tf.tensordot

TensorFlow 1 version View source on GitHub

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]).

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).

A Tensor with the same type as a.

ValueError If the shapes of a, b, and axes are incompatible.
IndexError If the values in axes exceed the rank of the corresponding tensor.