Additive planar transform
Compute the additive planar transform of a (dataset of) compositions or its inverse.
apt( x ,...)
aptInv( z ,..., orig=gsi.orig(z))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. |
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 additive planar transform is given by
apt(x)_i := clo(x)_i, i=1,…,D-1
apt gives the centered planar transform,
aptInv gives closed compositions with the given apt-transforms
K.Gerald v.d. Boogaart http://www.stat.boogaart.de
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.
(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=".")
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