Python - 矩阵外积

问题描述

给定两个矩阵

A: m * r
B: n * r

我想生成另一个矩阵C: m * n，每个条目C_ij是一个由A_i的外积计算的矩阵和 B_j.

I want to generate another matrix C: m * n, with each entry C_ij being a matrix calculated by the outer product of A_i and B_j.

例如

A: [[1, 2],
    [3, 4]]

B: [[3, 1],
    [1, 2]]

给予

C: [[[3, 1],  [[1 ,2],
     [6, 2]],  [2 ,4]],
     [9, 3],  [[3, 6],
     [12,4]],  [4, 8]]]

我可以使用 for 循环来实现，例如

I can do it using for loops, like

    for i in range (A.shape(0)):
      for j in range (B.shape(0)):
         C_ij = np.outer(A_i, B_j)

我想知道是否有一种矢量化的方式来进行这种计算以加快计算速度?

I wonder If there is a vectorised way of doing this calculation to speed it up?

推荐答案

temp = numpy.multiply.outer(A, B)
C = numpy.swapaxes(temp, 1, 2)

NumPy ufuncs，例如 multiply，有一个 outer 方法几乎可以满足您的需求.以下:

NumPy ufuncs, such as multiply, have an outer method that almost does what you want. The following:

temp = numpy.multiply.outer(A, B)

产生的结果使得 temp[a, b, c, d] == A[a, b] * B[c, d].你想要 C[a, b, c, d] == A[a, c] * B[b, d].swapaxes 调用重新排列 temp 把它放在你想要的顺序.

produces a result such that temp[a, b, c, d] == A[a, b] * B[c, d]. You want C[a, b, c, d] == A[a, c] * B[b, d]. The swapaxes call rearranges temp to put it in the order you want.

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