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# tf.tensordot

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.