Function dist

ot/utils.py:299–423

r"""Compute distance between samples in :math:`\mathbf{x_1}` and :math:`\mathbf{x_2}` .. note:: This function is backend-compatible and will work on arrays from all compatible backends for the following metrics: 'sqeuclidean', 'euclidean', 'cityblock', 'minkowski', 'cosine', 'co

(
    x1,
    x2=None,
    metric="sqeuclidean",
    p=2,
    w=None,
    backend="auto",
    nx=None,
    use_tensor=False,
)

def dist(
    x1,
    x2=None,
    metric="sqeuclidean",
    p=2,
    w=None,
    backend="auto",
    nx=None,
    use_tensor=False,
):
    r"""Compute distance between samples in :math:`\mathbf{x_1}` and :math:`\mathbf{x_2}`

    .. note:: This function is backend-compatible and will work on arrays
        from all compatible backends for the following metrics:
        'sqeuclidean', 'euclidean', 'cityblock', 'minkowski', 'cosine', 'correlation'.

    Parameters
    ----------

    x1 : array-like, shape (n1,d)
        matrix with `n1` samples of size `d`
    x2 : array-like, shape (n2,d), optional
        matrix with `n2` samples of size `d` (if None then :math:`\mathbf{x_2} = \mathbf{x_1}`)
    metric : str | callable, optional
        'sqeuclidean' or 'euclidean' on all backends. On numpy the function also
        accepts  from the scipy.spatial.distance.cdist function : 'braycurtis',
        'canberra', 'chebyshev', 'cityblock', 'correlation', 'cosine', 'dice',
        'euclidean', 'hamming', 'jaccard', 'kulczynski1', 'mahalanobis',
        'matching', 'minkowski', 'rogerstanimoto', 'russellrao', 'seuclidean',
        'sokalmichener', 'sokalsneath', 'sqeuclidean', 'wminkowski', 'yule'.
    p : float, optional
        p-norm for the Minkowski and the Weighted Minkowski metrics. Default value is 2.
    w : array-like, rank 1
        Weights for the weighted metrics.
    backend : str, optional
        Backend to use for the computation. If 'auto', the backend is
        automatically selected based on the input data. if 'scipy',
        the ``scipy.spatial.distance.cdist`` function is used (and gradients are
        detached).
    use_tensor : bool, optional
        If true use tensorized computation for the distance matrix which can
        cause memory issues for large datasets. Default is False and the
        parameter is used only for the 'cityblock' and 'minkowski' metrics.
    nx : Backend, optional
        Backend to perform computations on. If omitted, the backend defaults to that of `x1`.

    Returns
    -------

    M : array-like, shape (`n1`, `n2`)
        distance matrix computed with given metric

    """
    if nx is None:
        nx = get_backend(x1, x2)
    if x2 is None:
        x2 = x1
    if backend == "scipy":  # force scipy backend with cdist function