https://github.com/cran/robCompositions
Tip revision: 0e640ebe37b48ee7398ce510677e75b37b969440 authored by Matthias Templ on 22 August 2016, 12:00:07 UTC
version 2.0.2
version 2.0.2
Tip revision: 0e640eb
aDist.R
#' Aitchison distance
#'
#' Computes the Aitchison distance between two observations, between two data
#' sets or within observations of one data set.
#'
#' 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. It evaluates the 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 computes a n times n distance matrix (with n
#' the number of observations/compositions) if only \code{x} is provided.
#'
#'
#' The underlying code is partly written in C and allows a fast computation also for
#' large data sets whenever \code{y} is supplied.
#'
#' @param x a vector, matrix or data.frame
#' @param y a vector, matrix or data.frame with equal dimension as \code{x} or NULL.
#' @return The Aitchison distance between two compositions or between two data
#' sets, or a distance matrix in case code{y} is not supplied.
#' @author Matthias Templ, Bernhard Meindl
#' @export
#' @useDynLib robCompositions
#' @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 two 2 observations:
#' aDist(x[1, ], x[2, ])
#'
#' ## Aitchison distance of x:
#' aDist(x)
#'
#' ## Example of distances between matrices:
#' ## 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 = NULL){
n <- dim(x)[1]
p <- D <- dim(x)[2]
rn <- rownames(x)
if(!is.null(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))
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]]
} else {
out <- matrix(, ncol = n, nrow = n)
for(i in 1:(n-1)){
for(j in (i+1):n){
out[i, j] <- out[j, i] <-
1 / D * sum(log(as.numeric(x[i, 1:(D-1)]) / as.numeric(x[i, 2:D])) *
log(as.numeric(x[j, 1:(D-1)]) / as.numeric(x[j, 2:D])))
}
}
diag(out) <- 0
rownames(out) <- colnames(out) <- rn
}
return(out)
}