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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 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