包含在 2 个数组中的向量的元素交叉乘积与 Python [英] Element wise cross product of vectors contained in 2 arrays with Python

问题描述

我有两个数组，一个包含向量列表(A)，一个包含向量的二维列表(B).我正在寻找以特定方式对每个数组中的向量进行元素明智的叉积.

A 中的第一个向量应该与 B 的第一个元素中包含的所有 3 个向量进行交叉积(?).

这是一个最小的例子:

将 numpy 导入为 npA = np.random.rand(2,3)B = np.random.rand(2,3,3)C = np.random.rand(2,3,3)C[0,0] = np.cross(A[0],B[0,0])C[0,1] = np.cross(A[0],B[0,1])C[0,2] = np.cross(A[0],B[0,2])C[1,0] = np.cross(A[1],B[1,0])C[1,1] = np.cross(A[1],B[1,1])C[1,2] = np.cross(A[1],B[1,2])

为了提高效率，我想避免使用 for 循环.

我使用以下方法对点积进行了相同的操作:

C = np.einsum('aj,ijk->ij',A,B)

但我似乎无法对交叉产品做同样的事情.

解决方案

只是广播的问题:

<预><代码>>>>D = np.cross(A[:, None, :], B)>>>np.all(D==C)真的

I have two arrays, one containing a list of vectors (A) and one containing a 2D list of vectors (B). I am looking to do an element wise cross product of the vectors in each array in a specific way.

The fist vector in A should be cross producted (?) by all 3 vectors contained in the first element of B.

Here is a minimal example:

import numpy as np

A = np.random.rand(2,3)

B = np.random.rand(2,3,3)

C = np.random.rand(2,3,3)

C[0,0] = np.cross(A[0],B[0,0])
C[0,1] = np.cross(A[0],B[0,1])
C[0,2] = np.cross(A[0],B[0,2])

C[1,0] = np.cross(A[1],B[1,0])
C[1,1] = np.cross(A[1],B[1,1])
C[1,2] = np.cross(A[1],B[1,2])

I would like to avoid using for loops for efficiency.

I managed doing the same with the dot product by using:

C = np.einsum('aj,ijk->ij',A,B)

But I cant seem to be able to do the same with the cross product.

解决方案

Just a matter of broadcasting:

>>> D = np.cross(A[:, None, :], B)
>>> np.all(D==C)
True

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