将张量切片乘以矩阵行

Question

我正在尝试找到一种方法来有效地计算张量的每个深度二维切片 (shape: (n, n, m)) 与矩阵的每一行 (shape: (n, m)).我正在尝试做的事情在没有矢量化的情况下看起来像这样：

import numpy as np

np.random.seed(42)

np.random.seed(1)

a = np.arange(16).reshape(4, 4)
b = np.random.randn(4, 4, 4)
c = np.zeros((4, 4))

for i in range(4):
    c[i] = b[..., i] @ a[i]

产生：

<<< print(c)
>>> [[  0.53623421  -0.10257152  -1.34855819  -1.72774519]
     [-18.13932187   1.82230599 -11.99348739  15.0787884 ]
     [ 38.5704751   -0.38514407   4.19673794   9.01941574]
     [-68.11165212  -5.52586601  64.69279036  11.3196871 ]]

我最接近的是：

<<< print(np.einsum("ij,ijk->ki", a, b))
>>> [[  0.53623421,  -2.66288958, -16.91264496, -12.98103047],
     [ -3.95244251,   1.82230599, -20.5351456 ,  34.69343339],
     [  8.07033597,  -0.90215803,   4.19673794,  12.57858867],
     [ -8.18116212,  -3.54815874,  46.60443317,  11.3196871 ]]

至少左上角和 bottom.right 元素匹配。

Answer 1

你们非常亲密。

下面的结果应该与您的 for 循环相同

print(np.einsum('ikj,jk->ji',b,a))

将张量切片乘以矩阵行

Multiply Tensor-Slice by Matrix-Row

python

numpy

vectorization

numpy-einsum

tensor