Function to perform isometric log-ratio transformation

Usage

ilr(x)
  invilr(x)

Arguments

x

A numeric vector. Naturally, the forward transformation is only sensible for vectors with all elements being greater than zero.

Examples

# Order matters
ilr(c(0.1, 1, 10))
[1] -1.628174 -2.820079

ilr(c(10, 1, 0.1))
[1] 1.628174 2.820079

# Equal entries give ilr transformations with zeros as elements
ilr(c(3, 3, 3))
[1] 0 0

# Almost equal entries give small numbers
ilr(c(0.3, 0.4, 0.3))
[1] -0.2034219  0.1174457

# Only the ratio between the numbers counts, not their sum
invilr(ilr(c(0.7, 0.29, 0.01)))
[1] 0.70 0.29 0.01

invilr(ilr(2.1 * c(0.7, 0.29, 0.01)))
[1] 0.70 0.29 0.01

# Inverse transformation of larger numbers gives unequal elements
invilr(-10)
[1] 7.213536e-07 9.999993e-01

invilr(c(-10, 0))
[1] 7.207415e-07 9.991507e-01 8.486044e-04

# The sum of the elements of the inverse ilr is 1
sum(invilr(c(-10, 0)))
[1] 1

# This is why we do not need all elements of the inverse transformation to go back:
a <- c(0.1, 0.3, 0.5)
b <- invilr(a)
length(b) # Four elements
[1] 4

ilr(c(b[1:3], 1 - sum(b[1:3]))) # Gives c(0.1, 0.3, 0.5)
[1] 0.1 0.3 0.5