idt               package:compositions               R Documentation

_I_s_o_m_e_t_r_i_c _d_e_f_a_u_l_t _t_r_a_n_s_f_o_r_m

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

     Compute the isometric default transform of a vector (or dataset)
     of compositions or amounts in the selected class.

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

               idt(x,...)
               ## Default S3 method:
               idt( x,... )
               ## S3 method for class 'acomp':
               idt( x ,...)
               ## S3 method for class 'rcomp':
               idt( x ,...)
               ## S3 method for class 'aplus':
               idt( x ,...)
               ## S3 method for class 'rplus':
               idt( x ,...)
               ## S3 method for class 'rmult':
               idt( x ,...)
               ## S3 method for class 'factor':
               idt( x ,...)
               idt.inv(x,orig,...)
               ## Default S3 method:
               idt.inv( x ,orig,...)
               ## S3 method for class 'acomp':
               idt.inv( x ,orig,...)
               ## S3 method for class 'rcomp':
               idt.inv( x ,orig,...)
               ## S3 method for class 'aplus':
               idt.inv( x ,orig,...)
               ## S3 method for class 'rplus':
               idt.inv( x ,orig,...)
               ## S3 method for class 'rmult':
               idt.inv( x ,orig,...)

               

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

       x: a classed amount or composition, to be transformed with its
          isometric default transform, or its inverse

     ...: generic arguments past to underlying functions

    orig: a compositional object which should be mimicked by the
          inverse transformation. It is used to determine the
          backtransform to be used, and eventually to reconstruct the
          names of the parts. It is the generic argument. Typically the
          orig-argument is the dataset that has been transformed in the
          first place.

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

     The general idea of this package is to analyse the same data with
     different geometric concepts, in a fashion as similar as possible.
     For each of the four concepts there exists an isometric transform
     expressing the geometry in a full-rank euclidean vector space.
     Such a transformation is computed  by 'idt'. For 'acomp' the
     transform is 'ilr', for 'rcomp' it is 'ipt', for  'aplus' it is
     'ilt', and for 'rplus' it is 'iit'. Keep in mind that the
     transform does not keep the variable names, since there is no
     guaranteed  one-to-one relation between the original parts and
     each transformed variable. 
      The inverse 'idt.inv' is intended to allow for an "easy" and
     automatic  back-transformation, without intervention of the user.
     The argument 'orig'  (the one determining the behaviour of
     'idt.inv' as a generic function)  tells the function which
     back-transformation should be applied, and gives the column names
     of 'orig' to the back-transformed values of 'x'. Therefore, it is
     very conventient to give the original classed data set used in the
     analysis as 'orig'.

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

     A corresponding matrix of row-vectors containing the transforms.

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

     R. Tolosana-Delgado, K.Gerald v.d. Boogaart <URL:
     http://www.stat.boogaart.de>

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

     van den Boogaart, K.G. and R. Tolosana-Delgado (2007)
     "compositions": a unified  R package to analyze Compositional
     Data, _Computers & Geosciences_.  (in press).

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

     'cdt', 'ilr', 'ipt', 'ilt', 'cdt.inv', 'ilr.inv', 'ipt.inv', 
     'ilt.inv', 'iit.inv'

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

     ## Not run: 
     # the idt is defined by
     idt         <- function(x) UseMethod("idt",x)
     idt.default <- function(x) x
     idt.acomp   <- function(x) ilr(x) 
     idt.rcomp   <- function(x) ipt(x) 
     idt.aplus   <- ilt 
     idt.rplus   <- iit 
     ## End(Not run)
     idt(acomp(1:5))
     idt(rcomp(1:5))
       data(Hydrochem)
       x = Hydrochem[,c("Na","K","Mg","Ca")]
       y = acomp(x)
       z = idt(y)
       y2 = idt.inv(z,y)
       par(mfrow=c(2,2))
       for(i in 1:4){plot(y[,i],y2[,i])}

