ult {compositions}

Uncentered log transform

Description

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

Usage

          ult( x ,...)
          ultInv( z ,..., orig=gsi.orig(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

orig

a compositional object which should be mimicked by the inverse transformation. It is the generic argument. Typically the orig argument is stored as an attribute in z and will be extracted automatically by this function; if this fails, orig can be set equal to the dataset that was transformed in the first place.

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). DO NOT USE if you do not know what you are doing.

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

(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))