def approximate_cholesky(self, epsilon=1e-6):
        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.

        """
        # 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
def approximate_cholesky ( self , epsilon = 1e-6 ) : Wk = self . _C_k [ self . _columns , : ] L0 = spd_inv_split ( Wk , epsilon = epsilon ) L = np . dot ( self . _C_k , L0 ) return L
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.