Compute the uncentered log ratio transform of a (dataset of) composition(s) and its inverse.
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a composition or a data matrix of compositions, not necessarily closed
the ult-transform of a composition or clr-transforms of compositions (or a data matrix), not necessarily centered
for generic use only
The ult-transform is simply the elementwise log of the closed composition. The ult has some important properties in the scope of Information Theory of probability vectors (but might be mostly misleading for exploratory analysis of compositions).
ult gives the uncentered log transform,
ultInv gives closed compositions with the given
Kappa gives the difference between the clr and the ult
transforms. It is quite linked to information measures.
K.Gerald v.d. Boogaart http://www.stat.boogaart.de
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