Centered log-ratio basis

Construct the transformation matrix associated with centered log-ratio (clr) coordinates.

Usage

clr_basis(dim)

Arguments

dim

Number of parts. It can be a single integer, a matrix or data frame, or a character vector of part names.

Value

A square matrix defining the clr coordinate system.

Details

CLR coordinates are linearly dependent and lie in the \(D - 1\) dimensional clr-plane.

References

Aitchison, J. (1986). The Statistical Analysis of Compositional Data. Chapman & Hall, London.

Examples

B <- clr_basis(5)
clr_coordinates <- coordinates(c(1, 2, 3, 4, 5), B)
sum(clr_coordinates) < 1e-15
#> [1] TRUE