R: Additive planar transform

apt {compositions} | R Documentation

## Additive planar transform

### Description

Compute the additive planar transform of a (dataset of) compositions or its inverse.

### Usage

              apt( x ,...)
              aptInv( z ,..., orig=NULL)

### Arguments

`x` | a composition or a matrix of compositions, not necessarily closed
`z` | the apt-transform of a composition or a matrix of alr-transforms of compositions
`...` | generic arguments, not used.
`orig` | a compositional object which should be mimicked by the inverse transformation. It is especially used to reconstruct the names of the parts.

### Details

The apt-transform maps a composition in the D-part real-simplex linearly to a D-1 dimensional 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 not relying on distances. See `cpt` and `ipt` for alternatives. The interpretation of the results is easy since the relation to the first D-1 original variables is preserved.

The additive planar transform is given by

apt(x)_i := clo(x)_i, i=1,…,D-1

### Value

`apt` gives the centered planar transform, `aptInv` gives closed compositions with the given apt-transforms

### Author(s)

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

`alr`,`cpt`,`ipt`

### Examples

    (tmp <- apt(c(1,2,3)))
    aptInv(tmp)
    aptInv(tmp) - clo(c(1,2,3)) # 0
    data(Hydrochem)
    cdata <- Hydrochem[,6:19]
    pairs(apt(cdata),pch=".")

[Package compositions version 1.40-2 Index]