Function vector_norm

numpy/linalg/_linalg.py:3502–3595

Computes the vector norm of a vector (or batch of vectors) ``x``. This function is Array API compatible. Parameters ---------- x : array_like Input array. axis : {None, int, 2-tuple of ints}, optional If an integer, ``axis`` specifies the axis (dimension) a

(x, /, *, axis=None, keepdims=False, ord=2)

@array_function_dispatch(_vector_norm_dispatcher)
def vector_norm(x, /, *, axis=None, keepdims=False, ord=2):
    """
    Computes the vector norm of a vector (or batch of vectors) ``x``.

    This function is Array API compatible.

    Parameters
    ----------
    x : array_like
        Input array.
    axis : {None, int, 2-tuple of ints}, optional
        If an integer, ``axis`` specifies the axis (dimension) along which
        to compute vector norms. If an n-tuple, ``axis`` specifies the axes
        (dimensions) along which to compute batched vector norms. If ``None``,
        the vector norm must be computed over all array values (i.e.,
        equivalent to computing the vector norm of a flattened array).
        Default: ``None``.
    keepdims : bool, optional
        If this is set to True, the axes which are normed over are left in
        the result as dimensions with size one. Default: False.
    ord : {int, float, inf, -inf}, optional
        The order of the norm. For details see the table under ``Notes``
        in `numpy.linalg.norm`.

    See Also
    --------
    numpy.linalg.norm : Generic norm function

    Examples
    --------
    >>> from numpy import linalg as LA
    >>> a = np.arange(9) + 1
    >>> a
    array([1, 2, 3, 4, 5, 6, 7, 8, 9])
    >>> b = a.reshape((3, 3))
    >>> b
    array([[1, 2, 3],
           [4, 5, 6],
           [7, 8, 9]])

    >>> LA.vector_norm(b)
    16.881943016134134
    >>> LA.vector_norm(b, ord=np.inf)
    9.0
    >>> LA.vector_norm(b, ord=-np.inf)
    1.0

    >>> LA.vector_norm(b, ord=0)
    9.0
    >>> LA.vector_norm(b, ord=1)
    45.0
    >>> LA.vector_norm(b, ord=-1)
    0.3534857623790153
    >>> LA.vector_norm(b, ord=2)
    16.881943016134134
    >>> LA.vector_norm(b, ord=-2)
    0.8058837395885292