# perturbe: Perturbation of compositions In compositions: Compositional Data Analysis

 perturbe R Documentation

## Perturbation of compositions

### Description

The perturbation is the addition operation in the Aitchison geometry of the simplex.

### Usage

``````perturbe(x,y)
## Methods for class "acomp"
## x + y
## x - y
##   - x
``````

### Arguments

 `x` compositions of class `acomp` `y` compositions of class `acomp`

### Details

The perturbation is the basic addition operation of the Aitichson simplex as a vector space. It is defined by:

` (x+y)_i = clo( (x_i y_i)_i )_i `

`perturbe` and `+` compute this operation. The only difference is that `+` checks the class of its argument, while `perturbe` does not check the type of the arguments and can thus directly be applied to a composition in any form (unclassed, acomp, rcomp).
The `-` operation is the inverse of the addition in the usual way and defined by:

`(x-y)_i:=clo( (x_i/y_i)_i )_i`

and as unary operation respectively as:

`(-x)_i:=clo( (1/y_i)_i )_i`

### Value

An `acomp` vector or matrix.

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de, Raimon Tolosana-Delgado

### References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

`acomp`, `*.aplus`, `+.rplus`

### Examples

``````tmp <- -acomp(1:3)
tmp + acomp(1:3)

``````

compositions documentation built on June 22, 2024, 12:15 p.m.