Isometric identity transform

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Description

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

Usage

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          iit( x ,...)
          iitInv( z ,... )
          

Arguments

x

a vector or data matrix of amounts

z

the iit-transform of a vector or data.matrix of iit-transforms of amounts

...

generic arguments, to pass to other functions.

Details

The iit-transform maps D amounts (considered in a real geometry) isometrically to a D dimensonal euclidian vector. The iit is part of the rplus framework. Despite its trivial operation, it is present to achieve maximal analogy between the aplus and the rplus framework.
The data can then be analysed in this transformated space by all classical multivariate analysis tools. The interpretation of the results is easy since the relation to the original variables is preserved. However results may be inconsistent, since the multivariate analysis tools disregard the positivity condition and the inner laws of amounts.

The isometric identity transform is a simple identity given by

iit(x)_i := x_i

Value

ilt gives the isometric identity transform, i.e. simply the input stripped of the "rplus" class attribute, iptInv gives amounts with class "rplus" with the given iit, i.e. simply the argument checked to be a valid "rplus" object, and with this class attribute.

Note

iit can be used to unclass amounts.

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

ilt, ilr, rplus

Examples

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

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