clr               package:compositions               R Documentation

_U_n_c_e_n_t_e_r_e_d _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 uncentered log ratio transform of a (dataset of)
     composition(s) and its inverse.

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

               ult( x )
               ult.inv( z )
               Kappa( x )
               

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

       x: a composition or a data matrix of compositions, not
          necessarily closed

       z: the ult-transform of a composition or  a data matrix of
          clr-transforms of compositions, not necessarily centered

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

     The ult-transform is simply the elementwise log of the closed
     composition. The ult has some important properties in the scope of
     Information Theory.

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

     'ult' gives the uncentered log transform,
      'ult.inv' gives closed compositions with the given ult-transforms
      'Kappa' gives the difference between the clr and the ult
     transform. It is quite linked to information measures.

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

     'ilr','alr','apt'

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

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

