how to 3-way outer product in numpy?

Question

About the numpy.outer [link] .

Given two vectors, a = [a0, a1, ..., aM] and b = [b0, b1, ..., bN], the outer product will be M*N matrix.

Answer 1

The direct way of doing this, taking full advantage of broadcasting is:

a[:,None,None] * b[None,:,None] * c[None,None,:]

np.ix_ does this reshaping for you, at a modest cost in speed

In [919]: np.ix_(a,b,c)
Out[919]: 
(array([[[0]],

        [[1]],

        [[2]],

        [[3]],

        [[4]]]), array([[[10],
         [11],
         [12],
         [13]]]), array([[[20, 21, 22]]]))

and the resulting arrays can be multiplied with

np.prod(np.ix_(a,b,c))

The einsum version is simple, and fast

np.einsum('i,j,k',a,b,c)

It's a good idea to learn all 3 methods.

The problem with nesting outer is that expects the inputs to be 1d, or it flattens them. It can be used, but needs some reshaping

np.outer(a,np.outer(b,c)).reshape(a.shape[0],b.shape[0],c.shape[0])