numpy 中的快速外张量积 [英] Fast outer tensor product in numpy

问题描述

我有两个 numpy 数组:

I have two numpy arrays:

x of shape ((d1,...,d_m)) 
y of shape ((e_1,...e_n)) 

我想形成外张量积，即numpy数组

I would like to form the outer tensor product, that is the numpy array

z of shape ((d1,...,d_m,e_1,...,e_n))

这样

z[i_1,...,i_n,i_{n+1}...,i_{m+n}] == x[i_1,...i_m]*y[i_{m+1},...,i_{m+n}]

我必须多次执行上述外部乘法，所以我想尽可能加快速度.

I have to perform the above outer multiplication several times so I would like to speed this up as much as possible.

推荐答案

outer 的替代方法是显式扩展维度.对于一维数组，这将是

An alternative to outer is to explicitly expand the dimensions. For 1d arrays this would be

x[:,None]*y   # y[None,:] is automatic.

对于 10x10 数组，并概括维度扩展，我得到相同的次数

For 10x10 arrays, and generalizing the dimension expansion, I get the same times

In [74]: timeit x[[slice(None)]*x.ndim + [None]*y.ndim] * y
10000 loops, best of 3: 53.6 µs per loop

In [75]: timeit np.multiply.outer(x,y)
10000 loops, best of 3: 52.6 µs per loop

所以outer确实节省了一些编码，但是基本的广播乘法是一样的.

So outer does save some coding, but the basic broadcasted multiplication is the same.

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