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 ,...)
              ## S3 method for class 'data.frame'
    idt( x ,...)
              idtInv(x,orig=gsi.orig(x),...)
              ## Default S3 method:
    idtInv( x ,orig=gsi.orig(x),...)
              ## S3 method for class 'acomp'
    idtInv( x ,orig=gsi.orig(x), V=gsi.getV(x),...)
              ## S3 method for class 'rcomp'
    idtInv( x ,orig=gsi.orig(x), V=gsi.getV(x),...)
              ## S3 method for class 'aplus'
    idtInv( x ,orig=gsi.orig(x),...)
              ## S3 method for class 'rplus'
    idtInv( x ,orig=gsi.orig(x),...)
              ## S3 method for class 'ccomp'
    idtInv( x ,orig=gsi.orig(x),...)
              ## S3 method for class 'rmult'
    idtInv( x ,orig=gsi.orig(x),...)
              ## S3 method for class 'factor'
    idtInv( x ,orig=gsi.orig(x), V=gsi.getV(x),...)
              ## S3 method for class 'data.frame'
    idtInv( x , orig=gsi.orig(x), ...)

### Arguments

`x` | a classed amount or composition, to be transformed with its isometric default transform, or its inverse; in case of the method for `data.frame` objects, the function attempts to track information about a previous class (in an attribute `origClass`, and if found, a transformation is tried with it; for factors, idt expands the factor according to the contrasts represented by `V`, or vice-versa.)
`...` | generic arguments past to underlying functions
`orig` | a compositional object which should be mimicked by the inverse transformation. It is the generic argument. Typically the `orig` argument is stored as an attribute in `x` and will be extracted automatically by this function; if this fails, `orig` can be set equal to the dataset that was transformed in the first place.
`V` | matrix of (transposed, inverted) logcontrasts; together with `orig`, it defines the back-transformation. Typically the `V` argument is stored as an attribute in `x` and will be extracted automatically by this function; if this fails, `V` must be manually set to the matrix V used in the idt/ilr/ipt calculations. Argument not used in amounts or counts geometries.

### 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. (Exception: idt.data.frame can return a data.frame if the input has no "origClass"-attribute)

### 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

`backtransform`, `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 2.0-4 Index]