多维累积总和 [英] Multidimensional cumulative sum in numpy

问题描述

我希望能够计算一个大型n维numpy数组的累加和.最终数组中每个元素的值应该是索引大于或等于当前元素的所有元素的总和.

I want to be able to calculate the cumulative sum of a large n-dimensional numpy array. The value of each element in the final array should be the sum of all elements which have indices greater than or equal to the current element.

2D:xᶦʲ= ∑xᵐⁿ∀m≥i和n≥j

2D: xᶦʲ = ∑xᵐⁿ ∀ m ≥ i and n ≥ j

3D:xᶦʲᵏ= ∑xᵐⁿᵒ∀m≥i，n≥j，o≥k

3D: xᶦʲᵏ = ∑xᵐⁿᵒ ∀ m ≥ i and n ≥ j and o ≥ k

二维示例:

1 1 0       2  1  0
1 1 1  ->   5  3  1
1 1 1       8  5  2

1 2 3       6  5  3
4 5 6  ->  21 16  9
7 8 9      45 33 18

3D范例:

1 1 1       3   2   1
1 1 1       6   4   2
1 1 1       9   6   3

1 1 1       6   4   2
1 1 1  ->  12   8   4
1 1 1      18  12   6

1 1 1       9   6   3
1 1 1      18  12   6
1 1 1      27  18   9

推荐答案

沿最后一个轴翻转，沿相同的方向求和，将其向后翻转，最后沿第二个最后一个轴向后翻转，直到第一个轴-

Flip along the last axis, cumsum along the same, flip it back and finally cumsum along the second last axis onwards until the first axis -

def multidim_cumsum(a):
    out = a[...,::-1].cumsum(-1)[...,::-1]
    for i in range(2,a.ndim+1):
        np.cumsum(out, axis=-i, out=out)
    return out

示例2D案例运行-

In [107]: a
Out[107]: 
array([[1, 1, 0],
       [1, 1, 1],
       [1, 1, 1]])

In [108]: multidim_cumsum(a)
Out[108]: 
array([[2, 1, 0],
       [5, 3, 1],
       [8, 5, 2]])

3D案例运行示例-

In [110]: a
Out[110]: 
array([[[1, 1, 1],
        [1, 1, 1],
        [1, 1, 1]],

       [[1, 1, 1],
        [1, 1, 1],
        [1, 1, 1]],

       [[1, 1, 1],
        [1, 1, 1],
        [1, 1, 1]]])

In [111]: multidim_cumsum(a)
Out[111]: 
array([[[ 3,  2,  1],
        [ 6,  4,  2],
        [ 9,  6,  3]],

       [[ 6,  4,  2],
        [12,  8,  4],
        [18, 12,  6]],

       [[ 9,  6,  3],
        [18, 12,  6],
        [27, 18,  9]]])

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