numpy tensordot 用法及代码示例

用法：
numpy.tensordot(a, b, axes=2)
沿指定轴计算张量点积。

给定两个张量a和b，以及一个包含两个数组对象的数组对象，(a_axes, b_axes)，对的乘积求和a的和b在指定的轴上的元素(组件)a_axes和b_axes。第三个参数可以是单个非负integer_like标量，N;如果是这样，那么最后一个N的尺寸a和第一个N的尺寸b总结。

例子：

“traditional”示例：

>>> a = np.arange(60.).reshape(3,4,5)
>>> b = np.arange(24.).reshape(4,3,2)
>>> c = np.tensordot(a,b, axes=([1,0],[0,1]))
>>> c.shape
(5, 2)
>>> c
array([[4400., 4730.],
       [4532., 4874.],
       [4664., 5018.],
       [4796., 5162.],
       [4928., 5306.]])
>>> # A slower but equivalent way of computing the same...
>>> d = np.zeros((5,2))
>>> for i in range(5):
...   for j in range(2):
...     for k in range(3):
...       for n in range(4):
...         d[i,j] += a[k,n,i] * b[n,k,j]
>>> c == d
array([[ True,  True],
       [ True,  True],
       [ True,  True],
       [ True,  True],
       [ True,  True]])

利用+和*重载的扩展示例：

>>> a = np.array(range(1, 9))
>>> a.shape = (2, 2, 2)
>>> A = np.array(('a', 'b', 'c', 'd'), dtype=object)
>>> A.shape = (2, 2)
>>> a; A
array([[[1, 2],
        [3, 4]],
       [[5, 6],
        [7, 8]]])
array([['a', 'b'],
       ['c', 'd']], dtype=object)

>>> np.tensordot(a, A) # third argument default is 2 for double-contraction
array(['abbcccdddd', 'aaaaabbbbbbcccccccdddddddd'], dtype=object)

>>> np.tensordot(a, A, 1)
array([[['acc', 'bdd'],
        ['aaacccc', 'bbbdddd']],
       [['aaaaacccccc', 'bbbbbdddddd'],
        ['aaaaaaacccccccc', 'bbbbbbbdddddddd']]], dtype=object)

>>> np.tensordot(a, A, 0) # tensor product (result too long to incl.)
array([[[[['a', 'b'],
          ['c', 'd']],
          ...

>>> np.tensordot(a, A, (0, 1))
array([[['abbbbb', 'cddddd'],
        ['aabbbbbb', 'ccdddddd']],
       [['aaabbbbbbb', 'cccddddddd'],
        ['aaaabbbbbbbb', 'ccccdddddddd']]], dtype=object)

>>> np.tensordot(a, A, (2, 1))
array([[['abb', 'cdd'],
        ['aaabbbb', 'cccdddd']],
       [['aaaaabbbbbb', 'cccccdddddd'],
        ['aaaaaaabbbbbbbb', 'cccccccdddddddd']]], dtype=object)

>>> np.tensordot(a, A, ((0, 1), (0, 1)))
array(['abbbcccccddddddd', 'aabbbbccccccdddddddd'], dtype=object)

>>> np.tensordot(a, A, ((2, 1), (1, 0)))
array(['acccbbdddd', 'aaaaacccccccbbbbbbdddddddd'], dtype=object)

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