"""
Functions for acting on a axis of an array.
"""
from __future__ import division, print_function, absolute_import
import numpy as np
def axis_slice(a, start=None, stop=None, step=None, axis=-1):
"""Take a slice along axis 'axis' from 'a'.
Parameters
----------
a : numpy.ndarray
The array to be sliced.
start, stop, step : int or None
The slice parameters.
axis : int, optional
The axis of `a` to be sliced.
Examples
--------
>>> a = array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
>>> axis_slice(a, start=0, stop=1, axis=1)
array([[1],
[4],
[7]])
>>> axis_slice(a, start=1, axis=0)
array([[4, 5, 6],
[7, 8, 9]])
Notes
-----
The keyword arguments start, stop and step are used by calling
slice(start, stop, step). This implies axis_slice() does not
handle its arguments the exacty the same as indexing. To select
a single index k, for example, use
axis_slice(a, start=k, stop=k+1)
In this case, the length of the axis 'axis' in the result will
be 1; the trivial dimension is not removed. (Use numpy.squeeze()
to remove trivial axes.)
"""
a_slice = [slice(None)] * a.ndim
a_slice[axis] = slice(start, stop, step)
b = a[a_slice]
return b
def axis_reverse(a, axis=-1):
"""Reverse the 1-d slices of `a` along axis `axis`.
Returns axis_slice(a, step=-1, axis=axis).
"""
return axis_slice(a, step=-1, axis=axis)
def odd_ext(x, n, axis=-1):
"""Generate a new ndarray by making an odd extension of x along an axis.
Parameters
----------
x : ndarray
The array to be extended.
n : int
The number of elements by which to extend x at each end of the axis.
axis : int, optional
The axis along which to extend x. Default is -1.
Examples
--------
>>> a = array([[1.0,2.0,3.0,4.0,5.0], [0.0, 1.0, 4.0, 9.0, 16.0]])
>>> _odd_ext(a, 2)
array([[-1., 0., 1., 2., 3., 4., 5., 6., 7.],
[-4., -1, 0., 1., 4., 9., 16., 23., 28.]])
"""
if n < 1:
return x
if n > x.shape[axis] - 1:
raise ValueError(("The extension length n (%d) is too big. " +
"It must not exceed x.shape[axis]-1, which is %d.")
% (n, x.shape[axis] - 1))
left_end = axis_slice(x, start=0, stop=1, axis=axis)
left_ext = axis_slice(x, start=n, stop=0, step=-1, axis=axis)
right_end = axis_slice(x, start=-1, axis=axis)
right_ext = axis_slice(x, start=-2, stop=-(n + 2), step=-1, axis=axis)
ext = np.concatenate((2 * left_end - left_ext,
x,
2 * right_end - right_ext),
axis=axis)
return ext
def even_ext(x, n, axis=-1):
"""Create an ndarray that is an even extension of x along an axis.
Parameters
----------
x : ndarray
The array to be extended.
n : int
The number of elements by which to extend x at each end of the axis.
axis : int, optional
The axis along which to extend x. Default is -1.
Examples
--------
>>> a = array([[1.0,2.0,3.0,4.0,5.0], [0.0, 1.0, 4.0, 9.0, 16.0]])
>>> _even_ext(a, 2)
array([[ 3., 2., 1., 2., 3., 4., 5., 4., 3.],
[ 4., 1., 0., 1., 4., 9., 16., 9., 4.]])
"""
if n < 1:
return x
if n > x.shape[axis] - 1:
raise ValueError(("The extension length n (%d) is too big. " +
"It must not exceed x.shape[axis]-1, which is %d.")
% (n, x.shape[axis] - 1))
left_ext = axis_slice(x, start=n, stop=0, step=-1, axis=axis)
right_ext = axis_slice(x, start=-2, stop=-(n + 2), step=-1, axis=axis)
ext = np.concatenate((left_ext,
x,
right_ext),
axis=axis)
return ext
def const_ext(x, n, axis=-1):
"""Create an ndarray that is a constant extension of x along an axis.
The extension repeats the values at the first and last element of
the axis.
Parameters
----------
x : ndarray
The array to be extended.
n : int
The number of elements by which to extend x at each end of the axis.
axis : int, optional
The axis along which to extend x. Default is -1.
Examples
--------
>>> a = array([[1.0,2.0,3.0,4.0,5.0], [0.0, 1.0, 4.0, 9.0, 16.0]])
>>> _const_ext(a, 2)
array([[ 1., 1., 1., 2., 3., 4., 5., 5., 5.],
[ 0., 0., 0., 1., 4., 9., 16., 16., 16.]])
"""
if n < 1:
return x
left_end = axis_slice(x, start=0, stop=1, axis=axis)
ones_shape = [1] * x.ndim
ones_shape[axis] = n
ones = np.ones(ones_shape, dtype=x.dtype)
left_ext = ones * left_end
right_end = axis_slice(x, start=-1, axis=axis)
right_ext = ones * right_end
ext = np.concatenate((left_ext,
x,
right_ext),
axis=axis)
return ext