R: Isometric default transform

idt {compositions} | R Documentation

## Isometric default transform

### Description

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

### Usage

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

### Arguments

`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.

### Details

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 `idtInv` 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 `idtInv` 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`.

### Value

A corresponding matrix of row-vectors containing the transforms.

### Author(s)

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

### References

van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, doi:10.1016/j.cageo.2006.11.017.

### See Also

`cdt`, `ilr`, `ipt`, `ilt`, `cdtInv`, `ilrInv`, `iptInv`, `iltInv`, `iitInv`

### Examples

    ## 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 = idtInv(z,y)
      par(mfrow=c(2,2))
      for(i in 1:4){plot(y[,i],y2[,i])}

[Package compositions version 1.40-3 Index]