使用Python numpy einsum获得2个矩阵之间的点积 [英] Using Python numpy einsum to obtain dot product between 2 Matrices

问题描述

只是碰到了这一点:

计算行的矢量化方式用Scipy明智地将两个矩阵相乘

这个numpy.einsum确实很棒，但是使用起来有些混乱.假设我有:

This numpy.einsum is really awesome but its a little confusing to use. Suppose I have:

import numpy as np
a = np.array([[1,2,3], [3,4,5]])
b = np.array([[0,1,2], [1,1,7]])

我如何在einsum中使用"ij"来获得a和b之间的交叉点积"?

How would i use the "ij" in einsum to get a "cross dot product" between a and b?

基本上使用示例，我想计算的点积

Using the example basically I would like to compute dot product of

[1,2,3]和[0,1,2]

[1,2,3] and [0,1,2]

[1,2,3]和[1,2,7]

[1,2,3] and [1,2,7]

[3,4,5]和[0,1,2]

[3,4,5] and [0,1,2]

[3,4,5]和[1,1,7]

[3,4,5] and [1,1,7]

最后以[[8,26]，[14,42]]

and end up with [[8,26],[14,42]]

我知道我是否使用

np.einsum("ij,ij->i",a,b)

我只会得到[8，42]，这意味着我错过了十字"元素

I would just end up with [8, 42] which means I am missing the "cross" elements

推荐答案

您的结果仍然是二维的，因此您需要两个索引.您需要的是将第二个数组转置的矩阵乘法，因此，您可以用ij,kj->ik代替第二个矩阵ij,jk->ik:

Your result is still 2 dimensional, so you need two indices. What you need is a matrix multiplication with the second array transposed, so instead of normal ij,jk->ik, you transpose the second matrix by ij,kj->ik:

np.einsum('ij,kj->ik', a, b)

#array([[ 8, 24],
#       [14, 42]])

等效于:

np.dot(a, b.T)

#array([[ 8, 24],
#       [14, 42]])

---

import numpy as np
a = np.array([[1,2,3], [3,4,5]])
b = np.array([[0,1,2], [1,1,7]])

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