Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 2 3 4 5 | ```
perturbe(x,y)
## Methods for class "acomp"
## x + y
## x - y
## - x
``` |

`x` |
compositions of class |

`y` |
compositions of class |

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*

An `acomp`

vector or matrix.

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

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

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