R/alfa.R

In Compositional: Compositional Data Analysis

alfa <- function(x, a, h = TRUE) {
  ## x contains the compositional data
  ## a is the power parameter, usually between -1 and 1
  ## if h is TRUE the multiplication with the Helmert matrix takes place
  x <- as.matrix(x)
  n <- dim(x)[1]   ;   D <- dim(x)[2]   ;   d <- D - 1
  if ( D == 1 )   x <- t(x)
  lx <- Rfast::Log(x)

  if ( abs(a) > 1e-7 ) {
    z <- x^a
    ta <- Rfast::rowsums(z)
    z <- D / a * z / ta - 1/a
    sa <- n * d * log(D) + (a - 1) * sum(lx) - D * sum( log(ta) )
    if ( h ) {
      z <- tcrossprod(z, Compositional::helm(D) ) ## multiply by the Helmert sub-matrix
      sa <- n * (d + 0.5) * log(D) + (a - 1) * sum(lx) - D * sum( log(ta) )
    }
  } else {  ## if a = 0 the ilr is calculated
    z <- lx - Rfast::rowmeans( lx )   ## this is the clr
    sa <-  - sum(lx) - n * log(D)
    if ( h ) {
      z <- tcrossprod(z, Compositional::helm(D) ) ## multiply by the Helmert sub-matrix
      sa <-  - sum(lx) - 0.5 * n * log(D)
    }
  }

  list(sa = sa, aff = z)
}