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Tensor contraction of a and b along specified axes and outer product.

tf.tensordot( a, b, axes, name=None )

Tensordot (also known as tensor contraction) sums the product of elements from `a`

and `b`

over the indices specified by `a_axes`

and `b_axes`

. The lists `a_axes`

and `b_axes`

specify those pairs of axes along which to contract the tensors. The axis `a_axes[i]`

of `a`

must have the same dimension as axis `b_axes[i]`

of `b`

for all `i`

in `range(0, len(a_axes))`

. The lists `a_axes`

and `b_axes`

must have identical length and consist of unique integers that specify valid axes for each of the tensors. Additionally outer product is supported by passing `axes=0`

.

This operation corresponds to `numpy.tensordot(a, b, axes)`

.

Example 1: When `a`

and `b`

are matrices (order 2), the case `axes = 1`

is equivalent to matrix multiplication.

Example 2: When `a`

and `b`

are matrices (order 2), the case `axes = [[1], [0]]`

is equivalent to matrix multiplication.

Example 3: When `a`

and `b`

are matrices (order 2), the case `axes=0`

gives the outer product, a tensor of order 4.

Example 4: Suppose that \(a_{ijk}\) and \(b_{lmn}\) represent two tensors of order 3. Then, `contract(a, b, [[0], [2]])`

is the order 4 tensor \(c_{jklm}\) whose entry corresponding to the indices \((j,k,l,m)\) is given by:

\( c_{jklm} = \sum_i a_{ijk} b_{lmi} \).

In general, `order(c) = order(a) + order(b) - 2*len(axes[0])`

.

Args | |
---|---|

`a` | `Tensor` of type `float32` or `float64` . |

`b` | `Tensor` with the same type as `a` . |

`axes` | Either a scalar `N` , or a list or an `int32` `Tensor` of shape [2, k]. If axes is a scalar, sum over the last N axes of a and the first N axes of b in order. If axes is a list or `Tensor` the first and second row contain the set of unique integers specifying axes along which the contraction is computed, for `a` and `b` , respectively. The number of axes for `a` and `b` must be equal. If `axes=0` , computes the outer product between `a` and `b` . |

`name` | A name for the operation (optional). |

Returns | |
---|---|

A `Tensor` with the same type as `a` . |

Raises | |
---|---|

`ValueError` | If the shapes of `a` , `b` , and `axes` are incompatible. |

`IndexError` | If the values in axes exceed the rank of the corresponding tensor. |

© 2020 The TensorFlow Authors. All rights reserved.

Licensed under the Creative Commons Attribution License 3.0.

Code samples licensed under the Apache 2.0 License.

https://www.tensorflow.org/versions/r2.4/api_docs/python/tf/tensordot