mintvmon              package:ftnonpar              R Documentation

_M_i_n_i_m_i_z_a_t_i_o_n _o_f _t_o_t_a_l _v_a_r_i_a_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Finds a function vector which minimizes the total variation of 
     the function or a derivative under multiresolution constraints and
     monotonicity and convexity constraints.

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

     mintvmon(y, sigma = -1, DYADIC = TRUE, thresh = -1, method = 2, MONCONST = TRUE, CONVCONST = FALSE)

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

       y: observed values (ordered by value of independent variable).

   sigma: if set to a positive value the standard deviation is set to
          sigma and not estimated from the data

  DYADIC: logical, if T (default) the multiresolution constraints are
          only verifeid on intervals with dyadic endpoints

  thresh: if set to a positive value other thresholds for the
          multiresolution criterion than the default
          sqrt(2*log(n))*sigma can be used.

  method: Number of derivative the total variation of which is
          minimzed. Possible values are 0,1,2. Higher values lead to
          numerical inconsistencies.

MONCONST: logical, if T (default) additional monotonicty constraints
          are gathered from minimzing the total variation of f. Makes
          only sense, if method is 1 or 2.

CONVCONST: logical, if T (default) additional convexity constraints are
          gathered from minimzing the total variation of f'. Makes only
          sense, if method is 2.

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

     A list with components 

y        : The approximation of the given data

derivsign: Vector of 1 and -1, monotonicty constraints used if MONCONST
          was true

secsign  : Vector of 1 and -1, convexity constraints used if CONVCONST
          was true

jact     : Left endpoints of active multiresolution constraints for the
          final approximation

kact     : Right endpoints of active multiresolution constraints for
          the final approximation

signact  : Vector of 1 and -1, gives for each active multiresolution
          constraints, if the residuals on that interval attain upper
          or lower bound

pl       : Left endpoint of piecewise constant intervals of the 
          derivative of f being minmized

pr       : Right  endpoint of piecewise constant intervals of the
          derivative of f being minmized

_A_u_t_h_o_r(_s):

     Arne Kovac

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

     Kovac, A. (2003) Minimizing Total Variation under Multiresolution
     Conditions

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

     'pmreg'

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

     data(djdata)
     djdoppler.tv0 <- mintvmon(djdoppler,method=0)
     djdoppler.tv1 <- mintvmon(djdoppler,method=1)
     djdoppler.tv2 <- mintvmon(djdoppler)
     par(mfrow=c(2,2))
     plot(djdoppler,col="lightgrey")
     plot(djdoppler,col="lightgrey")
     lines(djdoppler.tv0$y,col="blue")
     plot(djdoppler,col="lightgrey")
     lines(djdoppler.tv1$y,col="green")
     plot(djdoppler,col="lightgrey")
     lines(djdoppler.tv2$y,col="red")

