Function dot

xarray/computation/computation.py:484–679

Generalized dot product for xarray objects. Like ``np.einsum``, but provides a simpler interface based on array dimension names. Parameters ---------- *arrays : DataArray or Variable Arrays to compute. dim : str, iterable of hashable, "..." or None, optional Whic

(
    *arrays,
    dim: Dims = None,
    **kwargs: Any,
)

@deprecate_dims
def dot(
    *arrays,
    dim: Dims = None,
    **kwargs: Any,
):
    """Generalized dot product for xarray objects. Like ``np.einsum``, but
    provides a simpler interface based on array dimension names.

    Parameters
    ----------
    *arrays : DataArray or Variable
        Arrays to compute.
    dim : str, iterable of hashable, "..." or None, optional
        Which dimensions to sum over. Ellipsis ('...') sums over all dimensions.
        If not specified, then all the common dimensions are summed over.
    **kwargs : dict
        Additional keyword arguments passed to ``numpy.einsum`` or
        ``dask.array.einsum``

    Returns
    -------
    DataArray

    See Also
    --------
    numpy.einsum
    dask.array.einsum
    opt_einsum.contract

    Notes
    -----
    We recommend installing the optional ``opt_einsum`` package, or alternatively passing ``optimize=True``,
    which is passed through to ``np.einsum``, and works for most array backends.

    **Coordinate Handling**

    Like all xarray operations, ``dot`` automatically aligns array coordinates.
    Coordinates are aligned by their **values**, not their order. By default, xarray uses
    an inner join, so only overlapping coordinate values are included. With the default
    ``arithmetic_join="inner"``, ``dot(a, b)`` is mathematically equivalent to ``(a * b).sum()``
    over the specified dimensions. See :ref:`math automatic alignment` for more details.

    Examples
    --------
    >>> da_a = xr.DataArray(np.arange(3 * 2).reshape(3, 2), dims=["a", "b"])
    >>> da_b = xr.DataArray(np.arange(3 * 2 * 2).reshape(3, 2, 2), dims=["a", "b", "c"])
    >>> da_c = xr.DataArray(np.arange(2 * 3).reshape(2, 3), dims=["c", "d"])

    >>> da_a
    <xarray.DataArray (a: 3, b: 2)> Size: 48B
    array([[0, 1],
           [2, 3],
           [4, 5]])
    Dimensions without coordinates: a, b

    >>> da_b
    <xarray.DataArray (a: 3, b: 2, c: 2)> Size: 96B
    array([[[ 0,  1],