"""
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
__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 _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))
if val == 0:
return np.concatenate((np.zeros(padshape, dtype=arr.dtype), arr),
axis=axis)
else:
return np.concatenate(((np.zeros(padshape) + val).astype(arr.dtype),
arr), axis=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))
if val == 0:
return np.concatenate((arr, np.zeros(padshape, dtype=arr.dtype)),
axis=axis)
else:
return np.concatenate(
(arr, (np.zeros(padshape) + val).astype(arr.dtype)), axis=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 = tuple(slice(None) if i != axis else 0
for (i, x) in enumerate(arr.shape))
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
edge_arr = arr[edge_slice].reshape(pad_singleton)
return np.concatenate((edge_arr.repeat(pad_amt, axis=axis), arr),
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 = tuple(slice(None) if i != axis else arr.shape[axis] - 1
for (i, x) in enumerate(arr.shape))
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
edge_arr = arr[edge_slice].reshape(pad_singleton)
return np.concatenate((arr, edge_arr.repeat(pad_amt, axis=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
# Generate shape for final concatenated array
padshape = tuple(x if i != axis else pad_amt
for (i, x) in enumerate(arr.shape))
# Generate an n-dimensional array incrementing along `axis`
ramp_arr = _arange_ndarray(arr, padshape, axis,
reverse=True).astype(np.float64)
# Appropriate slicing to extract n-dimensional edge along `axis`
edge_slice = tuple(slice(None) if i != axis else 0
for (i, x) in enumerate(arr.shape))
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
# Extract edge, reshape to original rank, and extend along `axis`
edge_pad = arr[edge_slice].reshape(pad_singleton).repeat(pad_amt, axis)
# Linear ramp
slope = (end - edge_pad) / float(pad_amt)
ramp_arr = ramp_arr * slope
ramp_arr += edge_pad
_round_ifneeded(ramp_arr, arr.dtype)
# Ramp values will most likely be float, cast them to the same type as arr
return np.concatenate((ramp_arr.astype(arr.dtype), arr), axis=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
# Generate shape for final concatenated array
padshape = tuple(x if i != axis else pad_amt
for (i, x) in enumerate(arr.shape))
# Generate an n-dimensional array incrementing along `axis`
ramp_arr = _arange_ndarray(arr, padshape, axis,
reverse=False).astype(np.float64)
# Slice a chunk from the edge to calculate stats on
edge_slice = tuple(slice(None) if i != axis else -1
for (i, x) in enumerate(arr.shape))
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
# Extract edge, reshape to original rank, and extend along `axis`
edge_pad = arr[edge_slice].reshape(pad_singleton).repeat(pad_amt, axis)
# Linear ramp
slope = (end - edge_pad) / float(pad_amt)
ramp_arr = ramp_arr * slope
ramp_arr += edge_pad
_round_ifneeded(ramp_arr, arr.dtype)
# Ramp values will most likely be float, cast them to the same type as arr
return np.concatenate((arr, ramp_arr.astype(arr.dtype)), axis=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 = tuple(slice(None) if i != axis else slice(num)
for (i, x) in enumerate(arr.shape))
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
# Extract slice, calculate max, reshape to add singleton dimension back
max_chunk = arr[max_slice].max(axis=axis).reshape(pad_singleton)
# Concatenate `arr` with `max_chunk`, extended along `axis` by `pad_amt`
return np.concatenate((max_chunk.repeat(pad_amt, axis=axis), arr),
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
end = arr.shape[axis] - 1
if num is not None:
max_slice = tuple(
slice(None) if i != axis else slice(end, end - num, -1)
for (i, x) in enumerate(arr.shape))
else:
max_slice = tuple(slice(None) for x in arr.shape)
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
# Extract slice, calculate max, reshape to add singleton dimension back
max_chunk = arr[max_slice].max(axis=axis).reshape(pad_singleton)
# Concatenate `arr` with `max_chunk`, extended along `axis` by `pad_amt`
return np.concatenate((arr, max_chunk.repeat(pad_amt, axis=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 = tuple(slice(None) if i != axis else slice(num)
for (i, x) in enumerate(arr.shape))
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
# Extract slice, calculate mean, reshape to add singleton dimension back
mean_chunk = arr[mean_slice].mean(axis).reshape(pad_singleton)
_round_ifneeded(mean_chunk, arr.dtype)
# Concatenate `arr` with `mean_chunk`, extended along `axis` by `pad_amt`
return np.concatenate((mean_chunk.repeat(pad_amt, axis).astype(arr.dtype),
arr), 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
end = arr.shape[axis] - 1
if num is not None:
mean_slice = tuple(
slice(None) if i != axis else slice(end, end - num, -1)
for (i, x) in enumerate(arr.shape))
else:
mean_slice = tuple(slice(None) for x in arr.shape)
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
# Extract slice, calculate mean, reshape to add singleton dimension back
mean_chunk = arr[mean_slice].mean(axis=axis).reshape(pad_singleton)
_round_ifneeded(mean_chunk, arr.dtype)
# Concatenate `arr` with `mean_chunk`, extended along `axis` by `pad_amt`
return np.concatenate(
(arr, mean_chunk.repeat(pad_amt, axis).astype(arr.dtype)), 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 = tuple(slice(None) if i != axis else slice(num)
for (i, x) in enumerate(arr.shape))
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
# Extract slice, calculate median, reshape to add singleton dimension back
med_chunk = np.median(arr[med_slice], axis=axis).reshape(pad_singleton)
_round_ifneeded(med_chunk, arr.dtype)
# Concatenate `arr` with `med_chunk`, extended along `axis` by `pad_amt`
return np.concatenate(
(med_chunk.repeat(pad_amt, axis).astype(arr.dtype), arr), 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
end = arr.shape[axis] - 1
if num is not None:
med_slice = tuple(
slice(None) if i != axis else slice(end, end - num, -1)
for (i, x) in enumerate(arr.shape))
else:
med_slice = tuple(slice(None) for x in arr.shape)
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
# Extract slice, calculate median, reshape to add singleton dimension back
med_chunk = np.median(arr[med_slice], axis=axis).reshape(pad_singleton)
_round_ifneeded(med_chunk, arr.dtype)
# Concatenate `arr` with `med_chunk`, extended along `axis` by `pad_amt`
return np.concatenate(
(arr, med_chunk.repeat(pad_amt, axis).astype(arr.dtype)), 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 = tuple(slice(None) if i != axis else slice(num)
for (i, x) in enumerate(arr.shape))
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
# Extract slice, calculate min, reshape to add singleton dimension back
min_chunk = arr[min_slice].min(axis=axis).reshape(pad_singleton)
# Concatenate `arr` with `min_chunk`, extended along `axis` by `pad_amt`
return np.concatenate((min_chunk.repeat(pad_amt, axis=axis), arr),
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
end = arr.shape[axis] - 1
if num is not None:
min_slice = tuple(
slice(None) if i != axis else slice(end, end - num, -1)
for (i, x) in enumerate(arr.shape))
else:
min_slice = tuple(slice(None) for x in arr.shape)
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
# Extract slice, calculate min, reshape to add singleton dimension back
min_chunk = arr[min_slice].min(axis=axis).reshape(pad_singleton)
# Concatenate `arr` with `min_chunk`, extended along `axis` by `pad_amt`
return np.concatenate((arr, min_chunk.repeat(pad_amt, axis=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 = tuple(slice(None) if i != axis else slice(pad_amt[0], 0, -1)
for (i, x) in enumerate(arr.shape))
ref_chunk1 = arr[ref_slice]
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
if pad_amt[0] == 1:
ref_chunk1 = ref_chunk1.reshape(pad_singleton)
# Memory/computationally more expensive, only do this if `method='odd'`
if 'odd' in method and pad_amt[0] > 0:
edge_slice1 = tuple(slice(None) if i != axis else 0
for (i, x) in enumerate(arr.shape))
edge_chunk = arr[edge_slice1].reshape(pad_singleton)
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 = tuple(slice(None) if i != axis else slice(start, end)
for (i, x) in enumerate(arr.shape))
rev_idx = tuple(slice(None) if i != axis else slice(None, None, -1)
for (i, x) in enumerate(arr.shape))
ref_chunk2 = arr[ref_slice][rev_idx]
if pad_amt[1] == 1:
ref_chunk2 = ref_chunk2.reshape(pad_singleton)
if 'odd' in method:
edge_slice2 = tuple(slice(None) if i != axis else -1
for (i, x) in enumerate(arr.shape))
edge_chunk = arr[edge_slice2].reshape(pad_singleton)
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 = tuple(slice(None) if i != axis else slice(0, pad_amt[0])
for (i, x) in enumerate(arr.shape))
rev_idx = tuple(slice(None) if i != axis else slice(None, None, -1)
for (i, x) in enumerate(arr.shape))
sym_chunk1 = arr[sym_slice][rev_idx]
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
if pad_amt[0] == 1:
sym_chunk1 = sym_chunk1.reshape(pad_singleton)
# Memory/computationally more expensive, only do this if `method='odd'`
if 'odd' in method and pad_amt[0] > 0:
edge_slice1 = tuple(slice(None) if i != axis else 0
for (i, x) in enumerate(arr.shape))
edge_chunk = arr[edge_slice1].reshape(pad_singleton)
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
start = arr.shape[axis] - pad_amt[1]
end = arr.shape[axis]
sym_slice = tuple(slice(None) if i != axis else slice(start, end)
for (i, x) in enumerate(arr.shape))
sym_chunk2 = arr[sym_slice][rev_idx]
if pad_amt[1] == 1:
sym_chunk2 = sym_chunk2.reshape(pad_singleton)
if 'odd' in method:
edge_slice2 = tuple(slice(None) if i != axis else -1
for (i, x) in enumerate(arr.shape))
edge_chunk = arr[edge_slice2].reshape(pad_singleton)
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
start = arr.shape[axis] - pad_amt[0]
end = arr.shape[axis]
wrap_slice = tuple(slice(None) if i != axis else slice(start, end)
for (i, x) in enumerate(arr.shape))
wrap_chunk1 = arr[wrap_slice]
# Shape to restore singleton dimension after slicing
pad_singleton = tuple(x if i != axis else 1
for (i, x) in enumerate(arr.shape))
if pad_amt[0] == 1:
wrap_chunk1 = wrap_chunk1.reshape(pad_singleton)
##########################################################################
# Appended region
# Slice off a reverse indexed chunk from far edge to pad `arr` after
wrap_slice = tuple(slice(None) if i != axis else slice(0, pad_amt[1])
for (i, x) in enumerate(arr.shape))
wrap_chunk2 = arr[wrap_slice]
if pad_amt[1] == 1:
wrap_chunk2 = wrap_chunk2.reshape(pad_singleton)
# Concatenate `arr` with both chunks, extending along `axis`
return np.concatenate((wrap_chunk1, arr, wrap_chunk2), axis=axis)
def _normalize_shape(ndarray, shape, cast_to_int=True):
"""
Private function which does some checks and normalizes the possibly
much simpler representations of 'pad_width', 'stat_length',
'constant_values', 'end_values'.
Parameters
----------
narray : ndarray
Input ndarray
shape : {sequence, array_like, float, int}, optional
The width of padding (pad_width), the number of elements on the
edge of the narray used for statistics (stat_length), the constant
value(s) to use when filling padded regions (constant_values), or the
endpoint target(s) for linear ramps (end_values).
((before_1, after_1), ... (before_N, after_N)) unique number of
elements for each axis where `N` is rank of `narray`.
((before, after),) yields same before and after constants for each
axis.
(constant,) or val is a shortcut for before = after = constant for
all axes.
cast_to_int : bool, optional
Controls if values in ``shape`` will be rounded and cast to int
before being returned.
Returns
-------
normalized_shape : tuple of tuples
val => ((val, val), (val, val), ...)
[[val1, val2], [val3, val4], ...] => ((val1, val2), (val3, val4), ...)
((val1, val2), (val3, val4), ...) => no change
[[val1, val2], ] => ((val1, val2), (val1, val2), ...)
((val1, val2), ) => ((val1, val2), (val1, val2), ...)
[[val , ], ] => ((val, val), (val, val), ...)
((val , ), ) => ((val, val), (val, val), ...)
"""
ndims = ndarray.ndim
# Shortcut shape=None
if shape is None:
return ((None, None), ) * ndims
# Convert any input `info` to a NumPy array
arr = np.asarray(shape)
# Switch based on what input looks like
if arr.ndim <= 1:
if arr.shape == () or arr.shape == (1,): # Single scalar input
# Create new array of ones, multiply by the scalar
arr = np.ones((ndims, 2), dtype=ndarray.dtype) * arr
elif arr.shape == (2,): # Apply padding (before, after) each axis
# Create new axis 0, repeat along it for every axis
arr = arr[np.newaxis, :].repeat(ndims, axis=0)
else:
fmt = "Unable to create correctly shaped tuple from %s"
raise ValueError(fmt % (shape,))
elif arr.ndim == 2:
if arr.shape[1] == 1 and arr.shape[0] == ndims:
# Padded before and after by the same amount
arr = arr.repeat(2, axis=1)
elif arr.shape[0] == ndims:
# Input correctly formatted, pass it on as `arr`
arr = shape
else:
fmt = "Unable to create correctly shaped tuple from %s"
raise ValueError(fmt % (shape,))
else:
fmt = "Unable to create correctly shaped tuple from %s"
raise ValueError(fmt % (shape,))
# Cast if necessary
if cast_to_int is True:
arr = np.round(arr).astype(int)
# Convert list of lists to tuple of tuples
return tuple(tuple(axis) for axis in arr.tolist())
def _validate_lengths(narray, number_elements):
"""
Private function which does some checks and reformats pad_width and
stat_length using _normalize_shape.
Parameters
----------
narray : ndarray
Input ndarray
number_elements : {sequence, int}, optional
The width of padding (pad_width) or the number of elements on the edge
of the narray used for statistics (stat_length).
((before_1, after_1), ... (before_N, after_N)) unique number of
elements 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.
Returns
-------
_validate_lengths : tuple of tuples
int => ((int, int), (int, int), ...)
[[int1, int2], [int3, int4], ...] => ((int1, int2), (int3, int4), ...)
((int1, int2), (int3, int4), ...) => no change
[[int1, int2], ] => ((int1, int2), (int1, int2), ...)
((int1, int2), ) => ((int1, int2), (int1, int2), ...)
[[int , ], ] => ((int, int), (int, int), ...)
((int , ), ) => ((int, int), (int, int), ...)
"""
normshp = _normalize_shape(narray, number_elements)
for i in normshp:
chk = [1 if x is None else x for x in i]
chk = [1 if x >= 0 else -1 for x in chk]
if (chk[0] < 0) or (chk[1] < 0):
fmt = "%s cannot contain negative values."
raise ValueError(fmt % (number_elements,))
return normshp
###############################################################################
# Public functions
[docs]def pad(array, pad_width, mode=None, **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 extented 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
-----
This function exists in NumPy >= 1.7.0, but is included in
``scikit-fuzzy`` for backwards compatibility with earlier versions.
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 : misc
Any keyword arguments the function requires.
Examples
--------
>>> a = [1, 2, 3, 4, 5]
>>> fuzz.pad(a, (2,3), 'constant', constant_values=(4, 6))
array([4, 4, 1, 2, 3, 4, 5, 6, 6, 6])
>>> fuzz.pad(a, (2, 3), 'edge')
array([1, 1, 1, 2, 3, 4, 5, 5, 5, 5])
>>> fuzz.pad(a, (2, 3), 'linear_ramp', end_values=(5, -4))
array([ 5, 3, 1, 2, 3, 4, 5, 2, -1, -4])
>>> fuzz.pad(a, (2,), 'maximum')
array([5, 5, 1, 2, 3, 4, 5, 5, 5])
>>> fuzz.pad(a, (2,), 'mean')
array([3, 3, 1, 2, 3, 4, 5, 3, 3])
>>> fuzz.pad(a, (2,), 'median')
array([3, 3, 1, 2, 3, 4, 5, 3, 3])
>>> a = [[1, 2], [3, 4]]
>>> fuzz.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]
>>> fuzz.pad(a, (2, 3), 'reflect')
array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2])
>>> fuzz.pad(a, (2, 3), 'reflect', reflect_type='odd')
array([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8])
>>> fuzz.pad(a, (2, 3), 'symmetric')
array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3])
>>> fuzz.pad(a, (2, 3), 'symmetric', reflect_type='odd')
array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7])
>>> fuzz.pad(a, (2, 3), 'wrap')
array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3])
>>> def padwithtens(vector, pad_width, iaxis, kwargs):
... vector[:pad_width[0]] = 10
... vector[-pad_width[1]:] = 10
... return vector
>>> a = np.arange(6)
>>> a = a.reshape((2, 3))
>>> fuzz.pad(a, 2, padwithtens)
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]])
"""
if not np.asarray(pad_width).dtype.kind == 'i':
raise TypeError('`pad_width` must be of integral type.')
narray = np.array(array)
pad_width = _validate_lengths(narray, pad_width)
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, str):
# 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] = _validate_lengths(narray, kwargs[i])
if i in ['end_values', 'constant_values']:
kwargs[i] = _normalize_shape(narray, kwargs[i],
cast_to_int=False)
elif mode is None:
raise ValueError('Keyword "mode" must be a function or one of %s.' %
(list(allowedkwargs.keys()),))
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(len(narray.shape)))
total_dim_increase = [np.sum(pad_width[i]) for i in rank]
offset_slices = [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):
# 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
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