Uncentered log transform

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Description

Compute the uncentered log ratio transform of a (dataset of) composition(s) and its inverse.

Usage

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          ult( x ,...)
          ultInv( z ,...)
          Kappa( x ,...)
          

Arguments

x

a composition or a data matrix of compositions, not necessarily closed

z

the ult-transform of a composition or clr-transforms of compositions (or a data matrix), not necessarily centered

...

for generic use only

Details

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).

Value

ult gives the uncentered log transform,
ultInv gives closed compositions with the given ult/clr-transforms
Kappa gives the difference between the clr and the ult transforms. It is quite linked to information measures.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

ilr,alr,apt

Examples

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(tmp <- ult(c(1,2,3)))
ultInv(tmp)
ultInv(tmp) - clo(c(1,2,3)) # 0
data(Hydrochem)
cdata <- Hydrochem[,6:19]
pairs(ult(cdata),pch=".")
Kappa(c(1,2,3))

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