Perturbation of compositions
The perturbation is the addition operation in the Aitchison geometry of the simplex.
perturbe(x,y) ## Methods for class "acomp" ## x + y ## x - y ## - x
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.
tmp <- -acomp(1:3) tmp + acomp(1:3)
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