ipt               package:compositions               R Documentation

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

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

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

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

               ipt( x , V = ilrBase(x) )
               ipt.inv( z , V = ilrBase(z=z) )
               ucipt.inv( z , V = ilrBase(z=z) )
               

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

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

       z: the ipt-transform of a composition or a data matrix of
          ipt-transforms of compositions

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

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

     The ipt-transform maps a composition in the D-part real-simplex
     isometrically to a D-1 dimensonal euclidian vector. Although the
     transformation does not reach the whole R^{D-1}, resulting
     covariance matrices are typically of full rank. 
       The data can then be analysed in this transformation by all
     classical multivariate analysis tools. However, interpretation of
     results may be difficult, since the transform does not keep the
     variable names, given that there is no one-to-one relation between
     the original parts and each transformed variables. See 'cpt' and
     'apt' for alternatives. 

     The isometric planar transform is given by

                         ipt(x) := V^t cpt(x)

     with 'cpt'(x) the centred planar 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:

     'ipt' gives the centered planar transform, 'ipt.inv' gives closed
     compositions with with the given ipt-transforms, 'ucipt.inv'
     unconstrained ipt.inv does the same as ipt.inv but sets illegal
     values to NA rather then giving an error. This is a workaround to
     allow procedures not honoring the constraints of the space.

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

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

     'ilr','ilrBase', 'cpt'

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

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

