` values along `axis`.

    """
    if pad_amt == 0:
        return arr

    # Equivalent to edge padding for single value, so do that instead
    if num == 1:
        return _prepend_edge(arr, pad_amt, axis)

    # Use entire array if `num` is too large
    if num is not None:
        if num >= arr.shape[axis]:
            num = None

    # Slice a chunk from the edge to calculate stats on
    med_slice = _slice_first(arr.shape, num, axis=axis)

    # Extract slice, calculate median
    med_chunk = np.median(arr[med_slice], axis=axis, keepdims=True)
    _round_ifneeded(med_chunk, arr.dtype)

    # Concatenate `arr` with `med_chunk`, extended along `axis` by `pad_amt`
    return _do_prepend(arr, med_chunk.repeat(pad_amt, axis), axis=axis)


def _append_med(arr, pad_amt, num, axis=-1):
    """
    Append `pad_amt` median values along `axis`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to append.
    num : int
        Depth into `arr` along `axis` to calculate median.
        Range: [1, `arr.shape[axis]`] or None (entire axis)
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` values appended along `axis`. The
        appended region is the median of the final `num` values along `axis`.

    """
    if pad_amt == 0:
        return arr

    # Equivalent to edge padding for single value, so do that instead
    if num == 1:
        return _append_edge(arr, pad_amt, axis)

    # Use entire array if `num` is too large
    if num is not None:
        if num >= arr.shape[axis]:
            num = None

    # Slice a chunk from the edge to calculate stats on
    if num is not None:
        med_slice = _slice_last(arr.shape, num, axis=axis)
    else:
        med_slice = tuple(slice(None) for x in arr.shape)

    # Extract slice, calculate median
    med_chunk = np.median(arr[med_slice], axis=axis, keepdims=True)
    _round_ifneeded(med_chunk, arr.dtype)

    # Concatenate `arr` with `med_chunk`, extended along `axis` by `pad_amt`
    return _do_append(arr, med_chunk.repeat(pad_amt, axis), axis=axis)


def _prepend_min(arr, pad_amt, num, axis=-1):
    """
    Prepend `pad_amt` minimum values along `axis`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to prepend.
    num : int
        Depth into `arr` along `axis` to calculate minimum.
        Range: [1, `arr.shape[axis]`] or None (entire axis)
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` values prepended along `axis`. The
        prepended region is the minimum of the first `num` values along
        `axis`.

    """
    if pad_amt == 0:
        return arr

    # Equivalent to edge padding for single value, so do that instead
    if num == 1:
        return _prepend_edge(arr, pad_amt, axis)

    # Use entire array if `num` is too large
    if num is not None:
        if num >= arr.shape[axis]:
            num = None

    # Slice a chunk from the edge to calculate stats on
    min_slice = _slice_first(arr.shape, num, axis=axis)

    # Extract slice, calculate min
    min_chunk = arr[min_slice].min(axis=axis, keepdims=True)

    # Concatenate `arr` with `min_chunk`, extended along `axis` by `pad_amt`
    return _do_prepend(arr, min_chunk.repeat(pad_amt, axis), axis=axis)


def _append_min(arr, pad_amt, num, axis=-1):
    """
    Append `pad_amt` median values along `axis`.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : int
        Amount of padding to append.
    num : int
        Depth into `arr` along `axis` to calculate minimum.
        Range: [1, `arr.shape[axis]`] or None (entire axis)
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt` values appended along `axis`. The
        appended region is the minimum of the final `num` values along `axis`.

    """
    if pad_amt == 0:
        return arr

    # Equivalent to edge padding for single value, so do that instead
    if num == 1:
        return _append_edge(arr, pad_amt, axis)

    # Use entire array if `num` is too large
    if num is not None:
        if num >= arr.shape[axis]:
            num = None

    # Slice a chunk from the edge to calculate stats on
    if num is not None:
        min_slice = _slice_last(arr.shape, num, axis=axis)
    else:
        min_slice = tuple(slice(None) for x in arr.shape)

    # Extract slice, calculate min
    min_chunk = arr[min_slice].min(axis=axis, keepdims=True)

    # Concatenate `arr` with `min_chunk`, extended along `axis` by `pad_amt`
    return _do_append(arr, min_chunk.repeat(pad_amt, axis), axis=axis)


def _pad_ref(arr, pad_amt, method, axis=-1):
    """
    Pad `axis` of `arr` by reflection.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : tuple of ints, length 2
        Padding to (prepend, append) along `axis`.
    method : str
        Controls method of reflection; options are 'even' or 'odd'.
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt[0]` values prepended and `pad_amt[1]`
        values appended along `axis`. Both regions are padded with reflected
        values from the original array.

    Notes
    -----
    This algorithm does not pad with repetition, i.e. the edges are not
    repeated in the reflection. For that behavior, use `mode='symmetric'`.

    The modes 'reflect', 'symmetric', and 'wrap' must be padded with a
    single function, lest the indexing tricks in non-integer multiples of the
    original shape would violate repetition in the final iteration.

    """
    # Implicit booleanness to test for zero (or None) in any scalar type
    if pad_amt[0] == 0 and pad_amt[1] == 0:
        return arr

    ##########################################################################
    # Prepended region

    # Slice off a reverse indexed chunk from near edge to pad `arr` before
    ref_slice = _slice_at_axis(arr.shape, slice(pad_amt[0], 0, -1), axis=axis)

    ref_chunk1 = arr[ref_slice]

    # Memory/computationally more expensive, only do this if `method='odd'`
    if 'odd' in method and pad_amt[0] > 0:
        edge_slice1 = _slice_first(arr.shape, 1, axis=axis)
        edge_chunk = arr[edge_slice1]
        ref_chunk1 = 2 * edge_chunk - ref_chunk1
        del edge_chunk

    ##########################################################################
    # Appended region

    # Slice off a reverse indexed chunk from far edge to pad `arr` after
    start = arr.shape[axis] - pad_amt[1] - 1
    end = arr.shape[axis] - 1
    ref_slice = _slice_at_axis(arr.shape, slice(start, end), axis=axis)
    rev_idx = _slice_at_axis(arr.shape, slice(None, None, -1), axis=axis)
    ref_chunk2 = arr[ref_slice][rev_idx]

    if 'odd' in method:
        edge_slice2 = _slice_last(arr.shape, 1, axis=axis)
        edge_chunk = arr[edge_slice2]
        ref_chunk2 = 2 * edge_chunk - ref_chunk2
        del edge_chunk

    # Concatenate `arr` with both chunks, extending along `axis`
    return np.concatenate((ref_chunk1, arr, ref_chunk2), axis=axis)


def _pad_sym(arr, pad_amt, method, axis=-1):
    """
    Pad `axis` of `arr` by symmetry.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : tuple of ints, length 2
        Padding to (prepend, append) along `axis`.
    method : str
        Controls method of symmetry; options are 'even' or 'odd'.
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt[0]` values prepended and `pad_amt[1]`
        values appended along `axis`. Both regions are padded with symmetric
        values from the original array.

    Notes
    -----
    This algorithm DOES pad with repetition, i.e. the edges are repeated.
    For padding without repeated edges, use `mode='reflect'`.

    The modes 'reflect', 'symmetric', and 'wrap' must be padded with a
    single function, lest the indexing tricks in non-integer multiples of the
    original shape would violate repetition in the final iteration.

    """
    # Implicit booleanness to test for zero (or None) in any scalar type
    if pad_amt[0] == 0 and pad_amt[1] == 0:
        return arr

    ##########################################################################
    # Prepended region

    # Slice off a reverse indexed chunk from near edge to pad `arr` before
    sym_slice = _slice_first(arr.shape, pad_amt[0], axis=axis)
    rev_idx = _slice_at_axis(arr.shape, slice(None, None, -1), axis=axis)
    sym_chunk1 = arr[sym_slice][rev_idx]

    # Memory/computationally more expensive, only do this if `method='odd'`
    if 'odd' in method and pad_amt[0] > 0:
        edge_slice1 = _slice_first(arr.shape, 1, axis=axis)
        edge_chunk = arr[edge_slice1]
        sym_chunk1 = 2 * edge_chunk - sym_chunk1
        del edge_chunk

    ##########################################################################
    # Appended region

    # Slice off a reverse indexed chunk from far edge to pad `arr` after
    sym_slice = _slice_last(arr.shape, pad_amt[1], axis=axis)
    sym_chunk2 = arr[sym_slice][rev_idx]

    if 'odd' in method:
        edge_slice2 = _slice_last(arr.shape, 1, axis=axis)
        edge_chunk = arr[edge_slice2]
        sym_chunk2 = 2 * edge_chunk - sym_chunk2
        del edge_chunk

    # Concatenate `arr` with both chunks, extending along `axis`
    return np.concatenate((sym_chunk1, arr, sym_chunk2), axis=axis)


def _pad_wrap(arr, pad_amt, axis=-1):
    """
    Pad `axis` of `arr` via wrapping.

    Parameters
    ----------
    arr : ndarray
        Input array of arbitrary shape.
    pad_amt : tuple of ints, length 2
        Padding to (prepend, append) along `axis`.
    axis : int
        Axis along which to pad `arr`.

    Returns
    -------
    padarr : ndarray
        Output array, with `pad_amt[0]` values prepended and `pad_amt[1]`
        values appended along `axis`. Both regions are padded wrapped values
        from the opposite end of `axis`.

    Notes
    -----
    This method of padding is also known as 'tile' or 'tiling'.

    The modes 'reflect', 'symmetric', and 'wrap' must be padded with a
    single function, lest the indexing tricks in non-integer multiples of the
    original shape would violate repetition in the final iteration.

    """
    # Implicit booleanness to test for zero (or None) in any scalar type
    if pad_amt[0] == 0 and pad_amt[1] == 0:
        return arr

    ##########################################################################
    # Prepended region

    # Slice off a reverse indexed chunk from near edge to pad `arr` before
    wrap_slice = _slice_last(arr.shape, pad_amt[0], axis=axis)
    wrap_chunk1 = arr[wrap_slice]

    ##########################################################################
    # Appended region

    # Slice off a reverse indexed chunk from far edge to pad `arr` after
    wrap_slice = _slice_first(arr.shape, pad_amt[1], axis=axis)
    wrap_chunk2 = arr[wrap_slice]

    # Concatenate `arr` with both chunks, extending along `axis`
    return np.concatenate((wrap_chunk1, arr, wrap_chunk2), axis=axis)


def _as_pairs(x, ndim, as_index=False):
    """
    Broadcast `x` to an array with the shape (`ndim`, 2).

    A helper function for `pad` that prepares and validates arguments like
    `pad_width` for iteration in pairs.

    Parameters
    ----------
    x : {None, scalar, array-like}
        The object to broadcast to the shape (`ndim`, 2).
    ndim : int
        Number of pairs the broadcasted `x` will have.
    as_index : bool, optional
        If `x` is not None, try to round each element of `x` to an integer
        (dtype `np.intp`) and ensure every element is positive.

    Returns
    -------
    pairs : nested iterables, shape (`ndim`, 2)
        The broadcasted version of `x`.

    Raises
    ------
    ValueError
        If `as_index` is True and `x` contains negative elements.
        Or if `x` is not broadcastable to the shape (`ndim`, 2).
    """
    if x is None:
        # Pass through None as a special case, otherwise np.round(x) fails
        # with an AttributeError
        return ((None, None),) * ndim

    x = np.array(x)
    if as_index:
        x = np.round(x).astype(np.intp, copy=False)

    if x.ndim < 3:
        # Optimization: Possibly use faster paths for cases where `x` has
        # only 1 or 2 elements. `np.broadcast_to` could handle these as well
        # but is currently slower

        if x.size == 1:
            # x was supplied as a single value
            x = x.ravel()  # Ensure x[0] works for x.ndim == 0, 1, 2
            if as_index and x < 0:
                raise ValueError("index can't contain negative values")
            return ((x[0], x[0]),) * ndim

        if x.size == 2 and x.shape != (2, 1):
            # x was supplied with a single value for each side
            # but except case when each dimension has a single value
            # which should be broadcasted to a pair,
            # e.g. [[1], [2]] -> [[1, 1], [2, 2]] not [[1, 2], [1, 2]]
            x = x.ravel()  # Ensure x[0], x[1] works
            if as_index and (x[0] < 0 or x[1] < 0):
                raise ValueError("index can't contain negative values")
            return ((x[0], x[1]),) * ndim

    if as_index and x.min() < 0:
        raise ValueError("index can't contain negative values")

    # Converting the array with `tolist` seems to improve performance
    # when iterating and indexing the result (see usage in `pad`)
    return np.broadcast_to(x, (ndim, 2)).tolist()


###############################################################################
# Public functions


def _pad_dispatcher(array, pad_width, mode, **kwargs):
    return (array,)


@array_function_dispatch(_pad_dispatcher, module='numpy')
def pad(array, pad_width, mode, **kwargs):
    """
    Pads an array.

    Parameters
    ----------
    array : array_like of rank N
        Input array
    pad_width : {sequence, array_like, int}
        Number of values padded to the edges of each axis.
        ((before_1, after_1), ... (before_N, after_N)) unique pad widths
        for each axis.
        ((before, after),) yields same before and after pad for each axis.
        (pad,) or int is a shortcut for before = after = pad width for all
        axes.
    mode : str or function
        One of the following string values or a user supplied function.

        'constant'
            Pads with a constant value.
        'edge'
            Pads with the edge values of array.
        'linear_ramp'
            Pads with the linear ramp between end_value and the
            array edge value.
        'maximum'
            Pads with the maximum value of all or part of the
            vector along each axis.
        'mean'
            Pads with the mean value of all or part of the
            vector along each axis.
        'median'
            Pads with the median value of all or part of the
            vector along each axis.
        'minimum'
            Pads with the minimum value of all or part of the
            vector along each axis.
        'reflect'
            Pads with the reflection of the vector mirrored on
            the first and last values of the vector along each
            axis.
        'symmetric'
            Pads with the reflection of the vector mirrored
            along the edge of the array.
        'wrap'
            Pads with the wrap of the vector along the axis.
            The first values are used to pad the end and the
            end values are used to pad the beginning.
        <function>
            Padding function, see Notes.
    stat_length : sequence or int, optional
        Used in 'maximum', 'mean', 'median', and 'minimum'.  Number of
        values at edge of each axis used to calculate the statistic value.

        ((before_1, after_1), ... (before_N, after_N)) unique statistic
        lengths for each axis.

        ((before, after),) yields same before and after statistic lengths
        for each axis.

        (stat_length,) or int is a shortcut for before = after = statistic
        length for all axes.

        Default is ``None``, to use the entire axis.
    constant_values : sequence or int, optional
        Used in 'constant'.  The values to set the padded values for each
        axis.

        ((before_1, after_1), ... (before_N, after_N)) unique pad constants
        for each axis.

        ((before, after),) yields same before and after constants for each
        axis.

        (constant,) or int is a shortcut for before = after = constant for
        all axes.

        Default is 0.
    end_values : sequence or int, optional
        Used in 'linear_ramp'.  The values used for the ending value of the
        linear_ramp and that will form the edge of the padded array.

        ((before_1, after_1), ... (before_N, after_N)) unique end values
        for each axis.

        ((before, after),) yields same before and after end values for each
        axis.

        (constant,) or int is a shortcut for before = after = end value for
        all axes.

        Default is 0.
    reflect_type : {'even', 'odd'}, optional
        Used in 'reflect', and 'symmetric'.  The 'even' style is the
        default with an unaltered reflection around the edge value.  For
        the 'odd' style, the extended part of the array is created by
        subtracting the reflected values from two times the edge value.

    Returns
    -------
    pad : ndarray
        Padded array of rank equal to `array` with shape increased
        according to `pad_width`.

    Notes
    -----
    .. versionadded:: 1.7.0

    For an array with rank greater than 1, some of the padding of later
    axes is calculated from padding of previous axes.  This is easiest to
    think about with a rank 2 array where the corners of the padded array
    are calculated by using padded values from the first axis.

    The padding function, if used, should return a rank 1 array equal in
    length to the vector argument with padded values replaced. It has the
    following signature::

        padding_func(vector, iaxis_pad_width, iaxis, kwargs)

    where

        vector : ndarray
            A rank 1 array already padded with zeros.  Padded values are
            vector[:pad_tuple[0]] and vector[-pad_tuple[1]:].
        iaxis_pad_width : tuple
            A 2-tuple of ints, iaxis_pad_width[0] represents the number of
            values padded at the beginning of vector where
            iaxis_pad_width[1] represents the number of values padded at
            the end of vector.
        iaxis : int
            The axis currently being calculated.
        kwargs : dict
            Any keyword arguments the function requires.

    Examples
    --------
    >>> a = [1, 2, 3, 4, 5]
    >>> np.pad(a, (2,3), 'constant', constant_values=(4, 6))
    array([4, 4, 1, 2, 3, 4, 5, 6, 6, 6])

    >>> np.pad(a, (2, 3), 'edge')
    array([1, 1, 1, 2, 3, 4, 5, 5, 5, 5])

    >>> np.pad(a, (2, 3), 'linear_ramp', end_values=(5, -4))
    array([ 5,  3,  1,  2,  3,  4,  5,  2, -1, -4])

    >>> np.pad(a, (2,), 'maximum')
    array([5, 5, 1, 2, 3, 4, 5, 5, 5])

    >>> np.pad(a, (2,), 'mean')
    array([3, 3, 1, 2, 3, 4, 5, 3, 3])

    >>> np.pad(a, (2,), 'median')
    array([3, 3, 1, 2, 3, 4, 5, 3, 3])

    >>> a = [[1, 2], [3, 4]]
    >>> np.pad(a, ((3, 2), (2, 3)), 'minimum')
    array([[1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1],
           [3, 3, 3, 4, 3, 3, 3],
           [1, 1, 1, 2, 1, 1, 1],
           [1, 1, 1, 2, 1, 1, 1]])

    >>> a = [1, 2, 3, 4, 5]
    >>> np.pad(a, (2, 3), 'reflect')
    array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2])

    >>> np.pad(a, (2, 3), 'reflect', reflect_type='odd')
    array([-1,  0,  1,  2,  3,  4,  5,  6,  7,  8])

    >>> np.pad(a, (2, 3), 'symmetric')
    array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3])

    >>> np.pad(a, (2, 3), 'symmetric', reflect_type='odd')
    array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7])

    >>> np.pad(a, (2, 3), 'wrap')
    array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3])

    >>> def pad_with(vector, pad_width, iaxis, kwargs):
    ...     pad_value = kwargs.get('padder', 10)
    ...     vector[:pad_width[0]] = pad_value
    ...     vector[-pad_width[1]:] = pad_value
    ...     return vector
    >>> a = np.arange(6)
    >>> a = a.reshape((2, 3))
    >>> np.pad(a, 2, pad_with)
    array([[10, 10, 10, 10, 10, 10, 10],
           [10, 10, 10, 10, 10, 10, 10],
           [10, 10,  0,  1,  2, 10, 10],
           [10, 10,  3,  4,  5, 10, 10],
           [10, 10, 10, 10, 10, 10, 10],
           [10, 10, 10, 10, 10, 10, 10]])
    >>> np.pad(a, 2, pad_with, padder=100)
    array([[100, 100, 100, 100, 100, 100, 100],
           [100, 100, 100, 100, 100, 100, 100],
           [100, 100,   0,   1,   2, 100, 100],
           [100, 100,   3,   4,   5, 100, 100],
           [100, 100, 100, 100, 100, 100, 100],
           [100, 100, 100, 100, 100, 100, 100]])
    """
    if not np.asarray(pad_width).dtype.kind == 'i':
        raise TypeError('`pad_width` must be of integral type.')

    narray = np.array(array)
    pad_width = _as_pairs(pad_width, narray.ndim, as_index=True)

    allowedkwargs = {
        'constant': ['constant_values'],
        'edge': [],
        'linear_ramp': ['end_values'],
        'maximum': ['stat_length'],
        'mean': ['stat_length'],
        'median': ['stat_length'],
        'minimum': ['stat_length'],
        'reflect': ['reflect_type'],
        'symmetric': ['reflect_type'],
        'wrap': [],
        }

    kwdefaults = {
        'stat_length': None,
        'constant_values': 0,
        'end_values': 0,
        'reflect_type': 'even',
        }

    if isinstance(mode, np.compat.basestring):
        # Make sure have allowed kwargs appropriate for mode
        for key in kwargs:
            if key not in allowedkwargs[mode]:
                raise ValueError('%s keyword not in allowed keywords %s' %
                                 (key, allowedkwargs[mode]))

        # Set kwarg defaults
        for kw in allowedkwargs[mode]:
            kwargs.setdefault(kw, kwdefaults[kw])

        # Need to only normalize particular keywords.
        for i in kwargs:
            if i == 'stat_length':
                kwargs[i] = _as_pairs(kwargs[i], narray.ndim, as_index=True)
            if i in ['end_values', 'constant_values']:
                kwargs[i] = _as_pairs(kwargs[i], narray.ndim)
    else:
        # Drop back to old, slower np.apply_along_axis mode for user-supplied
        # vector function
        function = mode

        # Create a new padded array
        rank = list(range(narray.ndim))
        total_dim_increase = [np.sum(pad_width[i]) for i in rank]
        offset_slices = tuple(
            slice(pad_width[i][0], pad_width[i][0] + narray.shape[i])
            for i in rank)
        new_shape = np.array(narray.shape) + total_dim_increase
        newmat = np.zeros(new_shape, narray.dtype)

        # Insert the original array into the padded array
        newmat[offset_slices] = narray

        # This is the core of pad ...
        for iaxis in rank:
            np.apply_along_axis(function,
                                iaxis,
                                newmat,
                                pad_width[iaxis],
                                iaxis,
                                kwargs)
        return newmat

    # If we get here, use new padding method
    newmat = narray.copy()

    # API preserved, but completely new algorithm which pads by building the
    # entire block to pad before/after `arr` with in one step, for each axis.
    if mode == 'constant':
        for axis, ((pad_before, pad_after), (before_val, after_val)) \
                in enumerate(zip(pad_width, kwargs['constant_values'])):
            newmat = _prepend_const(newmat, pad_before, before_val, axis)
            newmat = _append_const(newmat, pad_after, after_val, axis)

    elif mode == 'edge':
        for axis, (pad_before, pad_after) in enumerate(pad_width):
            newmat = _prepend_edge(newmat, pad_before, axis)
            newmat = _append_edge(newmat, pad_after, axis)

    elif mode == 'linear_ramp':
        for axis, ((pad_before, pad_after), (before_val, after_val)) \
                in enumerate(zip(pad_width, kwargs['end_values'])):
            newmat = _prepend_ramp(newmat, pad_before, before_val, axis)
            newmat = _append_ramp(newmat, pad_after, after_val, axis)

    elif mode == 'maximum':
        for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \
                in enumerate(zip(pad_width, kwargs['stat_length'])):
            newmat = _prepend_max(newmat, pad_before, chunk_before, axis)
            newmat = _append_max(newmat, pad_after, chunk_after, axis)

    elif mode == 'mean':
        for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \
                in enumerate(zip(pad_width, kwargs['stat_length'])):
            newmat = _prepend_mean(newmat, pad_before, chunk_before, axis)
            newmat = _append_mean(newmat, pad_after, chunk_after, axis)

    elif mode == 'median':
        for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \
                in enumerate(zip(pad_width, kwargs['stat_length'])):
            newmat = _prepend_med(newmat, pad_before, chunk_before, axis)
            newmat = _append_med(newmat, pad_after, chunk_after, axis)

    elif mode == 'minimum':
        for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \
                in enumerate(zip(pad_width, kwargs['stat_length'])):
            newmat = _prepend_min(newmat, pad_before, chunk_before, axis)
            newmat = _append_min(newmat, pad_after, chunk_after, axis)

    elif mode == 'reflect':
        for axis, (pad_before, pad_after) in enumerate(pad_width):
            if narray.shape[axis] == 0:
                # Axes with non-zero padding cannot be empty.
                if pad_before > 0 or pad_after > 0:
                    raise ValueError("There aren't any elements to reflect"
                                     " in axis {} of `array`".format(axis))
                # Skip zero padding on empty axes.
                continue

            # Recursive padding along any axis where `pad_amt` is too large
            # for indexing tricks. We can only safely pad the original axis
            # length, to keep the period of the reflections consistent.
            if ((pad_before > 0) or
                    (pad_after > 0)) and newmat.shape[axis] == 1:
                # Extending singleton dimension for 'reflect' is legacy
                # behavior; it really should raise an error.
                newmat = _prepend_edge(newmat, pad_before, axis)
                newmat = _append_edge(newmat, pad_after, axis)
                continue

            method = kwargs['reflect_type']
            safe_pad = newmat.shape[axis] - 1
            while ((pad_before > safe_pad) or (pad_after > safe_pad)):
                pad_iter_b = min(safe_pad,
                                 safe_pad * (pad_before // safe_pad))
                pad_iter_a = min(safe_pad, safe_pad * (pad_after // safe_pad))
                newmat = _pad_ref(newmat, (pad_iter_b,
                                           pad_iter_a), method, axis)
                pad_before -= pad_iter_b
                pad_after -= pad_iter_a
                safe_pad += pad_iter_b + pad_iter_a
            newmat = _pad_ref(newmat, (pad_before, pad_after), method, axis)

    elif mode == 'symmetric':
        for axis, (pad_before, pad_after) in enumerate(pad_width):
            # Recursive padding along any axis where `pad_amt` is too large
            # for indexing tricks. We can only safely pad the original axis
            # length, to keep the period of the reflections consistent.
            method = kwargs['reflect_type']
            safe_pad = newmat.shape[axis]
            while ((pad_before > safe_pad) or
                   (pad_after > safe_pad)):
                pad_iter_b = min(safe_pad,
                                 safe_pad * (pad_before // safe_pad))
                pad_iter_a = min(safe_pad, safe_pad * (pad_after // safe_pad))
                newmat = _pad_sym(newmat, (pad_iter_b,
                                           pad_iter_a), method, axis)
                pad_before -= pad_iter_b
                pad_after -= pad_iter_a
                safe_pad += pad_iter_b + pad_iter_a
            newmat = _pad_sym(newmat, (pad_before, pad_after), method, axis)

    elif mode == 'wrap':
        for axis, (pad_before, pad_after) in enumerate(pad_width):
            # Recursive padding along any axis where `pad_amt` is too large
            # for indexing tricks. We can only safely pad the original axis
            # length, to keep the period of the reflections consistent.
            safe_pad = newmat.shape[axis]
            while ((pad_before > safe_pad) or
                   (pad_after > safe_pad)):
                pad_iter_b = min(safe_pad,
                                 safe_pad * (pad_before // safe_pad))
                pad_iter_a = min(safe_pad, safe_pad * (pad_after // safe_pad))
                newmat = _pad_wrap(newmat, (pad_iter_b, pad_iter_a), axis)

                pad_before -= pad_iter_b
                pad_after -= pad_iter_a
                safe_pad += pad_iter_b + pad_iter_a
            newmat = _pad_wrap(newmat, (pad_before, pad_after), axis)

    return newmat