perturbe {compositions} | 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.

### See Also

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

### Examples

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

[Package compositions version 0.91-6 Index]