# jax.numpy.tensordot#

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 (ArrayLike) â€“ N-dimensional array

• b (ArrayLike) â€“ M-dimensional array

• axes (int | Sequence[int] | Sequence[Sequence[int]]) â€“ 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 (PrecisionLike) â€“ 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 (DTypeLike | None) â€“ 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)
```