Using Python numpy einsum to obtain dot product between 2 Matrices

问题

Just came across this:

Vectorized way of calculating row-wise dot product two matrices with Scipy

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

回答1:

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]])

来源：https://stackoverflow.com/questions/45896939/using-python-numpy-einsum-to-obtain-dot-product-between-2-matrices