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\title{ Isometric log-ratio transformation }
  An isometric log-ratio transformation with a special choice of the balances according to Hron et al. (2010).
%- maybe also 'usage' for other objects documented here.
  \item{x}{ object of class data.frame or matrix with positive entries}
The isomLR transformation moves D-part compositional data from the simplex into a (D-1)-dimensional real space isometrically.
  From this choice of the balances, all the relative information of the part \eqn{x_1} 
  from the remaining parts is separated. It is useful for estimating missing values in 
  \eqn{x_1} by regression of the remaining variables.
  The isomLR transformed data.
\references{ Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and
C. Barcel'o-Vidal (2003) Isometric logratio transformations for
compositional data analysis. \emph{Mathematical Geology}, \bold{35}(3)
279-300. \\

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.   
\author{ Karel Hron, Matthias Templ }
\seealso{ \code{\link{isomLRinv}}, \code{\link[compositions]{ilr}} }
Sigma <- matrix(c(5.05,4.95,4.95,5.05), ncol=2, byrow=TRUE)
z <- isomLRinv(mvrnorm(100, mu=c(0,2), Sigma=Sigma))

\keyword{ math }
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