r"""
    Clip inputs by its L2 norm when the L2 norm is larger than the threshold value (defined by clip_norm).
    If it is less than the threshold, inputs are not modified. If it is applied, the operation is represented as

    .. math::
      y = N \times \frac{x}{\|x\|_2}.

    where :math:`x` is the input, :math:`y` is the output,
    and :math:`N` is `clip_norm`. this is the case that `axes` is not set.
    When `axes` is set, the norm is computed over `axes`.

    Args:
        x (Variable): An input variable.
        clip_norm (`Variable` or `float`): An input scalar variable or float value. Must be positive.
        axis (None, int or tuple of ints): Axis or axes along which the reduction is performed. Passing the default value `None` will reduce all dimensions.

    Returns:
        ~nnabla.Variable: N-D array.

def clip_by_norm(x, clip_norm, axis=None):
    r"""
    Clip inputs by its L2 norm when the L2 norm is larger than the threshold value (defined by clip_norm).
    If it is less than the threshold, inputs are not modified. If it is applied, the operation is represented as

    .. math::
      y = N \times \frac{x}{\|x\|_2}.

    where :math:`x` is the input, :math:`y` is the output,
    and :math:`N` is `clip_norm`. this is the case that `axes` is not set.
    When `axes` is set, the norm is computed over `axes`.

    Args:
        x (Variable): An input variable.
        clip_norm (`Variable` or `float`): An input scalar variable or float value. Must be positive.
        axis (None, int or tuple of ints): Axis or axes along which the reduction is performed. Passing the default value `None` will reduce all dimensions.

    Returns:
        ~nnabla.Variable: N-D array.

    """
    from .function_bases import pow_scalar as pow_scalar_base
    from .function_bases import maximum2 as maximum2_base
    from .function_bases import maximum_scalar as maximum_scalar_base
    from .function_bases import sum as sum_base
    from ._variable import Variable as Variable_base
    from ._nd_array import NdArray as NdArray_base

    if axis is None:
        axis = range(x.ndim)
    elif not hasattr(axis, '__iter__'):
        axis = [axis]
    x_norm = pow_scalar_base(sum_base(x**2.0, axis, True), 0.5)
    if isinstance(clip_norm, (Variable_base, NdArray_base)):
        y = x * clip_norm / maximum2_base(x_norm, clip_norm)
    else:
        if clip_norm <= 0:
            raise ValueError("clip_norm must be positive.")
        y = x * clip_norm / maximum_scalar_base(x_norm, clip_norm)
    return y