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""" Functions for acting on a axis of an array. """
"""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.) """
"""Reverse the 1-d slices of `a` along axis `axis`.
Returns axis_slice(a, step=-1, axis=axis). """
""" Odd extension at the boundaries of an array
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 -------- >>> from scipy.signal._arraytools import odd_ext >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]]) >>> odd_ext(a, 2) array([[-1, 0, 1, 2, 3, 4, 5, 6, 7], [-4, -1, 0, 1, 4, 9, 16, 23, 28]])
Odd extension is a "180 degree rotation" at the endpoints of the original array:
>>> t = np.linspace(0, 1.5, 100) >>> a = 0.9 * np.sin(2 * np.pi * t**2) >>> b = odd_ext(a, 40) >>> import matplotlib.pyplot as plt >>> plt.plot(arange(-40, 140), b, 'b', lw=1, label='odd extension') >>> plt.plot(arange(100), a, 'r', lw=2, label='original') >>> plt.legend(loc='best') >>> plt.show() """ return x 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)) x, 2 * right_end - right_ext), axis=axis)
""" Even extension at the boundaries of an array
Generate a new ndarray by making 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 -------- >>> from scipy.signal._arraytools import even_ext >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]]) >>> even_ext(a, 2) array([[ 3, 2, 1, 2, 3, 4, 5, 4, 3], [ 4, 1, 0, 1, 4, 9, 16, 9, 4]])
Even extension is a "mirror image" at the boundaries of the original array:
>>> t = np.linspace(0, 1.5, 100) >>> a = 0.9 * np.sin(2 * np.pi * t**2) >>> b = even_ext(a, 40) >>> import matplotlib.pyplot as plt >>> plt.plot(arange(-40, 140), b, 'b', lw=1, label='even extension') >>> plt.plot(arange(100), a, 'r', lw=2, label='original') >>> plt.legend(loc='best') >>> plt.show() """ 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
""" Constant extension at the boundaries of an array
Generate a new 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 -------- >>> from scipy.signal._arraytools import const_ext >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]]) >>> const_ext(a, 2) array([[ 1, 1, 1, 2, 3, 4, 5, 5, 5], [ 0, 0, 0, 1, 4, 9, 16, 16, 16]])
Constant extension continues with the same values as the endpoints of the array:
>>> t = np.linspace(0, 1.5, 100) >>> a = 0.9 * np.sin(2 * np.pi * t**2) >>> b = const_ext(a, 40) >>> import matplotlib.pyplot as plt >>> plt.plot(arange(-40, 140), b, 'b', lw=1, label='constant extension') >>> plt.plot(arange(100), a, 'r', lw=2, label='original') >>> plt.legend(loc='best') >>> plt.show() """ 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
""" Zero padding at the boundaries of an array
Generate a new ndarray that is a zero padded 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 -------- >>> from scipy.signal._arraytools import zero_ext >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]]) >>> zero_ext(a, 2) array([[ 0, 0, 1, 2, 3, 4, 5, 0, 0], [ 0, 0, 0, 1, 4, 9, 16, 0, 0]]) """ if n < 1: return x zeros_shape = list(x.shape) zeros_shape[axis] = n zeros = np.zeros(zeros_shape, dtype=x.dtype) ext = np.concatenate((zeros, x, zeros), axis=axis) return ext |