NumPy ix_() 函數(shù)

ix_函數(shù)可用于組合不同的向量以獲得每個(gè) n-uplet 的結(jié)果。例如，如果要計(jì)算從向量 a、b 和 c 中的每一個(gè)中提取的所有三元組的所有 a+b*c：

>>> a = np.array([2, 3, 4, 5])
>>> b = np.array([8, 5, 4])
>>> c = np.array([5, 4, 6, 8, 3])
>>> ax, bx, cx = np.ix_(a, b, c)
>>> ax
array([[[2]],
       [[3]],
       [[4]],
       [[5]]])
>>> bx
array([[[8],
        [5],
        [4]]])
>>> cx
array([[[5, 4, 6, 8, 3]]])
>>> ax.shape, bx.shape, cx.shape
((4, 1, 1), (1, 3, 1), (1, 1, 5))
>>> result = ax + bx * cx
>>> result
array([[[42, 34, 50, 66, 26],
        [27, 22, 32, 42, 17],
        [22, 18, 26, 34, 14]],
       [[43, 35, 51, 67, 27],
        [28, 23, 33, 43, 18],
        [23, 19, 27, 35, 15]],
       [[44, 36, 52, 68, 28],
        [29, 24, 34, 44, 19],
        [24, 20, 28, 36, 16]],
       [[45, 37, 53, 69, 29],
        [30, 25, 35, 45, 20],
        [25, 21, 29, 37, 17]]])
>>> result[3, 2, 4]
17
>>> a[3] + b[2] * c[4]
17

還可以按如下方式實(shí)現(xiàn) reduce：

>>> def ufunc_reduce(ufct, *vectors):
...    vs = np.ix_(*vectors)
...    r = ufct.identity
...    for v in vs:
...        r = ufct(r, v)
...    return r

然后將其用作：

>>> ufunc_reduce(np.add, a, b, c)
array([[[15, 14, 16, 18, 13],
        [12, 11, 13, 15, 10],
        [11, 10, 12, 14,  9]],
       [[16, 15, 17, 19, 14],
        [13, 12, 14, 16, 11],
        [12, 11, 13, 15, 10]],
       [[17, 16, 18, 20, 15],
        [14, 13, 15, 17, 12],
        [13, 12, 14, 16, 11]],
       [[18, 17, 19, 21, 16],
        [15, 14, 16, 18, 13],
        [14, 13, 15, 17, 12]]])

與普通 ufunc.reduce 相比，此版本的 reduce 的優(yōu)勢在于它利用廣播規(guī)則來避免創(chuàng)建輸出大小乘以向量數(shù)量的參數(shù)數(shù)組。