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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_eig(self, epsilon=1e-6):
 """ Compute low-rank approximation of the eigenvalue decomposition of target matrix. If spd is True, 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 ------- s : ndarray((m,), dtype=float) approximated eigenvalues. Number of eigenvalues returned is at most the number of columns used in the Nystroem approximation, but may be smaller depending on epsilon. W : ndarray((n,m), dtype=float) approximated eigenvectors in columns. Number of eigenvectors returned is at most the number of columns used in the Nystroem approximation, but may be smaller depending on epsilon. """

        L = self.approximate_cholesky(epsilon=epsilon)
        LL = np.dot(L.T, L)
        s, V = np.linalg.eigh(LL)
        # sort
        s, V = sort_by_norm(s, V)

        # back-transform eigenvectors
        Linv = np.linalg.pinv(L.T)
        V = np.dot(Linv, V)

        # normalize eigenvectors
        ncol = V.shape[1]
        for i in range(ncol):
            if not np.allclose(V[:, i], 0):
                V[:, i] /= np.sqrt(np.dot(V[:, i], V[:, i]))

        return s, V