如何有效地扩展numpy中的因子张量?

我倾向于使用 einsum 因为这通常是最容易写的:

def fast(wxf, wyf, wzf):
    return np.einsum('if,jf,kf->ijk', wxf, wyf, wzf)

def slow(wxf, wyf, wzf):
    N = len(wxf)
    W = np.zeros((N, N, N))
    for i in range(N):
        for j in range(N):
            for k in range(N):
                W[i,j,k] = np.sum([wxf[i,f]*wyf[j,f]*wzf[k,f] for f in range(N)]) 
    return W

def gen_ws(N):
    wxf = np.random.random((N,N))
    wyf = np.random.random((N,N))
    wzf = np.random.random((N,N))
    return wxf, wyf, wzf

给予

>>> ws = gen_ws(25)
>>> via_slow = slow(*ws)
>>> via_fast = fast(*ws)
>>> np.allclose(via_slow, via_fast)
True

和

>>> ws = gen_ws(100)
>>> %timeit fast(*ws)
10 loops, best of 3: 91.6 ms per loop

通过您的示例,可以非常简单地使用 np.einsum() :

W = np.einsum('ij,jf,kf->ijk', wxf, wyf, wzf)