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jax.numpy.tensordot — JAX documentation

jax.numpy.tensordot(a, b, 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:

• a (Array | ndarray | bool | number | bool | int | float | complex) – N-dimensional array

• b (Array | ndarray | bool | number | bool | int | float | complex) – M-dimensional array

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

• precision (None | str | Precision | tuple[str, str] | tuple[Precision, Precision] | DotAlgorithm | DotAlgorithmPreset) – 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 a and b.

• preferred_element_type (str | type[Any] | dtype | SupportsDType | 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

Examples

>>> x1 = jnp.arange(24.).reshape(2, 3, 4)
>>> x2 = jnp.ones((3, 4, 5))
>>> jnp.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.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 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.outer(x1, x2)
Array([[1, 2, 3],
       [2, 4, 6]], dtype=int32)

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