ilr               package:compositions               R Documentation

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

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

     Compute the isometric log ratio transform of a (dataset of)
     composition(s) and its inverse.

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

               ilr( x , V = ilrBase(x) )
               ilr.inv( z , V = ilrBase(z=z))
               

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

       x: a composition, not necessarily closed

       z: the ilr-transform of a composition

       V: a matrix, with columns giving the chosen basis of the
          clr-plane

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

     The ilr-transform maps a composition in the D-part
     Aitchison-simplex isometrically to a D-1 dimensonal euclidian
     vector. The data can then be analysed in this transformation by
     all classical multivariate analysis tools. However the
     interpretation of the results may be difficult, since there is no
     one-to-one relation between the original parts  and the
     transformed variables.

     The isometric logratio transform is given by

                         ilr(x) := V^t clr(x)

     with 'clr'(x) the centred log ratio transform and V a matrix which
     columns form an orthonormal  basis of the clr-plane. A default
     matrix V is given by 'ilrBase(\var{D})'.

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

     'ilr' gives the isometric log ratio transform, 'ilr.inv' gives
     closed compositions with the given ilr-transforms

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

     Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and C.
     Barcel'o-Vidal (2003) Isometric logratio transformations for
     compositional data analysis. _Mathematical Geology_, *35*(3)
     279-300
      Aitchison, J, C. Barcel'o-Vidal, J.J. Egozcue, V. Pawlowsky-Glahn
     (2002) A consise guide to the algebraic geometric structure of the
     simplex, the sample space for compositional data analysis, _Terra
     Nostra_, Schriften der Alfred Wegener-Stiftung, 03/2003

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

     'clr','alr','apt', 'ilrBase', <URL:
     http://ima.udg.es/Activitats/CoDaWork03>

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

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

