ult {compositions} | R Documentation |

## 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 |

### 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

### 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))
```

*compositions*version 2.0-8 Index]