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TensorFlow 1 version View source on GitHub

Tensor contraction of a and b along specified axes.


  • tf.compat.v1.linalg.tensordot
  • tf.compat.v1.tensordot
  • tf.compat.v2.linalg.tensordot
  • tf.compat.v2.tensordot
  • tf.linalg.tensordot

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.

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: 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.
  • 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.