apt {compositions} | R Documentation |

## Additive planar transform

### Description

Compute the additive planar transform of a (dataset of) compositions or its inverse.

### Usage

```
apt( x ,...)
aptInv( z ,..., orig=gsi.orig(z))
```

### Arguments

`x` |
a composition or a matrix of compositions, not necessarily closed |

`z` |
the apt-transform of a composition or a matrix of alr-transforms of compositions |

`...` |
generic arguments, not used. |

`orig` |
a compositional object which should be mimicked by the inverse transformation. It is especially used to reconstruct the names of the parts. |

### Details

The apt-transform maps a composition in the D-part real-simplex
linearly to a D-1 dimensional euclidian vector. Although the
transformation does not reach the whole `R^{D-1}`

, resulting covariance
matrices are typically of full rank.

The data can then
be analysed in this transformation by all classical multivariate
analysis tools not relying on distances. See
`cpt`

and `ipt`

for alternatives. The
interpretation of the results is easy since the relation to the first
D-1 original variables is preserved.

The additive planar transform is given by

` apt(x)_i := clo(x)_i, i=1,\ldots,D-1 `

### Value

`apt`

gives the centered planar transform,
`aptInv`

gives closed compositions with the given apt-transforms

### Author(s)

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

### References

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.

### See Also

### Examples

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

*compositions*version 2.0-8 Index]