Inverse centred log-ratio transform

Formula: clr^-1(z) = C( exp(z_1), ..., exp(z_D) )

Usage

Clrinv(z, total = 1)

Arguments

z: Centred log-ratio coordinates, length D.
total: Constant kappa the closure sums to.

Value

List with composition, total, D.

References

Aitchison, J. (1986), The Statistical Analysis of Compositional Data, Chapman and Hall, is the primary source; the definitions below are as printed in Mateu-Figueras, G., Pawlowsky-Glahn, V. and Egozcue, J. J., The normal distribution in some constrained sample spaces, arXiv:0802.2643 (published as SORT 37(1):29-56, 2013), Sect. 4.1, which prints them with equation numbers and attributes them to Aitchison (1982, 1986). The inverse of clr is the closure of the exponentiated coordinates. It is well defined for any real z, not only for z summing to zero: adding a constant to every z_i leaves the closed result unchanged.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Clrinv(V)
#> $composition
#> [1] 0.0005766128 0.0015673960 0.0042606241 0.0115815771 0.0314819905
#> [6] 0.0855769227 0.2326221940 0.6323326828
#> 
#> $total
#> [1] 1
#> 
#> $D
#> [1] 8
#> 
#> $method
#> [1] "Inverse centred log-ratio transform"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"