lle                 package:funfits                 R Documentation

_C_a_l_c_u_l_a_t_e_s _l_o_c_a_l _L_y_a_p_u_n_o_v _e_x_p_o_n_e_n_t_s _f_o_r _p_l_o_t_t_i_n_g.

_U_s_a_g_e:

     lle(jac, model=1, nprod=c(5, 10, 20, 40, 80), skip, statevector=F, 
     lags=NA)

_A_r_g_u_m_e_n_t_s:

     jac: Jacobian matrix or a nnreg fit. 

   model: Model number of fit used to calculate Jacobians. 

   nprod: Vector of LLE products of Jacobians. 

    skip: Columns of Jacobian matrix to skip in calculating LLEs. For
          example, skip the columns associated with forcing functions. 

statevector: If false, a time-delay reconstruction model is assumed and
          a Jacobian matrix n by d is expected, where n is the length
          of the time series and d is the dimension of the state space.
           If true, a state space vector model is assumed and a
          Jacobian matrix n by d^2  is expected. 

    lags: Lagged time values used in the Jacobian matrix. 

_V_a_l_u_e:

   local: Matrix of LLEs with columns corresponding to the LLEs of the
          nprod values. 

   nprod: Vector of LLE products of Jacobians. 

     glb: Global Lyapunov exponent. 

   model: Model number used to calculate Jacobians. 

_R_e_f_e_r_e_n_c_e_s:

     S. Ellner, D.W. Nychka, and A.R. Gallant. 1992.  LENNS,  a program
      to  estimate  the  dominant  Lyapunov exponent of noisy nonlinear
     systems from time series  data.  Institute of  Statistics  Mimeo
     Series #2235, Statistics Department, North Carolina State
     University, Raleigh, NC 27695-8203.

_S_e_e _A_l_s_o:

     make.lle

_E_x_a_m_p_l_e_s:

     make.lags(rossler.state[1:200,1],c(1,2,3)) -> data.r  # create
     # 3-d time delay vector model of the x variable of rossler system.
     nnreg(data.r$x,data.r$y,5,5) -> fit # fit time series model using nnreg.
     jac<- predict(fit, derivative=1) 
     lle(jac) -> rossler.lle  # LLEs of Rossler data
     summary(lle)
     plot(rossler.lle)  # plot LLEs

     # here is an easier way
     nlar( rossler[1:200], lags=1:3, method="nnreg", k1=5)-> ou
     lle( out) -> rossler.lle

