code: def approximate_cholesky(self, epsilon=1e-6):
          r
          # compute the Eigenvalues of C0 using Schur factorization
          Wk = self._C_k[self._columns, :]
          L0 = spd_inv_split(Wk, epsilon=epsilon)
          L = np.dot(self._C_k, L0)
  
          return L
docs: r""" Compute low-rank approximation to the Cholesky decomposition of target matrix.
  
          The decomposition will be conducted while ensuring that the spectrum of `A_k^{-1}` is positive.
  
          Parameters
          ----------
          epsilon : float, optional, default 1e-6
              Cutoff for eigenvalue norms. If negative eigenvalues occur, with norms larger than epsilon, the largest
              negative eigenvalue norm will be used instead of epsilon, i.e. a band including all negative eigenvalues
              will be cut off.
  
          Returns
          -------
          L : ndarray((n,m), dtype=float)
              Cholesky matrix such that `A \approx L L^{\top}`. Number of columns :math:`m` is most at the number of columns
              used in the Nystroem approximation, but may be smaller depending on epsilon.