ult               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 clr-transforms of
          compositions (or a data matrix), not necessarily centered

     ...: for generic use only

_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 of probability vectors (but might be mostly 
     misleading for exploratory analysis of compositions).

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

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

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

     K.Gerald v.d. Boogaart <URL: http://www.stat.boogaart.de>

_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))

