clr2ilr             package:compositions             R Documentation

_C_o_n_v_e_r_t _b_e_t_w_e_e_n _c_l_r _a_n_d _i_l_r, _a_n_d _b_e_t_w_e_e_n _c_p_t _a_n_d _i_p_t. _A_c_t_s _i_n _v_e_c_t_o_r_s _a_n_d _i_n _b_i_l_i_n_e_a_r _f_o_r_m_s.

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

     Compute the centered log ratio transform of a (dataset of)
     isometric log-ratio transform(s) and its inverse. Equivalently, 
     compute centered and isometric planar transforms from each other.

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

     clr2ilr( x , V=ilrBase(x) )
     ilr2clr( z , V=ilrBase(z=z) )
     clrvar2ilr( varx , V=ilrBase(D=ncol(varx)) )
     ilrvar2clr( varz , V=ilrBase(D=ncol(varz)+1) )

               

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

       x: the clr/cpt-transform of composition(s)

       z: the ilr/ipt-transform of composition(s)

    varx: variance or covariance matrix of clr/cpt-transformed
          compositions

    varz: variance or covariance matrix of ilr/ipt-transformed
          compositions

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

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

     These functions perform a matrix multiplication with 'V' in an
     appropriate way.

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

     'clr2ilr' gives the ilr/ipt transform of the same composition(s),
      'ilr2clr' gives the clr/cpt transform of the same composition(s),
      'clrvar2ilr' gives the variance-/covariance-matrix of the ilr/ipt
     transform of the same compositional data set,
      'ilrvar2clr' gives the variance-/covariance-matrix of the clr/cpt
     transform of the same compositional data set.

_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:

     'ilr', 'ipt'

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

     data(SimulatedAmounts)
     ilr.inv(clr2ilr(clr(sa.lognormals)))-clo(sa.lognormals)
     clr.inv(ilr2clr(ilr(sa.lognormals)))-clo(sa.lognormals)
     ilrvar2clr(var(ilr(sa.lognormals)))-var(clr(sa.lognormals))
     clrvar2ilr(var(cpt(sa.lognormals)))-var(ipt(sa.lognormals))

