Compute the isometric identity transform of a vector (dataset) of amounts and its inverse.
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a vector or data matrix of amounts
the iit-transform of a vector or data.matrix of iit-transforms of amounts
generic arguments, to pass to other functions.
The iit-transform maps D amounts (considered in a real geometry)
isometrically to a D dimensonal euclidian vector. The
part of the
rplus framework. Despite its trivial
operation, it is present to achieve maximal analogy between the
aplus and the
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
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.
iit can be used to unclass amounts.
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.
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