ilt {compositions}

Isometric log transform

Description

Compute the isometric log transform of a vector (dataset) of amounts and its inverse.

Usage

          ilt( x ,...)
          iltInv( z ,... )
          

Arguments

x

a vector or data matrix of amounts

z

the ilt-transform of a vector or data matrix of ilt-transforms of amounts

...

generic arguments, not used.

Details

The ilt-transform maps D amounts (considered in log geometry) isometrically to a D dimensional euclidean vector. The ilt is part of the aplus framework.
The data can then be analysed in this transformation by all classical multivariate analysis tools. The interpretation of the results is easy since the relation to the original variables is preserved.

The isometric log transform is given by

ilt(x)_i := \ln x_i

Value

ilt gives the isometric log transform, i.e. simply the log of the argument, whereas iltInv gives amounts with the given ilt, i.e. simply the exp of the argument.

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

ilr, iit, aplus

Examples

(tmp <- ilt(c(1,2,3)))
iltInv(tmp)
iltInv(tmp) - c(1,2,3) # 0
data(Hydrochem)
cdata <- Hydrochem[,6:19]
pairs(ilt(cdata))