code: def _svd_sym_koopman(K, C00_train, Ctt_train):
      
      from pyemma._ext.variational.solvers.direct import spd_inv_sqrt
      # reweight operator to empirical distribution
      C0t_re = mdot(C00_train, K)
      # symmetrized operator and SVD
      K_sym = mdot(spd_inv_sqrt(C00_train), C0t_re, spd_inv_sqrt(Ctt_train))
      U, S, Vt = np.linalg.svd(K_sym, compute_uv=True, full_matrices=False)
      # projects back to singular functions of K
      U = mdot(spd_inv_sqrt(C00_train), U)
      Vt = mdot(Vt,spd_inv_sqrt(Ctt_train))
      return U, S, Vt.T
docs: Computes the SVD of the symmetrized Koopman operator in the empirical distribution.