create_v_mat {codaredistlm}

Create ilr basis matrix (V)

Description

Create ilr basis matrix (V)

Usage

create_v_mat(n_comp)

Arguments

n_comp

the number of compositional variables

Value

A n_comp by n_comp - 1 matrix where each column relates to one ilr variable

The ilr basis made so that the numerator (+ values) for the ith column is in the ith row. All values below the + value in the column are set to -1 (the denominator).

The ilr basis for 3 compositional vars is (2, -1, -1)/sqrt(6), (0, 1, -1)/sqrt(2).

The ilr basis for 4 comp vars is (3, -1, -1, -1)/sqrt(12), (0, 2, -1, -1)/sqrt(6), (0, 0, 1, -1)/sqrt(2).

etc