在numpy中创建外部产品数组 [英] Create array of outer products in numpy

问题描述

我有一组长度为m的n个向量。例如， n = 3 ， m = 2 ：

I have an array of n vectors of length m. For example, with n = 3, m = 2:

x = array([[1, 2], [3, 4], [5,6]])

我想将每个向量的外积与自身相连，然后将它们连接成一个形状（n，m，m）的方形矩阵数组。所以对于上面的 x ，我会得到

I want to take the outer product of each vector with itself, then concatenate them into an array of square matrices of shape (n, m, m). So for the x above I would get

array([[[ 1,  2],
        [ 2,  4]],

       [[ 9, 12],
        [12, 16]],

       [[25, 30],
        [30, 36]]])

我可以使用进行循环这样做

np.concatenate([np.outer(v, v) for v in x]).reshape(3, 2, 2)

是否有一个numpy表达式在没有Python for 循环的情况下执行此操作？

Is there a numpy expression that does this without the Python for loop?

奖金问题：因为外部产品是对称的，我不需要 mxm 乘法运算来计算它们。我可以从numpy获得这种对称优化吗？

Bonus question: since the outer products are symmetric, I don't need to m x m multiplication operations to calculate them. Can I get this symmetry optimization from numpy?

推荐答案

也许使用 einsum ？

>>> x = np.array([[1, 2], [3, 4], [5,6]])
>>> np.einsum('ij...,i...->ij...',x,x)
array([[[ 1,  2],
        [ 2,  4]],

       [[ 9, 12],
        [12, 16]],

       [[25, 30],
        [30, 36]]])

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