如何在numpy或pytorch中向量化自定义算法? [英] How to vectorize custom algorithms in numpy or pytorch?
问题描述
假设我有两个矩阵:
A: size k x m
B: size m x n
使用自定义操作,我的输出将为k x n.
Using a custom operation, my output will be k x n.
此自定义操作不是A
行和B
列之间的点积. 假设,此自定义操作定义为:
This custom operation is not a dot product between the rows of A
and columns of B
. Suppose this custom operation is defined as:
对于A
的第I行和B
的第J列,输出的i,j
元素为:
For the Ith row of A
and Jth column of B
, the i,j
element of the output is:
sum( (a[i] + b[j]) ^20 ), i loop over I, j loops over J
我看到的唯一实现此方法的方法是扩展此方程式,计算每个项,然后将它们求和.
The only way I can see to implement this is to expand this equation, calculate each term, them sum them.
在numpy或pytorch中是否有一种方法可以在不扩展方程式的情况下进行操作?
Is there a way in numpy or pytorch to do this without expanding the equation?
推荐答案
除了注释中的@hpaulj方法外,您还可以使用以下事实:您要计算的本质上是成对的Minkowski距离:>
Apart from the method @hpaulj outlines in the comments, you can also use the fact that what you are calculating is essentially a pair-wise Minkowski distance:
import numpy as np
from scipy.spatial.distance import cdist
k,m,n = 10,20,30
A = np.random.random((k,m))
B = np.random.random((m,n))
method1 = ((A[...,None]+B)**20).sum(axis=1)
method2 = cdist(A,-B.T,'m',p=20)**20
np.allclose(method1,method2)
# True
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