tensordot

Description

Compute tensor dot product along specified axes.

Given two tensors, a and b, and an integer or two array_like objects (a_axes and b_axes), calculate the product of a and b over the axes specified by a_axes and b_axes.

Mandatory Input Parameters

Parameter	Type	Description
a	array_like	First tensor
b	array_like	Second tensor
axes	int or (2,) array_like	If it is an integer, the last N axes of a and the first N axes of b are summed over in order. The sizes of the corresponding axes must match. If it is two arrays, it is a list of axes to be summed over. The first array applies to a and second to b. Both array_like elements must be of the same length. The array_like elements represent the axes to be deleted from the arrays a and b.

Parameter

Type

Description

array_like

First tensor

array_like

Second tensor

axes

int or (2,) array_like

If it is an integer, the last N axes of a and the first N axes of b are summed over in order. The sizes of the corresponding axes must match.

If it is two arrays, it is a list of axes to be summed over. The first array applies to a and second to b. Both array_like elements must be of the same length. The array_like elements represent the axes to be deleted from the arrays a and b.

Optional Input Parameters

None

Return Value

Type	Description
ndarray	Dot product of the input tensors

Examples

>>> import numpy as np
>>> a = np.arange(60).reshape(3,4,5)
>>> b = np.arange(24).reshape(4,3,2)
>>> a
array([[[ 0,  1,  2,  3,  4],
        [ 5,  6,  7,  8,  9],
        [10, 11, 12, 13, 14],
        [15, 16, 17, 18, 19]],

       [[20, 21, 22, 23, 24],
        [25, 26, 27, 28, 29],
        [30, 31, 32, 33, 34],
        [35, 36, 37, 38, 39]],

       [[40, 41, 42, 43, 44],
        [45, 46, 47, 48, 49],
        [50, 51, 52, 53, 54],
        [55, 56, 57, 58, 59]]])
>>> b
array([[[ 0,  1],
        [ 2,  3],
        [ 4,  5]],

       [[ 6,  7],
        [ 8,  9],
        [10, 11]],

       [[12, 13],
        [14, 15],
        [16, 17]],

       [[18, 19],
        [20, 21],
        [22, 23]]])
>>> c = np.tensordot(a, b, axes=([1,0],[0,1]))
>>> c
array([[4400, 4730],
       [4532, 4874],
       [4664, 5018],
       [4796, 5162],
       [4928, 5306]])
>>> c.shape
(5, 2)
>>>
>>> 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]])
>>>

Parent topic: Linear Algebra Functions