242 lines
7.3 KiB
Python
242 lines
7.3 KiB
Python
"""
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Functions for acting on a axis of an array.
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"""
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import numpy as np
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def axis_slice(a, start=None, stop=None, step=None, axis=-1):
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"""Take a slice along axis 'axis' from 'a'.
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Parameters
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----------
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a : numpy.ndarray
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The array to be sliced.
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start, stop, step : int or None
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The slice parameters.
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axis : int, optional
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The axis of `a` to be sliced.
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Examples
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--------
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>>> a = array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
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>>> axis_slice(a, start=0, stop=1, axis=1)
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array([[1],
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[4],
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[7]])
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>>> axis_slice(a, start=1, axis=0)
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array([[4, 5, 6],
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[7, 8, 9]])
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Notes
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-----
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The keyword arguments start, stop and step are used by calling
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slice(start, stop, step). This implies axis_slice() does not
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handle its arguments the exactly the same as indexing. To select
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a single index k, for example, use
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axis_slice(a, start=k, stop=k+1)
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In this case, the length of the axis 'axis' in the result will
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be 1; the trivial dimension is not removed. (Use numpy.squeeze()
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to remove trivial axes.)
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"""
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a_slice = [slice(None)] * a.ndim
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a_slice[axis] = slice(start, stop, step)
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b = a[tuple(a_slice)]
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return b
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def axis_reverse(a, axis=-1):
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"""Reverse the 1-D slices of `a` along axis `axis`.
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Returns axis_slice(a, step=-1, axis=axis).
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"""
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return axis_slice(a, step=-1, axis=axis)
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def odd_ext(x, n, axis=-1):
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"""
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Odd extension at the boundaries of an array
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Generate a new ndarray by making an odd extension of `x` along an axis.
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Parameters
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----------
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x : ndarray
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The array to be extended.
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n : int
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The number of elements by which to extend `x` at each end of the axis.
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axis : int, optional
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The axis along which to extend `x`. Default is -1.
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Examples
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--------
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>>> from scipy.signal._arraytools import odd_ext
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>>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
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>>> odd_ext(a, 2)
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array([[-1, 0, 1, 2, 3, 4, 5, 6, 7],
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[-4, -1, 0, 1, 4, 9, 16, 23, 28]])
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Odd extension is a "180 degree rotation" at the endpoints of the original
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array:
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>>> t = np.linspace(0, 1.5, 100)
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>>> a = 0.9 * np.sin(2 * np.pi * t**2)
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>>> b = odd_ext(a, 40)
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>>> import matplotlib.pyplot as plt
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>>> plt.plot(arange(-40, 140), b, 'b', lw=1, label='odd extension')
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>>> plt.plot(arange(100), a, 'r', lw=2, label='original')
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>>> plt.legend(loc='best')
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>>> plt.show()
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"""
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if n < 1:
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return x
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if n > x.shape[axis] - 1:
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raise ValueError(("The extension length n (%d) is too big. " +
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"It must not exceed x.shape[axis]-1, which is %d.")
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% (n, x.shape[axis] - 1))
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left_end = axis_slice(x, start=0, stop=1, axis=axis)
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left_ext = axis_slice(x, start=n, stop=0, step=-1, axis=axis)
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right_end = axis_slice(x, start=-1, axis=axis)
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right_ext = axis_slice(x, start=-2, stop=-(n + 2), step=-1, axis=axis)
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ext = np.concatenate((2 * left_end - left_ext,
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x,
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2 * right_end - right_ext),
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axis=axis)
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return ext
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def even_ext(x, n, axis=-1):
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"""
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Even extension at the boundaries of an array
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Generate a new ndarray by making an even extension of `x` along an axis.
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Parameters
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----------
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x : ndarray
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The array to be extended.
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n : int
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The number of elements by which to extend `x` at each end of the axis.
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axis : int, optional
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The axis along which to extend `x`. Default is -1.
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Examples
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--------
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>>> from scipy.signal._arraytools import even_ext
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>>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
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>>> even_ext(a, 2)
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array([[ 3, 2, 1, 2, 3, 4, 5, 4, 3],
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[ 4, 1, 0, 1, 4, 9, 16, 9, 4]])
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Even extension is a "mirror image" at the boundaries of the original array:
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>>> t = np.linspace(0, 1.5, 100)
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>>> a = 0.9 * np.sin(2 * np.pi * t**2)
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>>> b = even_ext(a, 40)
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>>> import matplotlib.pyplot as plt
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>>> plt.plot(arange(-40, 140), b, 'b', lw=1, label='even extension')
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>>> plt.plot(arange(100), a, 'r', lw=2, label='original')
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>>> plt.legend(loc='best')
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>>> plt.show()
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"""
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if n < 1:
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return x
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if n > x.shape[axis] - 1:
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raise ValueError(("The extension length n (%d) is too big. " +
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"It must not exceed x.shape[axis]-1, which is %d.")
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% (n, x.shape[axis] - 1))
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left_ext = axis_slice(x, start=n, stop=0, step=-1, axis=axis)
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right_ext = axis_slice(x, start=-2, stop=-(n + 2), step=-1, axis=axis)
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ext = np.concatenate((left_ext,
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x,
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right_ext),
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axis=axis)
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return ext
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def const_ext(x, n, axis=-1):
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"""
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Constant extension at the boundaries of an array
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Generate a new ndarray that is a constant extension of `x` along an axis.
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The extension repeats the values at the first and last element of
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the axis.
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Parameters
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----------
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x : ndarray
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The array to be extended.
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n : int
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The number of elements by which to extend `x` at each end of the axis.
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axis : int, optional
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The axis along which to extend `x`. Default is -1.
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Examples
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--------
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>>> from scipy.signal._arraytools import const_ext
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>>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
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>>> const_ext(a, 2)
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array([[ 1, 1, 1, 2, 3, 4, 5, 5, 5],
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[ 0, 0, 0, 1, 4, 9, 16, 16, 16]])
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Constant extension continues with the same values as the endpoints of the
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array:
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>>> t = np.linspace(0, 1.5, 100)
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>>> a = 0.9 * np.sin(2 * np.pi * t**2)
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>>> b = const_ext(a, 40)
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>>> import matplotlib.pyplot as plt
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>>> plt.plot(arange(-40, 140), b, 'b', lw=1, label='constant extension')
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>>> plt.plot(arange(100), a, 'r', lw=2, label='original')
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>>> plt.legend(loc='best')
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>>> plt.show()
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"""
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if n < 1:
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return x
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left_end = axis_slice(x, start=0, stop=1, axis=axis)
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ones_shape = [1] * x.ndim
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ones_shape[axis] = n
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ones = np.ones(ones_shape, dtype=x.dtype)
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left_ext = ones * left_end
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right_end = axis_slice(x, start=-1, axis=axis)
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right_ext = ones * right_end
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ext = np.concatenate((left_ext,
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x,
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right_ext),
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axis=axis)
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return ext
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def zero_ext(x, n, axis=-1):
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"""
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Zero padding at the boundaries of an array
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Generate a new ndarray that is a zero-padded extension of `x` along
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an axis.
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Parameters
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----------
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x : ndarray
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The array to be extended.
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n : int
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The number of elements by which to extend `x` at each end of the
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axis.
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axis : int, optional
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The axis along which to extend `x`. Default is -1.
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Examples
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--------
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>>> from scipy.signal._arraytools import zero_ext
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>>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
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>>> zero_ext(a, 2)
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array([[ 0, 0, 1, 2, 3, 4, 5, 0, 0],
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[ 0, 0, 0, 1, 4, 9, 16, 0, 0]])
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"""
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if n < 1:
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return x
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zeros_shape = list(x.shape)
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zeros_shape[axis] = n
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zeros = np.zeros(zeros_shape, dtype=x.dtype)
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ext = np.concatenate((zeros, x, zeros), axis=axis)
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return ext
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