Merge pull request jax-ml#24421 from jakevdp:cross-doc

PiperOrigin-RevId: 688175417

Author: Google-ML-Automation

jax/_src/numpy/lax_numpy.py

@@ -9544,10 +9544,82 @@ def outer(a: ArrayLike, b: ArrayLike, out: None = None) -> Array:
   a, b = util.promote_dtypes(a, b)
   return ravel(a)[:, None] * ravel(b)[None, :]
 
-@util.implements(np.cross)
+
 @partial(jit, static_argnames=('axisa', 'axisb', 'axisc', 'axis'))
 def cross(a, b, axisa: int = -1, axisb: int = -1, axisc: int = -1,
           axis: int | None = None):
+  r"""Compute the (batched) cross product of two arrays.
+
+  JAX implementation of :func:`numpy.cross`.
+
+  This computes the 2-dimensional or 3-dimensional cross product,
+
+  .. math::
+
+     c = a \times b
+
+  In 3 dimensions, ``c`` is a length-3 array. In 2 dimensions, ``c`` is
+  a scalar.
+
+  Args:
+    a: N-dimensional array. ``a.shape[axisa]`` indicates the dimension of
+       the cross product, and must be 2 or 3.
+    b: N-dimensional array. Must have ``b.shape[axisb] == a.shape[axisb]``,
+      and other dimensions of ``a`` and ``b`` must be broadcast compatible.
+    axisa: specicy the axis of ``a`` along which to compute the cross product.
+    axisb: specicy the axis of ``b`` along which to compute the cross product.
+    axisc: specicy the axis of ``c`` along which the cross product result
+      will be stored.
+    axis: if specified, this overrides ``axisa``, ``axisb``, and ``axisc``
+      with a single value.
+
+  Returns:
+    The array ``c`` containing the (batched) cross product of ``a`` and ``b``
+    along the specified axes.
+
+  See also:
+    - :func:`jax.numpy.linalg.cross`: an array API compatible function for
+      computing cross products over 3-vectors.
+
+  Examples:
+    A 2-dimensional cross product returns a scalar:
+
+    >>> a = jnp.array([1, 2])
+    >>> b = jnp.array([3, 4])
+    >>> jnp.cross(a, b)
+    Array(-2, dtype=int32)
+
+    A 3-dimensional cross product returns a length-3 vector:
+
+    >>> a = jnp.array([1, 2, 3])
+    >>> b = jnp.array([4, 5, 6])
+    >>> jnp.cross(a, b)
+    Array([-3,  6, -3], dtype=int32)
+
+    With multi-dimensional inputs, the cross-product is computed along
+    the last axis by default. Here's a batched 3-dimensional cross
+    product, operating on the rows of the inputs:
+
+    >>> a = jnp.array([[1, 2, 3],
+    ...                [3, 4, 3]])
+    >>> b = jnp.array([[2, 3, 2],
+    ...                [4, 5, 6]])
+    >>> jnp.cross(a, b)
+    Array([[-5,  4, -1],
+           [ 9, -6, -1]], dtype=int32)
+
+    Specifying axis=0 makes this a batched 2-dimensional cross product,
+    operating on the columns of the inputs:
+
+    >>> jnp.cross(a, b, axis=0)
+    Array([-2, -2, 12], dtype=int32)
+
+    Equivalently, we can independently specify the axis of the inputs ``a``
+    and ``b`` and the output ``c``:
+
+    >>> jnp.cross(a, b, axisa=0, axisb=0, axisc=0)
+    Array([-2, -2, 12], dtype=int32)
+  """
   # TODO(jakevdp): NumPy 2.0 deprecates 2D inputs. Follow suit here.
   util.check_arraylike("cross", a, b)
   if axis is not None: