如何爲另一個矩陣的每一行矢量化一個矩陣的點積？

Question

如果我有一個矩陣A，我希望得到的點積與B.

import numpy as np 

a = np.array([[1.0, 2.0], 
       [3.0, 4.0]]) 

b = np.array([[1.0, 1.0], 
       [2.0, 2.0], 
       [3.0, 3.0]]) 

的每一行，如果目標是做手工（或循環）：

c = np.array([np.dot(a, b[0])]) 
c = np.append(c, [np.dot(a, b[1])], axis=0) 
c = np.append(c, [np.dot(a, b[2])], axis=0) 

print(c) 

c = [[ 3. 7.] 
    [ 6. 14.] 
    [ 9. 21.]] 

Answer 1

對於某些移調和矩陣乘法使用np.dot -

a.dot(b.T).T 
b.dot(a.T) 

隨着np.einsum -

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

隨着np.tensordot -

np.tensordot(b,a,axes=((1,1))) 

運行測試 -

In [123]: a = np.random.rand(2000, 2000) 
    ...: b = np.random.rand(3000, 2000) 
    ...: 

In [124]: %timeit a.dot(b.T).T 
    ...: %timeit b.dot(a.T) 
    ...: %timeit np.einsum('ij,kj->ki',a,b) 
    ...: %timeit np.tensordot(b,a,axes=((1,1))) 
    ...: 
1 loops, best of 3: 234 ms per loop 
10 loops, best of 3: 169 ms per loop 
1 loops, best of 3: 7.59 s per loop 
10 loops, best of 3: 170 ms per loop