将矩阵行的成对差异放入3-d数组中 [英] Put pairwise differences of matrix rows in 3-d array

问题描述

我有一个形状为(n，d)的矩阵Y.我已经通过以下方式计算了成对行差异:

I have a matrix Y of shape (n, d). I already calculated the pairwise row-differences in the following way:

I, J = np.triu_indices(Y.shape[0], 0)
rowDiffs = (Y[I, :] - Y[J, :])

否，我想创建一个3d数组，其中包含位置(i，j，:)上Y行i和j的差.你会怎么做?

No i want to create a 3d-array, containing the differences of the rows i and j of Y at position (i,j, :). How would you do it?

它的目的是取代这个低效的循环:

The aim of it is to replace this inefficient loop:

   for i in range(Y.shape[0]): 
        for j in range(Y.shape[0]):
            C[i,:] = C[i,:] + W[i, j] * (Y[i, :]-Y[j, :])

推荐答案

我发现此方法有些成功:

I have found some success with this:

row_diffs = Y[:, np.newaxis] - Y

Y[:, np.newaxis]创建尺寸为(n，1，3)的Y版本.然后，减法使用广播来执行您想要的操作.

Y[:, np.newaxis] creates a version of Y with dimensions (n, 1, 3). Then, the subtraction uses broadcasting to do what you want.

不幸的是，我发现这种方法相对较慢，而且还没有找到更好的方法.

Unfortunately, I've found this approach to be relatively slow and I haven't yet found a better way.

完整示例:

>>> x = np.random.randint(10, size=(4, 3))
>>> x
array([[4, 0, 8],
       [8, 5, 3],
       [4, 1, 6],
       [2, 2, 4]])
>>> x[:, np.newaxis] - x
array([[[ 0,  0,  0],
        [-4, -5,  5],
        [ 0, -1,  2],
        [ 2, -2,  4]],

       [[ 4,  5, -5],
        [ 0,  0,  0],
        [ 4,  4, -3],
        [ 6,  3, -1]],

       [[ 0,  1, -2],
        [-4, -4,  3],
        [ 0,  0,  0],
        [ 2, -1,  2]],

       [[-2,  2, -4],
        [-6, -3,  1],
        [-2,  1, -2],
        [ 0,  0,  0]]])

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