Centered log-ratio basis

Compute the transformation matrix to express a composition using the linearly dependant centered log-ratio coordinates.

clr_basis(dim)

Arguments

dim

An integer indicating the number of components. If a dataframe or matrix is provided, the number of components is inferred from the number of columns. If a character vector specifying the names of the parts is provided the number of component is its length.

Value

matrix

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data. Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

Examples

(B <- clr_basis(5))
#>    clr1 clr2 clr3 clr4 clr5
#> c1  0.8 -0.2 -0.2 -0.2 -0.2
#> c2 -0.2  0.8 -0.2 -0.2 -0.2
#> c3 -0.2 -0.2  0.8 -0.2 -0.2
#> c4 -0.2 -0.2 -0.2  0.8 -0.2
#> c5 -0.2 -0.2 -0.2 -0.2  0.8
# CLR coordinates are linearly dependant coordinates.
(clr_coordinates <- coordinates(c(1,2,3,4,5), B))
#>       clr1       clr2       clr3       clr4       clr5 
#> -0.9574983 -0.2643512  0.1411139  0.4287960  0.6519396 
# The sum of all coordinates equal to zero
sum(clr_coordinates) < 1e-15
#> [1] TRUE