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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def bounding_ellipsoids(points, pointvol=0., vol_dec=0.5, vol_check=2.):
 """ Calculate a set of ellipsoids that bound the collection of points. Parameters points : `~numpy.ndarray` with shape (npoints, ndim) A set of coordinates. pointvol : float, optional Volume represented by a single point. When provided, used to set a minimum bound on the ellipsoid volume as `npoints * pointvol`. Default is `0.`. vol_dec : float, optional The required fractional reduction in volume after splitting an ellipsoid in order to to accept the split. Default is `0.5`. vol_check : float, optional The factor used to when checking whether the volume of the original bounding ellipsoid is large enough to warrant more trial splits via `ell.vol > vol_check * npoints * pointvol`. Default is `2.0`. Returns ------- mell : :class:`MultiEllipsoid` object The :class:`MultiEllipsoid` object used to bound the collection of points. """


    if not HAVE_KMEANS:
        raise ValueError("scipy.cluster.vq.kmeans2 is required to compute "
                         "ellipsoid decompositions.")  # pragma: no cover

    # Calculate the bounding ellipsoid for the points possibly
    # enlarged to a minimum volume.
    ell = bounding_ellipsoid(points, pointvol=pointvol)

    # Recursively split the bounding ellipsoid until the volume of each
    # split no longer decreases by a factor of `vol_dec`.
    ells = _bounding_ellipsoids(points, ell, pointvol=pointvol,
                                vol_dec=vol_dec, vol_check=vol_check)

    return MultiEllipsoid(ells=ells)