Power a composition by a real scalar

Formula: a (.) x = C( x_1^a, ..., x_D^a )

Usage

Powering(a, x, total = 1)

Arguments

a

Scalar.

x

Strictly positive vector of parts.

total

Constant the result sums to.

Value

List with composition, a, total, D.

References

Aitchison (1986), The Statistical Analysis of Compositional Data, Chapter 2. Verified against the reference implementation in the CRAN package compositions 2.0-9, whose power operator on an acomp closes the elementwise power.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Powering(V, V)
#> $composition
#> [1] 5.665457e-08 2.266183e-07 1.529673e-06 1.450357e-05 1.770455e-04
#> [6] 2.643275e-03 4.665747e-02 9.505059e-01
#> 
#> $a
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $total
#> [1] 1
#> 
#> $D
#> [1] 8
#> 
#> $method
#> [1] "Powering on the simplex"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"