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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/r2.3/api_docs/python/tf/tensordot