将一个数组的每一行与另一个数组的每个元素乘以numpy

问题描述

我在numpy中有两个数组A和B. A 保存笛卡尔坐标，每行是3D空间中的一个点，形状为(r，3). B 的形状为(r，n)，并保存整数.

I have two arrays A and B in numpy. A holds cartesian coordinates, each row is one point in 3D space and has the shape (r, 3). B has the shape (r, n) and holds integers.

我想做的是将B的每个元素与A中的每一行相乘，以使结果数组的形状为(r，n，3).例如:

What I would like to do is multiply each element of B with each row in A, so that the resulting array has the shape (r, n, 3). So for example:

# r = 3
A = np.array([1,1,1, 2,2,2, 3,3,3]).reshape(3,3)
# n = 2
B = np.array([10, 20, 30, 40, 50, 60]).reshape(3,2)

# Result with shape (3, 2, 3):
# [[[10,10,10], [20,20,20]],
# [[60,60,60], [80,80,80]]
# [[150,150,150], [180,180,180]]]

我非常确定可以使用 ，但我已经尝试了很长一段时间，无法正常工作.

I'm pretty sure this can be done with np.einsum, but I've been trying this for quite a while now and can't get it to work.

推荐答案

使用 broadcasting -

A[:,None,:]*B[:,:,None]

由于 np.einsum 也支持广播，您也可以使用它(感谢@ajcr建议这个简洁的版本)-

Since np.einsum also supports broadcasting, you can use that as well (thanks to @ajcr for suggesting this concise version) -

np.einsum('ij,ik->ikj',A,B)

样品运行-

In [22]: A
Out[22]:
array([[1, 1, 1],
       [2, 2, 2],
       [3, 3, 3]])

In [23]: B
Out[23]:
array([[10, 20],
       [30, 40],
       [50, 60]])

In [24]: A[:,None,:]*B[:,:,None]
Out[24]:
array([[[ 10,  10,  10],
        [ 20,  20,  20]],

       [[ 60,  60,  60],
        [ 80,  80,  80]],

       [[150, 150, 150],
        [180, 180, 180]]])

In [25]: np.einsum('ijk,ij->ijk',A[:,None,:],B)
Out[25]:
array([[[ 10,  10,  10],
        [ 20,  20,  20]],

       [[ 60,  60,  60],
        [ 80,  80,  80]],

       [[150, 150, 150],
        [180, 180, 180]]])

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