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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_ellipsoid(points, pointvol=0.):
 """ Calculate the bounding ellipsoid containing a collection of points. Parameters points : `~numpy.ndarray` with shape (npoints, ndim) A set of coordinates. pointvol : float, optional The minimum volume occupied by a single point. When provided, used to set a minimum bound on the ellipsoid volume as `npoints * pointvol`. Default is `0.`. Returns ------- ellipsoid : :class:`Ellipsoid` The bounding :class:`Ellipsoid` object. """


    npoints, ndim = points.shape

    # Check for valid `pointvol` value if provided.
    if pointvol < 0.:
        raise ValueError("You must specify a non-negative value "
                         "for `pointvol`.")

    # If there is only a single point, return an n-sphere with volume
    # `pointvol` centered at the point.
    if npoints == 1:
        if pointvol > 0.:
            ctr = points[0]
            r = np.exp((np.log(pointvol) - logvol_prefactor(ndim)) / ndim)
            covar = r**2 * np.identity(ndim)
            return Ellipsoid(ctr, covar)
        else:
            raise ValueError("Cannot compute a bounding ellipsoid to a "
                             "single point if `pointvol` is not specified.")

    # Calculate covariance of points.
    ctr = np.mean(points, axis=0)
    cov = mle_cov(points, rowvar=False)

    # When ndim = 1, `np.cov` returns a 0-d array. Make it a 1x1 2-d array.
    if ndim == 1:
        cov = np.atleast_2d(cov)

    # For a ball of uniformly distributed points, the sample covariance
    # will be smaller than the true covariance by a factor of 1/(n+2)
    # [see, e.g., goo.gl/UbsjYl]. Since we are assuming all points are
    # uniformly distributed within the unit cube, they are uniformly
    # distributed within any sub-volume within the cube. We expand
    # our sample covariance `cov` to compensate for this.
    cov *= (ndim + 2)

    # Define the axes of our ellipsoid. Ensures that `cov` is
    # nonsingular to deal with pathological cases where the ellipsoid has
    # "zero" volume. This can occur when `npoints <= ndim` or when enough
    # points are linear combinations of other points.
    covar = np.array(cov)
    for trials in range(100):
        try:
            # Check if matrix is invertible.
            am = lalg.pinvh(covar)
            l, v = lalg.eigh(covar)  # compute eigenvalues/vectors
            if np.all((l > 0.) & (np.isfinite(l))):
                break
            else:
                raise RuntimeError("The eigenvalue/eigenvector decomposition "
                                   "failed!")
        except:
            # If the matrix remains singular/unstable,
            # suppress the off-diagonal elements.
            coeff = 1.1**(trials+1) / 1.1**100
            covar = (1. - coeff) * cov + coeff * np.eye(ndim)
            pass
    else:
        warnings.warn("Failed to guarantee the ellipsoid axes will be "
                      "non-singular. Defaulting to a sphere.")
        am = np.eye(ndim)

    # Calculate expansion factor necessary to bound each point.
    # Points should obey `(x-v)^T A (x-v) <= 1`, so we calculate this for
    # each point and then scale A up or down to make the
    # "outermost" point obey `(x-v)^T A (x-v) = 1`. This can be done
    # quickly using `einsum` and `tensordot` to iterate over all points.
    delta = points - ctr
    f = np.einsum('...i, ...i', np.tensordot(delta, am, axes=1), delta)
    fmax = np.max(f)

    # Due to round-off errors, we actually scale the ellipsoid so the
    # outermost point obeys `(x-v)^T A (x-v) < 1 - (a bit) < 1`.
    one_minus_a_bit = 1. - SQRTEPS

    if fmax > one_minus_a_bit:
        covar *= fmax / one_minus_a_bit

    # Initialize our ellipsoid.
    ell = Ellipsoid(ctr, covar)

    # Expand our ellipsoid to encompass a minimum volume.
    if pointvol > 0.:
        minvol = npoints * pointvol
        if ell.vol < minvol:
            ell.scale_to_vol(minvol)

    return ell