Function cross

xarray/computation/computation.py:316–480

Compute the cross product of two (arrays of) vectors. The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular to both `a` and `b`. The vectors in `a` and `b` are defined by the values along the dimension `dim` and can have sizes 1, 2 or 3. Where the size of ei

(
    a: DataArray | Variable, b: DataArray | Variable, *, dim: Hashable
)

def cross(
    a: DataArray | Variable, b: DataArray | Variable, *, dim: Hashable
) -> DataArray | Variable:
    """
    Compute the cross product of two (arrays of) vectors.

    The cross product of `a` and `b` in :math:`R^3` is a vector
    perpendicular to both `a` and `b`. The vectors in `a` and `b` are
    defined by the values along the dimension `dim` and can have sizes
    1, 2 or 3. Where the size of either `a` or `b` is
    1 or 2, the remaining components of the input vector is assumed to
    be zero and the cross product calculated accordingly. In cases where
    both input vectors have dimension 2, the z-component of the cross
    product is returned.

    Parameters
    ----------
    a, b : DataArray or Variable
        Components of the first and second vector(s).
    dim : hashable
        The dimension along which the cross product will be computed.
        Must be available in both vectors.

    Examples
    --------
    Vector cross-product with 3 dimensions:

    >>> a = xr.DataArray([1, 2, 3])
    >>> b = xr.DataArray([4, 5, 6])
    >>> xr.cross(a, b, dim="dim_0")
    <xarray.DataArray (dim_0: 3)> Size: 24B
    array([-3,  6, -3])
    Dimensions without coordinates: dim_0

    Vector cross-product with 3 dimensions but zeros at the last axis
    yields the same results as with 2 dimensions:

    >>> a = xr.DataArray([1, 2, 0])
    >>> b = xr.DataArray([4, 5, 0])
    >>> xr.cross(a, b, dim="dim_0")
    <xarray.DataArray (dim_0: 3)> Size: 24B
    array([ 0,  0, -3])
    Dimensions without coordinates: dim_0

    Multiple vector cross-products. Note that the direction of the
    cross product vector is defined by the right-hand rule:

    >>> a = xr.DataArray(
    ...     [[1, 2, 3], [4, 5, 6]],
    ...     dims=("time", "cartesian"),
    ...     coords=dict(
    ...         time=(["time"], [0, 1]),
    ...         cartesian=(["cartesian"], ["x", "y", "z"]),
    ...     ),
    ... )
    >>> b = xr.DataArray(
    ...     [[4, 5, 6], [1, 2, 3]],
    ...     dims=("time", "cartesian"),