#' Aitchison distance
#' 
#' Computes the Aitchison distance between two observations or between two data
#' sets.
#' 
#' This distance measure accounts for the relative scale property of the
#' Aitchison distance. It measures the distance between two compositions if
#' \code{x} and \code{y} are vectors and evaluate sum of the distances between
#' \code{x} and \code{y} for each row of \code{x} and \code{y} if \code{x} and
#' \code{y} are matrices or data frames.
#' 
#' It is to compare two matrices.
#' 
#' The underlying code is written in C and allows a fast computation also for
#' large data sets.
#' 
#' @param x a vector, matrix or data.frame
#' @param y a vector, matrix or data.frame with equal dimension as \code{x}
#' @return The Aitchison distance between two compositions or between two data
#' sets.
#' @author Matthias Templ
#' @seealso \code{\link{isomLR}}
#' @references Aitchison, J. (1986) \emph{The Statistical Analysis of
#' Compositional Data} Monographs on Statistics and Applied Probability.
#' Chapman and Hall Ltd., London (UK). 416p.
#' 
#' Aitchison, J. and Barcelo-Vidal, C. and Martin-Fernandez, J.A. and
#' Pawlowsky-Glahn, V. (2000) Logratio analysis and compositional distance.
#' \emph{Mathematical Geology}, \bold{32}, 271-275.
#' 
#' Hron, K. and Templ, M. and Filzmoser, P. (2010) Imputation of missing values
#' for compositional data using classical and robust methods
#' \emph{Computational Statistics and Data Analysis}, vol 54 (12), pages
#' 3095-3107.
#' @keywords math arith
#' @examples
#' 
#' data(expenditures)
#' x <- xOrig <- expenditures
#' ## Aitchison distance between the first 2 observations:
#' aDist(x[,1], x[,2])
#' 
#' ## set some missing values:
#' x[1,3] <- x[3,5] <- x[2,4] <- x[5,3] <- x[8,3] <- NA
#' 
#' ## impute them:
#' xImp <- impCoda(x, method="ltsReg")$xImp
#' 
#' ## calculate the relative Aitchsion distance between xOrig and xImp:
#' aDist(xOrig, xImp)
#' 
`aDist` <-
  function(x, y){
      if(is.vector(x)) x <- matrix(x, ncol=length(x))
	  if(is.vector(y)) y <- matrix(y, ncol=length(y))	  
	  
	  matOrig <- as.numeric(t(x))
	  matImp <- as.numeric(t(y))
	  n <- dim(x)[1]
	  p <- dim(x)[2]
	  dims <- as.integer(c(n, p))
	  rowDists <-  as.numeric(rep(0.0, n))
	  distance <- as.numeric(0.0)
	  out <- .C("da", 
				  matOrig,
				  matImp,
				  dims,
				  rowDists,
				  distance,
				  PACKAGE="robCompositions", NUOK=TRUE
		  )[[5]]
	  return(out)
}