ilt               package:compositions               R Documentation

_I_s_o_m_e_t_r_i_c _l_o_g _t_r_a_n_s_f_o_r_m

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

     Compute the isometric log  transform of a vector (dataset) of
     amounts and its inverse.

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

               ilt( x )
               ilt.inv( z  )
               

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

       x: a vector or data matrix of amounts

       z: the ilt-transform of a vector or data matrix of
          ilt-transforms of amounts

_D_e_t_a_i_l_s:

     The ilt-transform maps  D amounts (considered in log geometry)
     isometrically to a D dimensional euclidean vector. The 'ilt' is
     part of the 'aplus' framework. 
       The data can then be analysed in this transformation by all
     classical multivariate analysis tools. The interpretation of the
     results is easy since the relation to the original variables is
     preserved. 

     The isometric log transform is given by

                          ilt(x)_i := ln x_i

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

     'ilt' gives the isometric log transform, i.e. simply the log of
     the argument, 'ilt.inv' gives amounts with the given ilt, i.e.
     simple the exp of the argument

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

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

     'ilr', 'iit', 'aplus'

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

     (tmp <- ilt(c(1,2,3)))
     ilt.inv(tmp)
     ilt.inv(tmp) - c(1,2,3) # 0
     data(Hydrochem)
     cdata <- Hydrochem[,6:19]
     pairs(ilt(cdata)) 

