对具有多个维度的numpy.argsort进行不变量排序 [英] Sort invariant for numpy.argsort with multiple dimensions

问题描述

numpy.argsort 文档状态

返回:
index_array:ndarray，int 沿指定轴对排序的索引数组.如果a是一维的，则a[index_array]会产生一个排序的a.

Returns:
index_array : ndarray, int Array of indices that sort a along the specified axis. If a is one-dimensional, a[index_array] yields a sorted a.

如何将numpy.argsort的结果应用于多维数组以返回已排序的数组? (不只是一维或二维数组；它可以是一个N维数组，其中N仅在运行时才知道)

How can I apply the result of numpy.argsort for a multidimensional array to get back a sorted array? (NOT just a 1-D or 2-D array; it could be an N-dimensional array where N is known only at runtime)

>>> import numpy as np
>>> np.random.seed(123)
>>> A = np.random.randn(3,2)
>>> A
array([[-1.0856306 ,  0.99734545],
       [ 0.2829785 , -1.50629471],
       [-0.57860025,  1.65143654]])
>>> i=np.argsort(A,axis=-1)
>>> A[i]
array([[[-1.0856306 ,  0.99734545],
        [ 0.2829785 , -1.50629471]],

       [[ 0.2829785 , -1.50629471],
        [-1.0856306 ,  0.99734545]],

       [[-1.0856306 ,  0.99734545],
        [ 0.2829785 , -1.50629471]]])

对我来说，这不仅仅是使用sort()的问题；我还有另一个数组B，我想沿着适当的轴使用np.argsort(A)的结果对B进行排序.考虑以下示例:

For me it's not just a matter of using sort() instead; I have another array B and I want to order B using the results of np.argsort(A) along the appropriate axis. Consider the following example:

>>> A = np.array([[3,2,1],[4,0,6]])
>>> B = np.array([[3,1,4],[1,5,9]])
>>> i = np.argsort(A,axis=-1)
>>> BsortA = ???             
# should result in [[4,1,3],[5,1,9]]
# so that corresponding elements of B and sort(A) stay together

---

该功能似乎是已经在numpy中进行了增强请求.

推荐答案

numpy问题#8708 具有take_along_axis的示例实现，该示例实现了我所需要的；我不确定大型阵列是否有效，但似乎可行.

The numpy issue #8708 has a sample implementation of take_along_axis that does what I need; I'm not sure if it's efficient for large arrays but it seems to work.

def take_along_axis(arr, ind, axis):
    """
    ... here means a "pack" of dimensions, possibly empty

    arr: array_like of shape (A..., M, B...)
        source array
    ind: array_like of shape (A..., K..., B...)
        indices to take along each 1d slice of `arr`
    axis: int
        index of the axis with dimension M

    out: array_like of shape (A..., K..., B...)
        out[a..., k..., b...] = arr[a..., inds[a..., k..., b...], b...]
    """
    if axis < 0:
       if axis >= -arr.ndim:
           axis += arr.ndim
       else:
           raise IndexError('axis out of range')
    ind_shape = (1,) * ind.ndim
    ins_ndim = ind.ndim - (arr.ndim - 1)   #inserted dimensions

    dest_dims = list(range(axis)) + [None] + list(range(axis+ins_ndim, ind.ndim))

    # could also call np.ix_ here with some dummy arguments, then throw those results away
    inds = []
    for dim, n in zip(dest_dims, arr.shape):
        if dim is None:
            inds.append(ind)
        else:
            ind_shape_dim = ind_shape[:dim] + (-1,) + ind_shape[dim+1:]
            inds.append(np.arange(n).reshape(ind_shape_dim))

    return arr[tuple(inds)]

产生

>>> A = np.array([[3,2,1],[4,0,6]])
>>> B = np.array([[3,1,4],[1,5,9]])
>>> i = A.argsort(axis=-1)
>>> take_along_axis(A,i,axis=-1)
array([[1, 2, 3],
       [0, 4, 6]])
>>> take_along_axis(B,i,axis=-1)
array([[4, 1, 3],
       [5, 1, 9]])

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