compositions (version 2.0-8)

apt: Additive planar transform

Description

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

Usage

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

Value

apt gives the centered planar transform,

aptInv gives closed compositions with the given apt-transforms

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.

Author

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

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 $$apt(x{)}_i:=clo(x{)}_i,i=1,\dots ,D-1$$

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, tools:::Rd_expr_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=".")