Arithmetic operations for compositions in a real geometry

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Description

The real compositions form a manifold of the real vector space. The induced operations +,-,*,/ give results valued in the real vector space, but possibly outside the simplex.

Usage

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convex.rcomp(x,y,alpha=0.5)
## Methods for class "rcomp"
##   x+y
##   x-y
##   -x
##   x*r
##   r*x
##   x/r
          

Arguments

x

an rcomp composition or dataset of compositions

y

an rcomp composition or dataset of compositions

r

a numeric vector of size 1 or nrow(x)

alpha

a numeric vector of size 1 or nrow(x) with values between 0 and 1

Details

The functions behave quite like +.rmult.
The convex combination is defined as: x*alpha + (1-alpha)*y

Value

rmult-objects containing the given operations on the simplex as subset of the R^D. Only the convex combination convex.rcomp results in an rcomp-object again, since only this operation is closed.

Note

For * the arguments x and y can be exchanged.

Author(s)

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

See Also

+.rmult, +.acomp,cpt, rcomp, rmult

Examples

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rcomp(1:5)* -1 + rcomp(1:5)
data(SimulatedAmounts)
cdata <- rcomp(sa.lognormals)
plot( tmp <- (cdata-mean(cdata))/msd(cdata) )
class(tmp)
mean(tmp)
msd(tmp)
var(tmp)
plot(convex.rcomp(rcomp(c(1,1,1)),sa.lognormals,0.1))

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