python求数列数量积_使用Python numpy einsum获得2个矩阵之间的点积

Just came across this:

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]])

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

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

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

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

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

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

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

I know if I use

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

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

解决方案

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]])

which is equivalent to:

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]])