882 lines
31 KiB
Python
882 lines
31 KiB
Python
|
"""
|
||
|
|
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
|
||
|
|
from numpy.lib.index_tricks import ndindex
|
||
|
|
|
||
|
|
|
||
|
|
__all__ = ['pad']
|
||
|
|
|
||
|
|
|
||
|
|
###############################################################################
|
||
|
|
# Private utility functions.
|
||
|
|
|
||
|
|
|
||
|
|
def _round_if_needed(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(sl, axis):
|
||
|
|
"""
|
||
|
|
Construct tuple of slices to slice an array in the given dimension.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
sl : slice
|
||
|
|
The slice for the given dimension.
|
||
|
|
axis : int
|
||
|
|
The axis to which `sl` is applied. All other dimensions are left
|
||
|
|
"unsliced".
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
sl : tuple of slices
|
||
|
|
A tuple with slices matching `shape` in length.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> _slice_at_axis(slice(None, 3, -1), 1)
|
||
|
|
(slice(None, None, None), slice(None, 3, -1), (...,))
|
||
|
|
"""
|
||
|
|
return (slice(None),) * axis + (sl,) + (...,)
|
||
|
|
|
||
|
|
|
||
|
|
def _view_roi(array, original_area_slice, axis):
|
||
|
|
"""
|
||
|
|
Get a view of the current region of interest during iterative padding.
|
||
|
|
|
||
|
|
When padding multiple dimensions iteratively corner values are
|
||
|
|
unnecessarily overwritten multiple times. This function reduces the
|
||
|
|
working area for the first dimensions so that corners are excluded.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
array : ndarray
|
||
|
|
The array with the region of interest.
|
||
|
|
original_area_slice : tuple of slices
|
||
|
|
Denotes the area with original values of the unpadded array.
|
||
|
|
axis : int
|
||
|
|
The currently padded dimension assuming that `axis` is padded before
|
||
|
|
`axis` + 1.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
roi : ndarray
|
||
|
|
The region of interest of the original `array`.
|
||
|
|
"""
|
||
|
|
axis += 1
|
||
|
|
sl = (slice(None),) * axis + original_area_slice[axis:]
|
||
|
|
return array[sl]
|
||
|
|
|
||
|
|
|
||
|
|
def _pad_simple(array, pad_width, fill_value=None):
|
||
|
|
"""
|
||
|
|
Pad array on all sides with either a single value or undefined values.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
array : ndarray
|
||
|
|
Array to grow.
|
||
|
|
pad_width : sequence of tuple[int, int]
|
||
|
|
Pad width on both sides for each dimension in `arr`.
|
||
|
|
fill_value : scalar, optional
|
||
|
|
If provided the padded area is filled with this value, otherwise
|
||
|
|
the pad area left undefined.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
padded : ndarray
|
||
|
|
The padded array with the same dtype as`array`. Its order will default
|
||
|
|
to C-style if `array` is not F-contiguous.
|
||
|
|
original_area_slice : tuple
|
||
|
|
A tuple of slices pointing to the area of the original array.
|
||
|
|
"""
|
||
|
|
# Allocate grown array
|
||
|
|
new_shape = tuple(
|
||
|
|
left + size + right
|
||
|
|
for size, (left, right) in zip(array.shape, pad_width)
|
||
|
|
)
|
||
|
|
order = 'F' if array.flags.fnc else 'C' # Fortran and not also C-order
|
||
|
|
padded = np.empty(new_shape, dtype=array.dtype, order=order)
|
||
|
|
|
||
|
|
if fill_value is not None:
|
||
|
|
padded.fill(fill_value)
|
||
|
|
|
||
|
|
# Copy old array into correct space
|
||
|
|
original_area_slice = tuple(
|
||
|
|
slice(left, left + size)
|
||
|
|
for size, (left, right) in zip(array.shape, pad_width)
|
||
|
|
)
|
||
|
|
padded[original_area_slice] = array
|
||
|
|
|
||
|
|
return padded, original_area_slice
|
||
|
|
|
||
|
|
|
||
|
|
def _set_pad_area(padded, axis, width_pair, value_pair):
|
||
|
|
"""
|
||
|
|
Set empty-padded area in given dimension.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
padded : ndarray
|
||
|
|
Array with the pad area which is modified inplace.
|
||
|
|
axis : int
|
||
|
|
Dimension with the pad area to set.
|
||
|
|
width_pair : (int, int)
|
||
|
|
Pair of widths that mark the pad area on both sides in the given
|
||
|
|
dimension.
|
||
|
|
value_pair : tuple of scalars or ndarrays
|
||
|
|
Values inserted into the pad area on each side. It must match or be
|
||
|
|
broadcastable to the shape of `arr`.
|
||
|
|
"""
|
||
|
|
left_slice = _slice_at_axis(slice(None, width_pair[0]), axis)
|
||
|
|
padded[left_slice] = value_pair[0]
|
||
|
|
|
||
|
|
right_slice = _slice_at_axis(
|
||
|
|
slice(padded.shape[axis] - width_pair[1], None), axis)
|
||
|
|
padded[right_slice] = value_pair[1]
|
||
|
|
|
||
|
|
|
||
|
|
def _get_edges(padded, axis, width_pair):
|
||
|
|
"""
|
||
|
|
Retrieve edge values from empty-padded array in given dimension.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
padded : ndarray
|
||
|
|
Empty-padded array.
|
||
|
|
axis : int
|
||
|
|
Dimension in which the edges are considered.
|
||
|
|
width_pair : (int, int)
|
||
|
|
Pair of widths that mark the pad area on both sides in the given
|
||
|
|
dimension.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
left_edge, right_edge : ndarray
|
||
|
|
Edge values of the valid area in `padded` in the given dimension. Its
|
||
|
|
shape will always match `padded` except for the dimension given by
|
||
|
|
`axis` which will have a length of 1.
|
||
|
|
"""
|
||
|
|
left_index = width_pair[0]
|
||
|
|
left_slice = _slice_at_axis(slice(left_index, left_index + 1), axis)
|
||
|
|
left_edge = padded[left_slice]
|
||
|
|
|
||
|
|
right_index = padded.shape[axis] - width_pair[1]
|
||
|
|
right_slice = _slice_at_axis(slice(right_index - 1, right_index), axis)
|
||
|
|
right_edge = padded[right_slice]
|
||
|
|
|
||
|
|
return left_edge, right_edge
|
||
|
|
|
||
|
|
|
||
|
|
def _get_linear_ramps(padded, axis, width_pair, end_value_pair):
|
||
|
|
"""
|
||
|
|
Construct linear ramps for empty-padded array in given dimension.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
padded : ndarray
|
||
|
|
Empty-padded array.
|
||
|
|
axis : int
|
||
|
|
Dimension in which the ramps are constructed.
|
||
|
|
width_pair : (int, int)
|
||
|
|
Pair of widths that mark the pad area on both sides in the given
|
||
|
|
dimension.
|
||
|
|
end_value_pair : (scalar, scalar)
|
||
|
|
End values for the linear ramps which form the edge of the fully padded
|
||
|
|
array. These values are included in the linear ramps.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
left_ramp, right_ramp : ndarray
|
||
|
|
Linear ramps to set on both sides of `padded`.
|
||
|
|
"""
|
||
|
|
edge_pair = _get_edges(padded, axis, width_pair)
|
||
|
|
|
||
|
|
left_ramp = np.linspace(
|
||
|
|
start=end_value_pair[0],
|
||
|
|
stop=edge_pair[0].squeeze(axis), # Dimensions is replaced by linspace
|
||
|
|
num=width_pair[0],
|
||
|
|
endpoint=False,
|
||
|
|
dtype=padded.dtype,
|
||
|
|
axis=axis,
|
||
|
|
)
|
||
|
|
|
||
|
|
right_ramp = np.linspace(
|
||
|
|
start=end_value_pair[1],
|
||
|
|
stop=edge_pair[1].squeeze(axis), # Dimension is replaced by linspace
|
||
|
|
num=width_pair[1],
|
||
|
|
endpoint=False,
|
||
|
|
dtype=padded.dtype,
|
||
|
|
axis=axis,
|
||
|
|
)
|
||
|
|
# Reverse linear space in appropriate dimension
|
||
|
|
right_ramp = right_ramp[_slice_at_axis(slice(None, None, -1), axis)]
|
||
|
|
|
||
|
|
return left_ramp, right_ramp
|
||
|
|
|
||
|
|
|
||
|
|
def _get_stats(padded, axis, width_pair, length_pair, stat_func):
|
||
|
|
"""
|
||
|
|
Calculate statistic for the empty-padded array in given dimnsion.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
padded : ndarray
|
||
|
|
Empty-padded array.
|
||
|
|
axis : int
|
||
|
|
Dimension in which the statistic is calculated.
|
||
|
|
width_pair : (int, int)
|
||
|
|
Pair of widths that mark the pad area on both sides in the given
|
||
|
|
dimension.
|
||
|
|
length_pair : 2-element sequence of None or int
|
||
|
|
Gives the number of values in valid area from each side that is
|
||
|
|
taken into account when calculating the statistic. If None the entire
|
||
|
|
valid area in `padded` is considered.
|
||
|
|
stat_func : function
|
||
|
|
Function to compute statistic. The expected signature is
|
||
|
|
``stat_func(x: ndarray, axis: int, keepdims: bool) -> ndarray``.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
left_stat, right_stat : ndarray
|
||
|
|
Calculated statistic for both sides of `padded`.
|
||
|
|
"""
|
||
|
|
# Calculate indices of the edges of the area with original values
|
||
|
|
left_index = width_pair[0]
|
||
|
|
right_index = padded.shape[axis] - width_pair[1]
|
||
|
|
# as well as its length
|
||
|
|
max_length = right_index - left_index
|
||
|
|
|
||
|
|
# Limit stat_lengths to max_length
|
||
|
|
left_length, right_length = length_pair
|
||
|
|
if left_length is None or max_length < left_length:
|
||
|
|
left_length = max_length
|
||
|
|
if right_length is None or max_length < right_length:
|
||
|
|
right_length = max_length
|
||
|
|
|
||
|
|
if (left_length == 0 or right_length == 0) \
|
||
|
|
and stat_func in {np.amax, np.amin}:
|
||
|
|
# amax and amin can't operate on an emtpy array,
|
||
|
|
# raise a more descriptive warning here instead of the default one
|
||
|
|
raise ValueError("stat_length of 0 yields no value for padding")
|
||
|
|
|
||
|
|
# Calculate statistic for the left side
|
||
|
|
left_slice = _slice_at_axis(
|
||
|
|
slice(left_index, left_index + left_length), axis)
|
||
|
|
left_chunk = padded[left_slice]
|
||
|
|
left_stat = stat_func(left_chunk, axis=axis, keepdims=True)
|
||
|
|
_round_if_needed(left_stat, padded.dtype)
|
||
|
|
|
||
|
|
if left_length == right_length == max_length:
|
||
|
|
# return early as right_stat must be identical to left_stat
|
||
|
|
return left_stat, left_stat
|
||
|
|
|
||
|
|
# Calculate statistic for the right side
|
||
|
|
right_slice = _slice_at_axis(
|
||
|
|
slice(right_index - right_length, right_index), axis)
|
||
|
|
right_chunk = padded[right_slice]
|
||
|
|
right_stat = stat_func(right_chunk, axis=axis, keepdims=True)
|
||
|
|
_round_if_needed(right_stat, padded.dtype)
|
||
|
|
|
||
|
|
return left_stat, right_stat
|
||
|
|
|
||
|
|
|
||
|
|
def _set_reflect_both(padded, axis, width_pair, method, include_edge=False):
|
||
|
|
"""
|
||
|
|
Pad `axis` of `arr` with reflection.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
padded : ndarray
|
||
|
|
Input array of arbitrary shape.
|
||
|
|
axis : int
|
||
|
|
Axis along which to pad `arr`.
|
||
|
|
width_pair : (int, int)
|
||
|
|
Pair of widths that mark the pad area on both sides in the given
|
||
|
|
dimension.
|
||
|
|
method : str
|
||
|
|
Controls method of reflection; options are 'even' or 'odd'.
|
||
|
|
include_edge : bool
|
||
|
|
If true, edge value is included in reflection, otherwise the edge
|
||
|
|
value forms the symmetric axis to the reflection.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
pad_amt : tuple of ints, length 2
|
||
|
|
New index positions of padding to do along the `axis`. If these are
|
||
|
|
both 0, padding is done in this dimension.
|
||
|
|
"""
|
||
|
|
left_pad, right_pad = width_pair
|
||
|
|
old_length = padded.shape[axis] - right_pad - left_pad
|
||
|
|
|
||
|
|
if include_edge:
|
||
|
|
# Edge is included, we need to offset the pad amount by 1
|
||
|
|
edge_offset = 1
|
||
|
|
else:
|
||
|
|
edge_offset = 0 # Edge is not included, no need to offset pad amount
|
||
|
|
old_length -= 1 # but must be omitted from the chunk
|
||
|
|
|
||
|
|
if left_pad > 0:
|
||
|
|
# Pad with reflected values on left side:
|
||
|
|
# First limit chunk size which can't be larger than pad area
|
||
|
|
chunk_length = min(old_length, left_pad)
|
||
|
|
# Slice right to left, stop on or next to edge, start relative to stop
|
||
|
|
stop = left_pad - edge_offset
|
||
|
|
start = stop + chunk_length
|
||
|
|
left_slice = _slice_at_axis(slice(start, stop, -1), axis)
|
||
|
|
left_chunk = padded[left_slice]
|
||
|
|
|
||
|
|
if method == "odd":
|
||
|
|
# Negate chunk and align with edge
|
||
|
|
edge_slice = _slice_at_axis(slice(left_pad, left_pad + 1), axis)
|
||
|
|
left_chunk = 2 * padded[edge_slice] - left_chunk
|
||
|
|
|
||
|
|
# Insert chunk into padded area
|
||
|
|
start = left_pad - chunk_length
|
||
|
|
stop = left_pad
|
||
|
|
pad_area = _slice_at_axis(slice(start, stop), axis)
|
||
|
|
padded[pad_area] = left_chunk
|
||
|
|
# Adjust pointer to left edge for next iteration
|
||
|
|
left_pad -= chunk_length
|
||
|
|
|
||
|
|
if right_pad > 0:
|
||
|
|
# Pad with reflected values on right side:
|
||
|
|
# First limit chunk size which can't be larger than pad area
|
||
|
|
chunk_length = min(old_length, right_pad)
|
||
|
|
# Slice right to left, start on or next to edge, stop relative to start
|
||
|
|
start = -right_pad + edge_offset - 2
|
||
|
|
stop = start - chunk_length
|
||
|
|
right_slice = _slice_at_axis(slice(start, stop, -1), axis)
|
||
|
|
right_chunk = padded[right_slice]
|
||
|
|
|
||
|
|
if method == "odd":
|
||
|
|
# Negate chunk and align with edge
|
||
|
|
edge_slice = _slice_at_axis(
|
||
|
|
slice(-right_pad - 1, -right_pad), axis)
|
||
|
|
right_chunk = 2 * padded[edge_slice] - right_chunk
|
||
|
|
|
||
|
|
# Insert chunk into padded area
|
||
|
|
start = padded.shape[axis] - right_pad
|
||
|
|
stop = start + chunk_length
|
||
|
|
pad_area = _slice_at_axis(slice(start, stop), axis)
|
||
|
|
padded[pad_area] = right_chunk
|
||
|
|
# Adjust pointer to right edge for next iteration
|
||
|
|
right_pad -= chunk_length
|
||
|
|
|
||
|
|
return left_pad, right_pad
|
||
|
|
|
||
|
|
|
||
|
|
def _set_wrap_both(padded, axis, width_pair):
|
||
|
|
"""
|
||
|
|
Pad `axis` of `arr` with wrapped values.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
padded : ndarray
|
||
|
|
Input array of arbitrary shape.
|
||
|
|
axis : int
|
||
|
|
Axis along which to pad `arr`.
|
||
|
|
width_pair : (int, int)
|
||
|
|
Pair of widths that mark the pad area on both sides in the given
|
||
|
|
dimension.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
pad_amt : tuple of ints, length 2
|
||
|
|
New index positions of padding to do along the `axis`. If these are
|
||
|
|
both 0, padding is done in this dimension.
|
||
|
|
"""
|
||
|
|
left_pad, right_pad = width_pair
|
||
|
|
period = padded.shape[axis] - right_pad - left_pad
|
||
|
|
|
||
|
|
# If the current dimension of `arr` doesn't contain enough valid values
|
||
|
|
# (not part of the undefined pad area) we need to pad multiple times.
|
||
|
|
# Each time the pad area shrinks on both sides which is communicated with
|
||
|
|
# these variables.
|
||
|
|
new_left_pad = 0
|
||
|
|
new_right_pad = 0
|
||
|
|
|
||
|
|
if left_pad > 0:
|
||
|
|
# Pad with wrapped values on left side
|
||
|
|
# First slice chunk from right side of the non-pad area.
|
||
|
|
# Use min(period, left_pad) to ensure that chunk is not larger than
|
||
|
|
# pad area
|
||
|
|
right_slice = _slice_at_axis(
|
||
|
|
slice(-right_pad - min(period, left_pad),
|
||
|
|
-right_pad if right_pad != 0 else None),
|
||
|
|
axis
|
||
|
|
)
|
||
|
|
right_chunk = padded[right_slice]
|
||
|
|
|
||
|
|
if left_pad > period:
|
||
|
|
# Chunk is smaller than pad area
|
||
|
|
pad_area = _slice_at_axis(slice(left_pad - period, left_pad), axis)
|
||
|
|
new_left_pad = left_pad - period
|
||
|
|
else:
|
||
|
|
# Chunk matches pad area
|
||
|
|
pad_area = _slice_at_axis(slice(None, left_pad), axis)
|
||
|
|
padded[pad_area] = right_chunk
|
||
|
|
|
||
|
|
if right_pad > 0:
|
||
|
|
# Pad with wrapped values on right side
|
||
|
|
# First slice chunk from left side of the non-pad area.
|
||
|
|
# Use min(period, right_pad) to ensure that chunk is not larger than
|
||
|
|
# pad area
|
||
|
|
left_slice = _slice_at_axis(
|
||
|
|
slice(left_pad, left_pad + min(period, right_pad),), axis)
|
||
|
|
left_chunk = padded[left_slice]
|
||
|
|
|
||
|
|
if right_pad > period:
|
||
|
|
# Chunk is smaller than pad area
|
||
|
|
pad_area = _slice_at_axis(
|
||
|
|
slice(-right_pad, -right_pad + period), axis)
|
||
|
|
new_right_pad = right_pad - period
|
||
|
|
else:
|
||
|
|
# Chunk matches pad area
|
||
|
|
pad_area = _slice_at_axis(slice(-right_pad, None), axis)
|
||
|
|
padded[pad_area] = left_chunk
|
||
|
|
|
||
|
|
return new_left_pad, new_right_pad
|
||
|
|
|
||
|
|
|
||
|
|
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()
|
||
|
|
|
||
|
|
|
||
|
|
def _pad_dispatcher(array, pad_width, mode=None, **kwargs):
|
||
|
|
return (array,)
|
||
|
|
|
||
|
|
|
||
|
|
###############################################################################
|
||
|
|
# Public functions
|
||
|
|
|
||
|
|
|
||
|
|
@array_function_dispatch(_pad_dispatcher, module='numpy')
|
||
|
|
def pad(array, pad_width, mode='constant', **kwargs):
|
||
|
|
"""
|
||
|
|
Pad an array.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
array : array_like of rank N
|
||
|
|
The array to pad.
|
||
|
|
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, optional
|
||
|
|
One of the following string values or a user supplied function.
|
||
|
|
|
||
|
|
'constant' (default)
|
||
|
|
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.
|
||
|
|
'empty'
|
||
|
|
Pads with undefined values.
|
||
|
|
|
||
|
|
.. versionadded:: 1.17
|
||
|
|
|
||
|
|
<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 scalar, 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 ``constant`` is a shortcut for ``before = after = constant`` for
|
||
|
|
all axes.
|
||
|
|
|
||
|
|
Default is 0.
|
||
|
|
end_values : sequence or scalar, 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 ``constant`` is a shortcut for ``before = after = constant`` 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 modify a rank 1 array in-place. 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[:iaxis_pad_width[0]] and vector[-iaxis_pad_width[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, ..., 6, 6, 6])
|
||
|
|
|
||
|
|
>>> np.pad(a, (2, 3), 'edge')
|
||
|
|
array([1, 1, 1, ..., 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
|
||
|
|
>>> 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]])
|
||
|
|
"""
|
||
|
|
array = np.asarray(array)
|
||
|
|
pad_width = np.asarray(pad_width)
|
||
|
|
|
||
|
|
if not pad_width.dtype.kind == 'i':
|
||
|
|
raise TypeError('`pad_width` must be of integral type.')
|
||
|
|
|
||
|
|
# Broadcast to shape (array.ndim, 2)
|
||
|
|
pad_width = _as_pairs(pad_width, array.ndim, as_index=True)
|
||
|
|
|
||
|
|
if callable(mode):
|
||
|
|
# Old behavior: Use user-supplied function with np.apply_along_axis
|
||
|
|
function = mode
|
||
|
|
# Create a new zero padded array
|
||
|
|
padded, _ = _pad_simple(array, pad_width, fill_value=0)
|
||
|
|
# And apply along each axis
|
||
|
|
|
||
|
|
for axis in range(padded.ndim):
|
||
|
|
# Iterate using ndindex as in apply_along_axis, but assuming that
|
||
|
|
# function operates inplace on the padded array.
|
||
|
|
|
||
|
|
# view with the iteration axis at the end
|
||
|
|
view = np.moveaxis(padded, axis, -1)
|
||
|
|
|
||
|
|
# compute indices for the iteration axes, and append a trailing
|
||
|
|
# ellipsis to prevent 0d arrays decaying to scalars (gh-8642)
|
||
|
|
inds = ndindex(view.shape[:-1])
|
||
|
|
inds = (ind + (Ellipsis,) for ind in inds)
|
||
|
|
for ind in inds:
|
||
|
|
function(view[ind], pad_width[axis], axis, kwargs)
|
||
|
|
|
||
|
|
return padded
|
||
|
|
|
||
|
|
# Make sure that no unsupported keywords were passed for the current mode
|
||
|
|
allowed_kwargs = {
|
||
|
|
'empty': [], 'edge': [], 'wrap': [],
|
||
|
|
'constant': ['constant_values'],
|
||
|
|
'linear_ramp': ['end_values'],
|
||
|
|
'maximum': ['stat_length'],
|
||
|
|
'mean': ['stat_length'],
|
||
|
|
'median': ['stat_length'],
|
||
|
|
'minimum': ['stat_length'],
|
||
|
|
'reflect': ['reflect_type'],
|
||
|
|
'symmetric': ['reflect_type'],
|
||
|
|
}
|
||
|
|
try:
|
||
|
|
unsupported_kwargs = set(kwargs) - set(allowed_kwargs[mode])
|
||
|
|
except KeyError:
|
||
|
|
raise ValueError("mode '{}' is not supported".format(mode))
|
||
|
|
if unsupported_kwargs:
|
||
|
|
raise ValueError("unsupported keyword arguments for mode '{}': {}"
|
||
|
|
.format(mode, unsupported_kwargs))
|
||
|
|
|
||
|
|
stat_functions = {"maximum": np.amax, "minimum": np.amin,
|
||
|
|
"mean": np.mean, "median": np.median}
|
||
|
|
|
||
|
|
# Create array with final shape and original values
|
||
|
|
# (padded area is undefined)
|
||
|
|
padded, original_area_slice = _pad_simple(array, pad_width)
|
||
|
|
# And prepare iteration over all dimensions
|
||
|
|
# (zipping may be more readable than using enumerate)
|
||
|
|
axes = range(padded.ndim)
|
||
|
|
|
||
|
|
if mode == "constant":
|
||
|
|
values = kwargs.get("constant_values", 0)
|
||
|
|
values = _as_pairs(values, padded.ndim)
|
||
|
|
for axis, width_pair, value_pair in zip(axes, pad_width, values):
|
||
|
|
roi = _view_roi(padded, original_area_slice, axis)
|
||
|
|
_set_pad_area(roi, axis, width_pair, value_pair)
|
||
|
|
|
||
|
|
elif mode == "empty":
|
||
|
|
pass # Do nothing as _pad_simple already returned the correct result
|
||
|
|
|
||
|
|
elif array.size == 0:
|
||
|
|
# Only modes "constant" and "empty" can extend empty axes, all other
|
||
|
|
# modes depend on `array` not being empty
|
||
|
|
# -> ensure every empty axis is only "padded with 0"
|
||
|
|
for axis, width_pair in zip(axes, pad_width):
|
||
|
|
if array.shape[axis] == 0 and any(width_pair):
|
||
|
|
raise ValueError(
|
||
|
|
"can't extend empty axis {} using modes other than "
|
||
|
|
"'constant' or 'empty'".format(axis)
|
||
|
|
)
|
||
|
|
# passed, don't need to do anything more as _pad_simple already
|
||
|
|
# returned the correct result
|
||
|
|
|
||
|
|
elif mode == "edge":
|
||
|
|
for axis, width_pair in zip(axes, pad_width):
|
||
|
|
roi = _view_roi(padded, original_area_slice, axis)
|
||
|
|
edge_pair = _get_edges(roi, axis, width_pair)
|
||
|
|
_set_pad_area(roi, axis, width_pair, edge_pair)
|
||
|
|
|
||
|
|
elif mode == "linear_ramp":
|
||
|
|
end_values = kwargs.get("end_values", 0)
|
||
|
|
end_values = _as_pairs(end_values, padded.ndim)
|
||
|
|
for axis, width_pair, value_pair in zip(axes, pad_width, end_values):
|
||
|
|
roi = _view_roi(padded, original_area_slice, axis)
|
||
|
|
ramp_pair = _get_linear_ramps(roi, axis, width_pair, value_pair)
|
||
|
|
_set_pad_area(roi, axis, width_pair, ramp_pair)
|
||
|
|
|
||
|
|
elif mode in stat_functions:
|
||
|
|
func = stat_functions[mode]
|
||
|
|
length = kwargs.get("stat_length", None)
|
||
|
|
length = _as_pairs(length, padded.ndim, as_index=True)
|
||
|
|
for axis, width_pair, length_pair in zip(axes, pad_width, length):
|
||
|
|
roi = _view_roi(padded, original_area_slice, axis)
|
||
|
|
stat_pair = _get_stats(roi, axis, width_pair, length_pair, func)
|
||
|
|
_set_pad_area(roi, axis, width_pair, stat_pair)
|
||
|
|
|
||
|
|
elif mode in {"reflect", "symmetric"}:
|
||
|
|
method = kwargs.get("reflect_type", "even")
|
||
|
|
include_edge = True if mode == "symmetric" else False
|
||
|
|
for axis, (left_index, right_index) in zip(axes, pad_width):
|
||
|
|
if array.shape[axis] == 1 and (left_index > 0 or right_index > 0):
|
||
|
|
# Extending singleton dimension for 'reflect' is legacy
|
||
|
|
# behavior; it really should raise an error.
|
||
|
|
edge_pair = _get_edges(padded, axis, (left_index, right_index))
|
||
|
|
_set_pad_area(
|
||
|
|
padded, axis, (left_index, right_index), edge_pair)
|
||
|
|
continue
|
||
|
|
|
||
|
|
roi = _view_roi(padded, original_area_slice, axis)
|
||
|
|
while left_index > 0 or right_index > 0:
|
||
|
|
# Iteratively pad until dimension is filled with reflected
|
||
|
|
# values. This is necessary if the pad area is larger than
|
||
|
|
# the length of the original values in the current dimension.
|
||
|
|
left_index, right_index = _set_reflect_both(
|
||
|
|
roi, axis, (left_index, right_index),
|
||
|
|
method, include_edge
|
||
|
|
)
|
||
|
|
|
||
|
|
elif mode == "wrap":
|
||
|
|
for axis, (left_index, right_index) in zip(axes, pad_width):
|
||
|
|
roi = _view_roi(padded, original_area_slice, axis)
|
||
|
|
while left_index > 0 or right_index > 0:
|
||
|
|
# Iteratively pad until dimension is filled with wrapped
|
||
|
|
# values. This is necessary if the pad area is larger than
|
||
|
|
# the length of the original values in the current dimension.
|
||
|
|
left_index, right_index = _set_wrap_both(
|
||
|
|
roi, axis, (left_index, right_index))
|
||
|
|
|
||
|
|
return padded
|