% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/aDist.R
\name{aDist}
\alias{aDist}
\alias{iprod}
\title{Aitchison distance}
\usage{
aDist(x, y = NULL)

iprod(x, y)
}
\arguments{
\item{x}{a vector, matrix or data.frame}

\item{y}{a vector, matrix or data.frame with equal dimension as \code{x} or NULL.}
}
\value{
The Aitchison distance between two compositions or between two data
sets, or a distance matrix in case code{y} is not supplied.
}
\description{
Computes the Aitchison distance between two observations, between two data
sets or within observations of one data set.
}
\details{
This distance measure accounts for the relative scale property of
compositional data. 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.
}
\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 the missing values:
xImp <- impCoda(x, method="ltsReg")$xImp

## calculate the relative Aitchsion distance between xOrig and xImp:
aDist(xOrig, xImp)

data("expenditures") 
aDist(expenditures)  
x <- expenditures[, 1]
y <- expenditures[, 2]
aDist(x, y)
aDist(expenditures, expenditures)
}
\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.
}
\seealso{
\code{\link{pivotCoord}}
}
\author{
Matthias Templ, Bernhard Meindl
}
\keyword{arith}
\keyword{math}