jax.numpy.linalg.tensordot#

jax.numpy.linalg.tensordot(x1, x2, /, *, axes=2, precision=None, preferred_element_type=None)[source]#

Compute the tensor dot product of two N-dimensional arrays.

JAX implementation of numpy.linalg.tensordot().

Parameters:

  • x1 (ArrayLike) – N-dimensional array

  • x2 (ArrayLike) – M-dimensional array

  • axes (int | tuple[Sequence[int], Sequence[int]]) – integer or tuple of sequences of integers. If an integer k, then sum over the last k axes of x1 and the first k axes of x2, in order. If a tuple, then axes[0] specifies the axes of x1 and axes[1] specifies the axes of x2.

  • precision (PrecisionLike | None) – either None (default), which means the default precision for the backend, a Precision enum value (Precision.DEFAULT, Precision.HIGH or Precision.HIGHEST) or a tuple of two such values indicating precision of x1 and x2.

  • preferred_element_type (DTypeLike | None | None) – either None (default), which means the default accumulation type for the input types, or a datatype, indicating to accumulate results to and return a result with that datatype.

Returns:

array containing the tensor dot product of the inputs

Return type:

Array

See also

Examples

>>> x1 = jnp.arange(24.).reshape(2, 3, 4)
>>> x2 = jnp.ones((3, 4, 5))
>>> jnp.linalg.tensordot(x1, x2)
Array([[ 66.,  66.,  66.,  66.,  66.],
       [210., 210., 210., 210., 210.]], dtype=float32)

Equivalent result when specifying the axes as explicit sequences:

>>> jnp.linalg.tensordot(x1, x2, axes=([1, 2], [0, 1]))
Array([[ 66.,  66.,  66.,  66.,  66.],
       [210., 210., 210., 210., 210.]], dtype=float32)

Equivalent result via einsum():

>>> jnp.einsum('ijk,jkm->im', x1, x2)
Array([[ 66.,  66.,  66.,  66.,  66.],
       [210., 210., 210., 210., 210.]], dtype=float32)

Setting axes=1 for two-dimensional inputs is equivalent to a matrix multiplication:

>>> x1 = jnp.array([[1, 2],
...                 [3, 4]])
>>> x2 = jnp.array([[1, 2, 3],
...                 [4, 5, 6]])
>>> jnp.linalg.tensordot(x1, x2, axes=1)
Array([[ 9, 12, 15],
       [19, 26, 33]], dtype=int32)
>>> x1 @ x2
Array([[ 9, 12, 15],
       [19, 26, 33]], dtype=int32)

Setting axes=0 for one-dimensional inputs is equivalent to jax.numpy.linalg.outer():

>>> x1 = jnp.array([1, 2])
>>> x2 = jnp.array([1, 2, 3])
>>> jnp.linalg.tensordot(x1, x2, axes=0)
Array([[1, 2, 3],
       [2, 4, 6]], dtype=int32)
>>> jnp.linalg.outer(x1, x2)
Array([[1, 2, 3],
       [2, 4, 6]], dtype=int32)