How to multiply specific rows/columns of matrices with each other in python?-CodePudding

I have to input matrices of shape

m1: (n,3)
m2: (n,3)

I want to multiply each row (each n of size 3) with its correspondence of the other matrix, such that i get a (3,3) matrix for each row.

When im trying to just use e.g. m1[0]@m2.T[0] the operation doesnt work, as m[0] delivers a (3,) list instead of a (3,1) matrix, on which i could use matrix operations.

Is there a relatively easy or elegant way to get the desired (3,1) matrix for the matrix multiplication?

CodePudding user response：

Generally, I would recommend using np.einsum for most matrix operations as it very elegant. To obtain a the row-wise outer product of the vectors contained in m1 and m2 of shape (n, 3) you could do the following:

import numpy as np
m1 = np.array([1, 2, 3]).reshape(1, 3)
m2 = np.array([1, 2, 3]).reshape(1, 3)
result = np.einsum("ni, nj -> nij", m1, m2)
print(result)
>>>array([[[1, 2, 3],
        [2, 4, 6],
        [3, 6, 9]]])

CodePudding user response：

By default, numpy gets rid of the singleton dimension, as you have noticed.
You can use np.newaxis (or equivalently None. That is an implementation detail, but also works in pytorch) for the second axis to tell numpy to "invent" a new one.

import numpy as np
a = np.ones((3,3))
a[1].shape                 # this is (3,)
a[1,:].shape               # this is (3,)
a[1][...,np.newaxis].shape # this is (3,1)

However, you can also use dot or outer directly:

>>> a = np.eye(3)
>>> np.outer(a[1], a[1])
array([[0., 0., 0.],
       [0., 1., 0.],
       [0., 0., 0.]])
>>> np.dot(a[1], a[1])
1.0