Closure operator C(x) onto the simplex of constant sum total

Formula: C(x) = kappa * (x_1, ..., x_D) / sum_j x_j

Usage

Compclos(x, total = 1)

Arguments

x: Strictly positive vector of parts.
total: Constant kappa the closed vector sums to.

Value

List with closed, total, sum_raw, D.

References

Aitchison (1986), The Statistical Analysis of Compositional Data, Chapter 2. Definition verified against the reference implementation in the CRAN package compositions 2.0-9 (van den Boogaart & Tolosana-Delgado), whose clo/acomp divide by the row sum and rescale to the requested total.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Compclos(V)
#> $closed
#> [1] 0.02777778 0.05555556 0.08333333 0.11111111 0.13888889 0.16666667 0.19444444
#> [8] 0.22222222
#> 
#> $total
#> [1] 1
#> 
#> $sum_raw
#> [1] 36
#> 
#> $D
#> [1] 8
#> 
#> $method
#> [1] "Closure C(x) onto the simplex"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"