R/compositions.R
In compositions: Compositional Data Analysis

Documented in acomp acompmargin AitchisonDistributionIntegrals alr alrInv aplus apt aptInv as.data.frame.acomp as.data.frame.aplus as.data.frame.ccomp as.data.frame.rcomp as.data.frame.rmult as.data.frame.rplus backtransform.rmult balance balance01 balance01.acomp balance01.rcomp balance.acomp balance.aplus balanceBase balanceBase.acomp balanceBase.aplus balanceBase.rcomp balanceBase.rplus balance.rcomp balance.rplus barplot.acomp boxplot.acomp boxplot.aplus boxplot.rcomp boxplot.rplus ccomp cdt cdt.ccomp cdt.default cdt.factor cdtInv cdtInv.acomp cdtInv.aplus cdtInv.ccomp cdtInv.default cdtInv.factor cdtInv.rcomp cdtInv.rmult cdtInv.rplus cdt.rmult clo clr clr2ilr clrInv clrvar2ilr clrvar2variation ConfRadius convex.rcomp cor cor.acomp cov cpt cptInv dAitchison dDirichlet dist dist.default dlnorm.rplus dnorm.acomp dnorm.aplus dnorm.rmult ellipses ellipses.acomp ellipses.aplus endmemberCoordinates endmemberCoordinates.acomp endmemberCoordinates.aplus endmemberCoordinates.default endmemberCoordinatesInv endmemberCoordinatesInv endmemberCoordinatesInv.acomp endmemberCoordinatesInv.aplus endmemberCoordinatesInv.rcomp endmemberCoordinatesInv.rmult endmemberCoordinatesInv.rplus endmemberCoordinates.rplus geometricmean geometricmeanCol geometricmeanRow groupparts groupparts.acomp groupparts.aplus groupparts.ccomp groupparts.rcomp groupparts.rplus gsi2.invperm gsi.add gsi.add2pairs gsi.addclass gsi.addCoorInfo gsi.buildilrBase gsi.call gsi.closespread gsi.csum gsi.diagExtract gsi.diagGenerate gsi.div gsi.drop gsi.eq gsi.eq gsi.expandrcomp gsi.geometricmean gsi.geometricmeanCol gsi.geometricmeanRow gsi.getBalStruct gsi.getCoorInfo gsi.getD gsi.getN gsi.getV gsi.ilrBase gsi.ilrBase gsi.isSingleRow gsi.mapfrom01 gsi.mapin01 gsi.mapmax gsi.mapmin gsi.merge2signary gsi.mul gsi.optimalilrBase gsi.orig gsi.pairrelativeMatrix gsi.plain gsi.plotmargin gsi.rsum gsi.setCoorInfo gsi.simshape gsi.spreadToIsoSpace gsi.sub gsi.svdsolve gsi.textpanel idt idt.acomp idt.ccomp idt.default idt.factor idtInv idtInv.acomp idtInv.aplus idtInv.ccomp idtInv.default idtInv.factor idtInv.rcomp idtInv.rmult idtInv.rplus idt.rcomp idt.rmult iit iitInv ilr ilr2clr ilrBase ilrInv ilrvar2clr ilt iltInv ipt iptInv is.acomp is.aplus is.ccomp is.clrvar is.ilrvar isoPortionLines isoPortionLines.acomp isoPortionLines.rcomp isoProportionLines isoProportionLines.acomp isoProportionLines.rcomp is.rcomp is.rmult is.rplus is.variation Kappa kingTetrahedron lines.acomp lines.aplus lines.rcomp lines.rmult lines.rplus mcor mcor.default mcov mcov.default mean.acomp mean.ccomp meanCol mean.rmult meanRow msd msd.default mul.rplus mvar mvar.default names.acomp noreplot norm norm.acomp normalize normalize.default norm.default norm.matrix norm.rmult oneOrDataset perturbe perturbe.aplus pHotellingsTsq plot.acomp plot.ccomp plot.princomp.acomp plot.princomp.acomp plot.princomp.aplus plot.princomp.aplus plot.princomp.rcomp plot.princomp.rplus plot.rcomp plot.relativeLoadings.princomp.acomp plot.relativeLoadings.princomp.aplus plot.relativeLoadings.princomp.rcomp plot.relativeLoadings.princomp.rplus plot.rmult power.acomp power.aplus powerofpsdmatrix predict.princomp.acomp predict.princomp.aplus predict.princomp.rcomp predict.princomp.rplus princomp.acomp princomp.aplus princomp.rcomp princomp.rmult princomp.rplus print.acomp print.princomp.acomp print.princomp.aplus print.princomp.rcomp print.princomp.rplus print.relativeLoadings.princomp.acomp print.relativeLoadings.princomp.rcomp print.relativeLoadings.princomp.rplus pwlr pwlrInv qHotellingsTsq qqnorm.acomp qqnorm.aplus qqnorm.rcomp qqnorm.rplus R2 R2.default R2.lm rAitchison rcomp rcompmargin rDirichlet.acomp rDirichlet.rcomp read.geoEAS relativeLoadings relativeLoadings.princomp.acomp relativeLoadings.princomp.aplus relativeLoadings.princomp.rcomp relativeLoadings.princomp.rplus replot replotable rlnorm.rplus rmult rmultinom.ccomp rnorm.aplus rnorm.ccomp rnorm.rcomp rnorm.rmult rnorm.rplus rplus rpois.ccomp runif.acomp runif.rcomp scalar scalar.default scale.acomp scale.rmult segments segments.acomp segments.aplus segments.default segments.rcomp segments.rmult segments.rplus simpleMissingSubplot split.acomp straight straight.acomp straight.aplus straight.rcomp straight.rmult straight.rplus summary.acomp summary.aplus summary.rcomp summary.rmult summary.rplus ternaryAxis totals totals.acomp uciptInv ult var var.acomp var.aplus variation variation2clrvar variation.acomp variation.aplus variation.rcomp variation.rmult var.lm var.mlm vcovAcomp vp.boxplot vp.logboxplot vp.qqnorm

# (C) 2005/2008 by Gerald van den Boogaart, Greifswald
# License: GPL version 2 or newer


gsiInt <- function(x,n=NULL) {if(!is.null(n))stopifnot(length(x)==n);as.integer(x)}
gsiDouble <- function(x,n=NULL) {if(!is.null(n))stopifnot(length(x)==n);as.numeric(x)}

gsi.plain <- function(x) {
  if( is.data.frame(x) )
    unclass(data.matrix(x))
  else 
    unclass(x)
}

gsi.simshape <- function(x,oldx) {
  if(length(dim(oldx))>=2 )
    oneOrDataset(x)
  else if( length(dim(oldx)) == 1 )
    gsi.mystructure(c(x),dim=length(x))
  else 
    c(drop(x))
}

gsi.diagExtract <- function(x) {
  if( length(x) > 1 )
    diag(x)
  else
    c(x)
}

gsi.diagGenerate <- function(x) {
  if( length(x) > 1 )
    diag(x)
  else
    matrix(x)
}

gsi.getD  <- function(x) ncol(oneOrDataset(x))
gsi.getN  <- function(x) nrow(oneOrDataset(x))   

gsi.eq <-  function(x,y) {
  if( is.null(y) ) return(is.null(x)) # null
  if( is.finite(y) ) {           
    if( is.infinite(1/y) & (1/y)<0 )  # -0
      return(is.infinite(1/x) & (1/x)<0)
      else
        return(is.finite(x) & x==y)     # Zahlencodes 
  }
  if( is.nan(y) ) return(is.nan(x))   # NaN
  if( is.infinite(y)&y>0) return(is.infinite(x)&x>0) # Inf
  if( is.infinite(y)&y<0) return(is.infinite(x)&x<0) # -Inf
  if( is.na(y) ) return(is.na(y))                    # NA
  stop("Unkown comparison type ",y)                  # Was wurde vergessen?
}


names.acomp <- function(x) colnames(oneOrDataset(x))
names.rcomp <- names.acomp
names.aplus <- names.acomp
names.rplus <- names.acomp
names.rmult <- names.acomp
names.ccomp <- names.acomp

"names<-.acomp" <- "names<-.rcomp" <- "names<-.aplus" <- "names<-.rplus" <- "names<-.rmult" <- "names<-.ccomp" <-
  function(x,value) {
    if(is.matrix(x)) {
      colnames(x) <- value
      x
    }
    else
      NextMethod("names",x,value=value)
  }


groupparts <- function(x,...) UseMethod("groupparts",x)

groupparts.rcomp <- function(x,...,groups=list(...)) {
                                        # BDL=SZ->0, MAR->MAR, MNAR->MNAR
  x <- rmult(gsi.recodeM2C(x,clo(x),BDL=0.0,SZ=0.0,MAR=NaN,MNAR=NA))
  usedparts <- unique(unlist(lapply(groups,function(i) {
    if( is.character(i) ) {
      parts <- match(i,names(x))
      if( any(is.na(parts)))
        stop("Unknown part",i[is.na(parts)])
      parts
    } else i
  })))
  otherparts <- (1:gsi.getD(x))[-usedparts]
  if( length(otherparts) >0 ) {
    names(otherparts) <- names(x)[otherparts]
    groups <- c(groups,otherparts)
  }
  erg <- sapply(groups,function(idx) {
    ss <- rplus(x,idx)
    ss %*% rep(1,gsi.getD(ss))
  })
  rcomp(gsi.recodeC2M(erg,na=MNARvalue,nan=MARvalue))
}

groupparts.rplus <- function(x,...,groups=list(...)) {
                                        # BDL=SZ->0, MAR->MAR, MNAR->MNAR
  x <- rmult(gsi.recodeM2C(x,BDL=0.0,SZ=0.0,MAR=NaN,MNAR=NA))
  usedparts <- unique(unlist(lapply(groups,function(i) {
    if( is.character(i) ) {
      parts <- match(i,names(x))
      if( any(is.na(parts)))
        stop("Unknown part",i[is.na(parts)])
      parts
    } else i
  })))
  otherparts <- (1:gsi.getD(x))[-usedparts]
  if( length(otherparts) >0 ) {
    names(otherparts) <- names(x)[otherparts]
    groups <- c(groups,otherparts)
  }
  erg <- sapply(groups,function(idx) {
    ss <- rplus(x,idx)
    ss %*% rep(1,gsi.getD(ss))
  })
  rplus(gsi.recodeC2M(erg,na=MNARvalue,nan=MARvalue))
}

groupparts.acomp <- function(x,...,groups=list(...)) {
                                        # BDL: BDL, NA: NA, 0: 0
  x <- rmult(gsi.recodeM2C(x,clo(x),BDL=NaN,SZ=NA,MAR=Inf,MNAR=NaN))
  #SZ <- is.SZ(x)               # keep regardless of the rest NA
  #MNAR <- is.MNAR(x)|is.BDL(x) # keep if no SZ               NaN
  #MAR  <- is.MAR(x)            # keep if no SZ or MNAR are in the way Inf
  usedparts <- unique(unlist(lapply(groups,function(i) {
    if( is.character(i) ) {
      parts <- match(i,names(x))
      if( any(is.na(parts)))
        stop("Unknown part",i[is.na(parts)])
      parts
    } else i
  })))
  otherparts <- (1:gsi.getD(x))[-usedparts]
  if( length(otherparts) >0 ) {
    names(otherparts) <- names(x)[otherparts]
    groups <- c(groups,otherparts)
  }
  erg <- sapply(groups,function(idx) {
    ss <- aplus(x,idx)
    if( is.matrix(ss) )
      gsi.geometricmeanRow(ss)
    else
      gsi.geometricmean(ss)
  })
  acomp(gsi.recodeC2M(erg,na=SZvalue,nan=MNARvalue,inf=MARvalue))
  
#  SZ   <- is.na(x)&!is.na(x)   # keep regardless of the rest NA
#  MNAR <- is.nan(x)            # keep if no SZ               NaN
#  MAR  <- !is.finite(x)&!is.na(x) # keep if no SZ or MNAR are in the way Inf
}

groupparts.aplus <- function(x,...,groups=list(...)) {
  x <- rmult(gsi.recodeM2C(x,clo(x),BDL=NaN,SZ=NA,MAR=Inf,MNAR=NaN))
  usedparts <- unique(unlist(lapply(groups,function(i) {
    if( is.character(i) ) {
      parts <- match(i,names(x))
      if( any(is.na(parts)))
        stop("Unknown part",i[is.na(parts)])
      parts
    } else i
  })))
  otherparts <- (1:gsi.getD(x))[-usedparts]
  if( length(otherparts) >0 ) {
    names(otherparts) <- names(x)[otherparts]
    groups <- c(groups,otherparts)
  }
  erg <- sapply(groups,function(idx) {
    ss <- aplus(x,idx)
    if( is.matrix(ss) )
      gsi.geometricmeanRow(ss)
    else
      gsi.geometricmean(ss)
  })
  aplus(gsi.recodeC2M(erg,na=SZvalue,nan=MNARvalue,inf=MARvalue))
}

groupparts.acomp <- function(x,...,groups=list(...)) {
                                        # BDL: BDL, NA: NA, 0: 0
  x <- rmult(gsi.recodeM2C(x,clo(x),BDL=NaN,SZ=NA,MAR=Inf,MNAR=NaN))
  #SZ <- is.SZ(x)               # keep regardless of the rest NA
  #MNAR <- is.MNAR(x)|is.BDL(x) # keep if no SZ               NaN
  #MAR  <- is.MAR(x)            # keep if no SZ or MNAR are in the way Inf
  usedparts <- unique(unlist(lapply(groups,function(i) {
    if( is.character(i) ) {
      parts <- match(i,names(x))
      if( any(is.na(parts)))
        stop("Unknown part",i[is.na(parts)])
      parts
    } else i
  })))
  otherparts <- (1:gsi.getD(x))[-usedparts]
  if( length(otherparts) >0 ) {
    names(otherparts) <- names(x)[otherparts]
    groups <- c(groups,otherparts)
  }
  erg <- sapply(groups,function(idx) {
    ss <- aplus(x,idx)
    if( is.matrix(ss) )
      gsi.geometricmeanRow(ss)
    else
      gsi.geometricmean(ss)
  })
  acomp(gsi.recodeC2M(erg,na=SZvalue,nan=MNARvalue,inf=MARvalue))
  
#  SZ   <- is.na(x)&!is.na(x)   # keep regardless of the rest NA
#  MNAR <- is.nan(x)            # keep if no SZ               NaN
#  MAR  <- !is.finite(x)&!is.na(x) # keep if no SZ or MNAR are in the way Inf
}

groupparts.ccomp <- function(x,...,groups=list(...)) {
  x <- rmult(x)
  usedparts <- unique(unlist(lapply(groups,function(i) {
    if( is.character(i) ) {
      parts <- match(i,names(x))
      if( any(is.na(parts)))
        stop("Unknown part",i[is.na(parts)])
      parts
    } else i
  })))
  otherparts <- (1:gsi.getD(x))[-usedparts]
  if( length(otherparts) >0 ) {
    names(otherparts) <- names(x)[otherparts]
    groups <- c(groups,otherparts)
  }
  erg <- sapply(groups,function(idx) {
    totals(ccomp(x,idx))
  })
  ccomp(erg)
}


# groupparts(x,G1=c("Cd","S"),G2=c("Co","Ni"),G3=c("As","F"))

clo <- function(X,parts=1:NCOL(oneOrDataset(X)),total=1,
                detectionlimit=attr(X,"detectionlimit"),
                BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL,
                storelimit=!is.null(attr(X,"detectionlimit"))) {
  X <- gsi.plain(X)
  # Collect the parts
  parts  <- unique(parts)
  if( is.character(parts) ) {
    partsn <- match(parts,colnames(X))
    if( any(is.na(partsn)) )
      stop("Unknown variable name",parts[is.na(partsn)])
    parts <- partsn
  }
  nparts <- length(parts)
  Xn <- gsi.plain(oneOrDataset(X))[,parts,drop=FALSE]
  drop <- length(dim(X)) < 2
  #if( any(na.omit(c(Xn)<0)) )
  #  stop("Negative values are not valid for amounts")
  # Processing of missings
  iMAR <- if( !is.null(MAR) ) gsi.eq(Xn,MAR) else FALSE
  iMNAR<- if( !is.null(MNAR) ) gsi.eq(Xn,MNAR) else FALSE
  iSZ  <- if( !is.null(SZ) ) gsi.eq(Xn,SZ) else FALSE
  iBDL <- if( !is.null(BDL) ) gsi.eq(Xn,BDL) else FALSE
  if( is.null(detectionlimit) ) {
    if( any(iBDL) )
      Xn[iBDL]<- BDLvalue
  } else if( is.matrix(detectionlimit) ) {
    if( nrow(Xn)!=nrow(detectionlimit) | ncol(Xn)!=ncol(detectionlimit) )
      warning("Matrix of Detectionlimits does not fit x")
    Xn <- ifelse( is.finite(detectionlimit) & detectionlimit>=0,
                ifelse( (is.finite(Xn) & X <= detectionlimit)|iBDL ,
                       -detectionlimit, Xn ),
                Xn)
  } else if( length( detectionlimit) > 1 ) {
    if( ncol(Xn)!=length(detectionlimit)  )
      warning("Length of Detectionlimits does not fit x")
    detectionlimit <- outer(rep(1,nrow(Xn),detectionlimit))
    Xn <- ifelse( is.finite(detectionlimit) & detectionlimit>=0,
                ifelse( (is.finite(Xn) & X <= detectionlimit)|iBDL ,
                       -detectionlimit, Xn ),
                Xn)
  } else if( is.finite(detectionlimit) && detectionlimit > 0 ) {
    Xn <- ifelse((Xn<=detectionlimit&Xn>=0)|iBDL,-detectionlimit,Xn)
  } else
    Xn <- ifelse(iBDL,BDLvalue,Xn)
  if( any(iMAR) ) Xn[iMAR] <- MARvalue
  if( any(iMNAR)) Xn[iMNAR]<- MNARvalue
  if( any(iSZ) )  Xn[iSZ]  <- SZvalue
  # Make the sum 1 ignoring missings
  scaling <- 1
  if( length(total) > 1 || !is.na(total) ) {
    nas <- !is.NMV(Xn)&!is.BDL(Xn) # Missings are not included in closing
    bdl <- is.BDL(Xn)              # BDLs are accordingly scaled 
    naValues <- Xn[nas]
    Xn[nas]<-0
    s <- c(ifelse(bdl,0,Xn) %*% rep(1,nparts))
    scaling <-  matrix(rep(s/total,nparts),ncol=nparts)
    Xn  <- Xn / scaling
    Xn[nas] <- naValues
  }
  erg <- gsi.simshape(Xn,X)
  if( storelimit) {
    if( length(detectionlimit) == 1 )
      detectionlimit <- matrix(detectionlimit,nrow=nrow(Xn),ncol=ncol(Xn))
    detectionlimit/scaling
    detectionlimit <- gsi.simshape(detectionlimit[,parts,drop=FALSE],X)
    attr(erg,"detectionlimit") <- detectionlimit
  }
  erg
}



acomp <- function(X,parts=1:NCOL(oneOrDataset(X)),total=1,warn.na=FALSE,detectionlimit=NULL,BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL) {
  eq <- function(x,y) identical(as.numeric(x),as.numeric(y),single.NA=FALSE)
  if( is.list(X) )
    X<-data.matrix(X)
  if( is.ccomp(X) )
    X <- X+0.5
  # X <- oneOrDataset(X)[,parts]
  if( !is.null(BDL) ) {
    if( is.finite(BDL) )
      bdl <- X==BDL
    else
      bdl <- sapply(X,eq,BDL)
  } else bdl <- FALSE
  if( !is.null(MAR) ) {
    if( is.finite(MAR) )
      mar <- X==MAR
    else
      mar <- sapply(X,eq,MAR)
  } else mar <- FALSE
  if( !is.null(MNAR) ) {
    if( is.finite(MNAR) )
      mnar <- X==MNAR
    else
      mnar <- sapply(X,eq,MNAR)
  } else mnar <- FALSE
  if( !is.null(SZ) ) {
    if( is.finite(SZ) )
      sz <- X==SZ
    else
      sz <- sapply(X,eq,SZ)
  } else sz <- FALSE
  if( any( is.finite(X) & X < 0 & !(mar|mnar|bdl|sz)))
    warning("Negative values in composition are used as detection limits")
  if( !is.null(MAR) && any(mar) ) X[mar]<-BDLvalue
  if( !is.null(MNAR)&& any(mnar) ) X[mnar]<-BDLvalue
  if( !is.null(bdl) && any(bdl)) X[bdl]<-MARvalue
  if( !is.null(SZ)&&any(sz) ) X[sz]<-SZvalue
  X <-  gsi.mystructure(clo(X,parts,total),class="acomp")
  if( !is.null(detectionlimit) && any(X==BDLvalue) ) {
    X[sapply(X,eq,BDLvalue)]<- -detectionlimit
  }
  if( warn.na ) {
    if( any(is.SZ(X))) 
      warning("Composition has structural zeros: check ?missingsInCompositions")
    if( any(is.MAR(X) | is.MNAR(X)))
      warning("Composition has missings: check ?missingsInCompositions")
    if( any(is.BDL(X)) )
      warning("Composition has values below detection limit: check ?missingsInCompositions")
  }
  X
}



rcomp <- function(X,parts=1:NCOL(oneOrDataset(X)),total=1,warn.na=FALSE,detectionlimit=NULL,BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL) {
  X <-  gsi.mystructure(clo(X,parts,total,detectionlimit=detectionlimit,BDL=BDL,MAR=MAR,MNAR=MNAR,SZ=SZ),class="rcomp")
  if( warn.na ) {
    if( any(is.SZ(X))) 
      warning("Composition has structural zeros: check ?missingsInCompositions")
    if( any(is.MAR(X) | is.MNAR(X)))
      warning("Composition has missings: check ?missingsInCompositions")
    #if( any(is.BDL(X)) )
     # warning("Composition has values below detection limit")
  }
  X
}


aplus <- function(X,parts=1:NCOL(oneOrDataset(X)),total=NA,warn.na=FALSE,detectionlimit=NULL,BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL) {
  if( is.ccomp(X) )
    X <- unclass(X)+0.5
  X <- gsi.simshape(clo(X,parts,total,detectionlimit=detectionlimit,BDL=BDL,MAR=MAR,MNAR=MNAR,SZ=SZ),X)
  if( warn.na ) {
    if( any(is.SZ(X))) 
      warning("aplus has structural zeros: check ?missingsInCompositions")
    if( any(is.MAR(X) | is.MNAR(X)))
      warning("aplus has missings: check ?missingsInCompositions")
    if( any(is.BDL(X)) )
      warning("aplus has values below detection limit: check ?missingsInCompositions")
  }
  class(X) <-"aplus"
  X
}

rplus <- function(X,parts=1:NCOL(oneOrDataset(X)),total=NA,warn.na=FALSE,detectionlimit=NULL,BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL) {
  X <- gsi.simshape(clo(X,parts,total,detectionlimit=detectionlimit,BDL=BDL,MAR=MAR,MNAR=MNAR,SZ=SZ),X)
  if( warn.na ) {
    if( any(na.omit(c(X)==0)) )
      warning("rplus has structural zeros: check ?missingsInCompositions")
    if( any(is.na(c(X)) & ! is.nan(c(X))))
      warning("rplus has missings: check ?missingsInCompositions")
    if( any(is.nan(c(X))))
      warning("rplus has values below detection limit: check ?missingsInCompositions")
  }
  class(X) <-"rplus"
  X
}

ccomp <- function(X,parts=1:NCOL(oneOrDataset(X)),total=NA,warn.na=FALSE,detectionlimit=NULL,BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL) {
  X <- gsi.simshape(clo(X,parts,total,detectionlimit=detectionlimit,BDL=BDL,MAR=MAR,MNAR=MNAR,SZ=SZ),X)
  if( warn.na ) {
    if( any(na.omit(c(X)==0)) )
      warning("ccomp has structural zeros: check ?missingsInCompositions")
    if( any(is.na(c(X)) & ! is.nan(c(X))))
      warning("ccomp has missings: check ?missingsInCompositions")
    if( any(is.nan(c(X))))
      warning("ccomp has values below detection limit: check ?missingsInCompositions")
  }
  class(X) <-"ccomp"
  X
}


rmult <- function(X, parts=1:NCOL(oneOrDataset(X)),
                  orig=gsi.orig(X),
                  missingProjector=attr(X,"missingProjector"),
                  V = gsi.getV(X)) {
  .drop = gsi.ORsequentially(length(dim(X))==0, nrow(X)==1)
  X <- gsi.simshape(oneOrDataset(X)[,parts,drop=.drop],X)
  if(.drop) X = drop(X)
  attr(X,"orig") <- orig
  attr(X,"V") <- V
  attr(X,"missingProjector")<-missingProjector
  class(X) <-"rmult"
  X
}

gsi.orig <- function(x,y=NULL){
  a = attr(x,"orig")
  if(is.null(y)) return(a)
  b = attr(y,"orig")
  if(is.null(a)) return(b)
  return(a)
}

gsi.getV <- function(x,y=NULL){
  a = attr(x,"V")
  if(is.null(y)) return(a)
  b = attr(y,"V")
  if(is.null(a)) return(b)
  return(a)
}

print.rmult <- function (x, ..., verbose=FALSE) {
  Odata <- attr(x, "orig")
  if (!is.null(Odata) & verbose){
    attr(x, "orig") <- missingSummary(Odata)
  } else{
    attr(x, "orig") <- NULL
  }
  mp <- attr(x, "missingProjector")
  if (!is.null(mp) & verbose){
    attr(x, "missingProjector") <- dim(mp)
  } else{
    attr(x, "missingProjector") <- NULL
  } 
  .V <- attr(x, "V")
  if (!is.null(.V) & !verbose){
    attr(x, "V") <- NULL
  }else{} 
  NextMethod(x, ...)
}

gsi2.invperm <- function(i,n){
  i <- unique(c(i,1:n))
  j <- numeric(length(i))
  j[i]<-1:length(i)
  j
}




rcompmargin <- function(X,d=c(1,2),name="+",pos=length(d)+1,what="data") {
  if( what=="data" ) {
    X <- rcomp(X)
    drop <- length(dim(X)) < 2
    if( mode(d)=="character" )
      d <- match(d,colnames(X))
    X <- oneOrDataset(gsi.plain(X))
    d <- unique(d)
    if( NCOL(X) <= length(d) )
      return(rcomp(X))
    else if( NCOL(X) == length(d) +1)
      return( rcomp(cbind(X[,d,drop=FALSE],X[,-d,drop=FALSE]) ))
    Xm <- gsi.recodeM2C(X[,-d,drop=FALSE],BDL=0.0,SZ=0.0,MAR=NaN,MNAR=NA)
    rest =gsi.recodeC2M(Xm %*% rep(1,NCOL(Xm)),zero=BDLvalue,nan=MARvalue,na=MNARvalue)
    tmp <- rcomp(cbind(rest=rest ,X[,d,drop=FALSE] ))
    if( !is.null(colnames(tmp)) )
      colnames(tmp)[1]<-name
    if( pos != 1 )
      tmp <- tmp[,gsi2.invperm(pos,ncol(tmp))]
    if( drop )
      tmp <- drop(tmp)
    rcomp(tmp)
  } else if( what=="var" ) {
    if( mode(d)=="character" )
      d <- match(d,colnames(X))
    Vrest <- sum(X[-d,-d])
    V     <- X[d,d,drop=FALSE]
    C     <- c(apply(X[d,-d,drop=FALSE],1,sum))
    erg   <- rbind(c(Vrest,C),cbind(C,V))
    #erg   <- erg - apply(erg,1,mean)
    #erg   <- t(t(erg)-apply(erg,2,mean))
    if( abs(sum(erg)) >1E-10)
      warning("Scaling problem in rcompmarin for variances")
    if( is.null(colnames(X)) )
      colnames(X) <- paste("var",1:ncol(X))
    colnames(erg)<-c(name,colnames(X)[d])
    row.names(erg) <-colnames(erg)
    if( pos != 1 )
      erg <- erg[gsi2.invperm(pos,ncol(erg)),gsi2.invperm(pos,ncol(erg))]
    erg
  } else
  stop("Unkown type of data in rcompmargin:",what)
}


acompmargin <- function(X,d=c(1,2),name="*",pos=length(d)+1,what="data") {
  if( what == "data" ) {
    drop <- length(dim(X)) < 2
    if( mode(d)=="character" )
      d <- match(d,colnames(X))
    X <- oneOrDataset(gsi.plain(X))
    d <- unique(d)
    if( NCOL(X) <= length(d) )
      return(X)
    else if( NCOL(X) == length(d) +1)
      return( cbind(X[,d,drop=FALSE],X[,-d,drop=FALSE]) )
    Xm <- X[,-d,drop=FALSE]
    Xm <- gsi.recodeM2C(Xm,log(ifelse(Xm>0,Xm,NA)),BDL=-Inf,MAR=NaN,MNAR=NA)
    rest <- Xm %*% rep(1/NCOL(Xm),NCOL(Xm))
    rest <- gsi.recodeC2M(rest,exp(rest),inf=BDLvalue,nan=MARvalue,na=MNARvalue)
    tmp <- acomp(cbind(rest=rest ,X[,d,drop=FALSE] ))
    if( !is.null(colnames(tmp)) )
      colnames(tmp)[1]<-name
    if( pos != 1 )
      tmp <- tmp[,gsi2.invperm(pos,ncol(tmp))]
    if( drop )
      tmp <- drop(tmp)
    acomp(tmp)
  } else if(what=="var") {
    if( mode(d)=="character" )
      d <- match(d,colnames(X))
    Vrest <- mean(X[-d,-d])
    V     <- X[d,d,drop=FALSE]
    C     <- c(apply(X[d,-d,drop=FALSE],1,mean))
    erg   <- rbind(c(Vrest,C),cbind(C,V))
    erg   <- erg - apply(erg,1,mean)
    erg   <- t(t(erg)-apply(erg,2,mean))
    if( abs(sum(erg)) >1E-10)
      warning("Scaling problem in acompmargin for variances")
    erg <- ilrvar2clr(clrvar2ilr(erg))
    if( is.null(colnames(X)) )
      colnames(X) <- paste("var",1:ncol(X))
    colnames(erg)<-c(name,colnames(X)[d])
    row.names(erg) <-colnames(erg)
    if( pos != 1 )
      erg <- erg[gsi2.invperm(pos,ncol(erg)),gsi2.invperm(pos,ncol(erg))]
    erg
  } else 
  stop("Unkown type of data in acompmargin:",what)
}


oneOrDataset <- function(W,B=NULL) {
  W <- gsi.plain(W)
  if( missing(B) || length(dim(B))!= 2 ) {
    if( length(dim(W)) == 2) {
      return( W )
    }
    else {
      tmp <- matrix(c(W),nrow=1)
      colnames(tmp) <- names(W)
      return(tmp)
    }
  } else {
    if( length(dim(W)) == 2) {
      return( W )
    }
    else {
      tmp <- matrix(c(W),nrow=NROW(B),ncol=length(W),byrow=TRUE)
      colnames(tmp)<- names(W)
      return(tmp)
    }
  }
}

gsi.geometricmean <- function(x,...) {
    exp(mean(log(c(unclass(x))),...))
}

gsi.geometricmeanRow <- function(x,...) apply(x,1,gsi.geometricmean,...)
gsi.geometricmeanCol <- function(x,...) apply(x,2,gsi.geometricmean,...)


geometricmean <- function(x,...) {
  if( any(na.omit(x==0)) )
    0
  else
    exp(mean(log(unclass(x)[is.finite(x)&x>0]),...))
}

geometricmeanRow <- function(x,...) apply(x,1,geometricmean,...)
geometricmeanCol <- function(x,...) apply(x,2,geometricmean,...)

meanCol <- function( x , ... , na.action=get(getOption("na.action"))) {
  apply(oneOrDataset(x),2,function(x,...) mean(x,na.action=na.action,...),...)
}

meanRow <- function( x , ... , na.action=get(getOption("na.action"))) {
  meanCol(t(x),...,na.action=na.action)
}


totals <- function( x , ... ) UseMethod("totals",x)

totals.acomp <- function(x,...,missing.ok=TRUE) {
  x <- oneOrDataset(x)
  if( missing.ok )
    x <- gsi.recodeM2C(x,BDL=0.0,SZ=0.0,MAR=0.0,MNAR=0.0)
  else 
    x <- gsi.recodeM2C(x,BDL=0.0,SZ=0.0,MAR=NaN,MNAR=NA)
  erg <- gsi.recodeC2M(apply(x,1,sum,...),zero=BDLvalue,nan=MARvalue,na=MNARvalue)
  erg
}

totals.aplus <- totals.acomp
totals.rcomp <- totals.acomp
totals.rplus <- totals.acomp
totals.ccomp <- totals.acomp

gsi.svdsolve <- function(a,b,...,cond=1E-10) {
  s <- svd(a,...)
  lambda1 <- s$d[1] 
  drop(s$v %*% (gsi.diagGenerate(ifelse(s$d<lambda1*cond,0,1/s$d)) %*% (t(s$u) %*% b)))
  
}

gsi.svdinverse <- function(a,...,cond=1E-10) {
  s <- svd(a,...)
  lambda1 <- s$d[1] 
  s$v %*% (gsi.diagGenerate(ifelse(s$d<lambda1*cond,0,1/s$d)) %*% t(s$u))
}


gsi.csum <- function(x) {c(rep(1,nrow(x)) %*% ifelse(is.finite(x),x,0))}
gsi.rsum <- function(x) {c(ifelse(is.finite(x),x,0)%*%rep(1,ncol(x))) }


mean.aplus<- mean.rplus <- mean.rcomp <- mean.acomp <- function( x, ... ,robust=getOption("robust")) {
  idtInv(mean(idt(x),...,robust=robust),x)
}

mean.ccomp <- function( x, ... ,robust=getOption("robust")) {
  ccomp(c(rep(1,nrow(x))%*% unclass(x)))
}

#mean.acomp <- function( x, ... ) {
#  if( has.missings(x) ) 
#    clrInv(gsi.svdsolve(sumMissingProjector(x),gsi.csum(gsi.cleanR(clr(x)))))
#  else
#    clrInv(mean(clr(x),...))
#}


#mean.rcomp <- function( x,... ) {
#  if( has.missings(x) ) 
#    cptInv(gsi.svdsolve(sumMissingProjector(x), gsi.csum(gsi.cleanR(cpt(x))) ) )
#  else
#    cptInv(meanCol(cpt(x),...))
#}

#mean.aplus <- function( x,... ) {
#  if( has.missings(x) ) 
#    iltInv(gsi.svdsolve(sumMissingProjector(x), gsi.csum(gsi.cleanR(ilt(x))) ) )
#  else
#    iltInv(meanCol(ilt(x),...))
#}

#mean.rplus <- function( x,...) {
#  if( has.missings(x) ) 
#    iitInv(gsi.svdsolve(sumMissingProjector(x), gsi.csum(gsi.cleanR(iit(x))) ) )
 # else
#    iitInv(meanCol(iit(x),...))
#}


  

mean.rmult <- function( x,...,na.action=NULL,robust=getOption("robust")) {
  if( !is.null(na.action) ) {
    x <- na.action(x)
  }
  control <- attr(robust,"control")
  if( is.logical(robust) ) robust <- if(robust) "mcd" else "pearson"
  if( has.missings(x) ) {
    if( !(is.character(robust) && robust=="pearson" ))
      warning("mean.rmult: Robust estimation currently not supported with missings")
    erg=gsi.svdsolve(sumMissingProjector(x), gsi.csum(x,...))  
  }
  else {
    if( is.character(robust) ) {
      erg= rmult(switch(robust,
             pearson=do.call(meanCol,c(list(x=unclass(x)),control,...)),
             mcd={
               #require("robustbase")
               if(!is.null(control)) covMcd(unclass(x),...,control=control)$center else covMcd(unclass(x),...)$center},
                   
             stop("mean.rmult: Unkown robustness type:",robust)
               ))
    } else if(is.function(robust)) {
      erg=rmult(robust("mean",unclass(x),...,robust=robust))
    } else stop("mean.rmult: Unkown robustness type:",robust)
    .orig = gsi.orig(x)
    .V = gsi.getV(x)
    rmult(erg, orig=.orig, V=.V)
  }
  
}


clr2ilr <- function( x , V=ilrBase(x=x) ) {
  rmult(
    gsi.simshape(
      gsi.recodeC2M(
        oneOrDataset(x), ninf=0,nan=0,na=0,inf=0
        ) %*% V , x),
    orig=gsi.orig(x), V=t(gsi.svdinverse(V))
  )
}

ilr2clr <- function( z , V=ilrBase(z=z), x=gsi.orig(z) ) {
  if(is.null(V)) V = ilrBase(D=1+ncol(oneOrDataset(z)))
  if(ncol(V)-nrow(V)==1){
    warning("ilr2clr: provided V apparently transposed. Check your calculations! avoid apt/alr! Attempting a patch")
    V = t(V)
  }
  erg <- oneOrDataset(z) %*% t(V)
  if( !is.null(x) )
    colnames(erg)<-colnames(x)
  rmult(gsi.simshape( erg , z), orig=gsi.orig(z) )
}


clrvar2ilr <- function( varx , V=ilrBase(D=ncol(varx)) ) {
  t(V) %*% varx %*% V
}

ilrvar2clr <- function( varz , V=ilrBase(D=ncol(varz)+1), x=NULL ) {
  erg <- V %*% varz %*% t(V)
  if( !is.null(x)) {
    colnames(erg) <- colnames(x)
    row.names(erg) <- colnames(x)
  }
  erg
}



#################################################
## utility function to convert one clr variance matrix into a variation matrix
clrvar2variation = function(Sigma){
  diagSigma = diag(Sigma)
  one = rep(1, length(diagSigma))
  erg = outer(one, diagSigma) + outer(diagSigma, one) - 2*Sigma
  colnames(erg) = colnames(Sigma)
  rownames(erg) = rownames(Sigma)
  return(erg)
}

## utility function to convert one variation matrix into a clr variance matrix
variation2clrvar = function(TT){
  D = ncol(TT)
  H = diag(D) - 1/D * matrix(1, ncol=D, nrow=D)
  erg = -0.5 * H %*% TT %*% H
  colnames(erg) = colnames(TT)
  rownames(erg) = rownames(TT)
  return(erg)
}


## functions to check if a given matrix M can be a variation matrix,
#     or a clr or ilr/alr variance-covariance matrix
is.variation = function(M, tol=1e-10){
  egv = eigen(M)$values
  diagnull = all(abs(diag(M))<tol)
  rightsigns = sum(egv>tol)==1
  return(diagnull & rightsigns)
}

is.ilrvar  = function(M, tol=1e-10){
  egv = eigen(M)$values
  rightsigns = all(egv>(-tol))
  return(rightsigns)
}

is.clrvar  = function(M, tol=1e-10){
  egv = eigen(M)$values
  D = length(egv)
  nullegvs = egv[egv<tol]
  rightsigns = all(egv>(-tol)) & (length(nullegvs)>=1) 
  return(rightsigns)
}



#################################################




var         <- function(x,...) UseMethod("var",x)
var.default <- function (x, y = NULL, na.rm = FALSE, use,...) stats::var(x,y,na.rm,use)

var.acomp <- function(x,y=NULL,...,
                      robust=getOption("robust"), use="all.obs",
                      giveCenter=FALSE) {
  control <- attr(robust,"control")
  if( is.logical(robust) ) robust <- if(robust) "mcd" else "pearson"
  if( has.missings(x) ||  has.missings(y) ) {
    if( !(is.character(robust) && robust=="pearson" ))
      warning("var.*: Robust estimation with losts not yet implemented")
    if(is.null(y)){
      if(use=="pairwise.complete.obs"){
        return(gsi.varwithlosts(cdt(x),giveCenter=giveCenter) )
      }else{
        tk = as.logical( gsi.geometricmeanRow( is.NMV(x) ) )
        xaux = x[tk,]
          class(xaux) = class(x)
        return(var(cdt(xaux),giveCenter=giveCenter))
      }
    }else{
      warning("Covariance with losts not yet implemented. Omitting lost values.")
        tk = as.logical( gsi.geometricmeanRow( is.NMV(cbind(x,y)) ) )
        xaux = x[tk,]
          class(xaux) = class(x)
        yaux = y[tk,]
          class(yaux) = class(y)
        return(var(unclass(cdt(xaux)),unclass(cdt(yaux)),...))
    }
  } else {
    switch(robust,
           pearson={
             erg <- var(unclass(cdt(x)),unclass(cdt(y)),...)
             if(giveCenter)
               attr(erg,"center")<-mean(x,robust=FALSE)
             erg
             },
           mcd={
             #require("robustbase")
             if(is.null(y)) {
               erg <- ilrvar2clr(if( is.null(control)) covMcd(unclass(idt(x)),...)$cov else covMcd(unclass(idt(x)),...,control=control)$cov,x=x)
               if(giveCenter)
                 attr(erg,"center")<-mean(x,robust=FALSE)
               erg
             } else {
               Dx<- ncol(x)
               Dy<- ncol(y)
               x1 <- idt(x)
               y1 <- idt(y)
               erg <- if( is.null(control)) covMcd(cbind(x1,y1),...) else covMcd(cbind(x1,y1),...,control=control)
               m <- erg$center
               erg <- erg$cov
               erg <- t(ilrBase(D=Dx)) %*% erg[1:(Dx-1),Dx:ncol(erg)] %*% ilrBase(D=Dy)
               row.names(erg) <- colnames(x)
               colnames(erg) <- colnames(y)
               if( giveCenter )
                 attr(erg,"center")<-idtInv(m,x)
               erg
             }},
           stop("var.*: unkown robust method",robust)
           )
  }
}
var.rcomp <- var.acomp

var.aplus  <- function(x,y=NULL,...,robust=getOption("robust"), use="all.obs",
                       giveCenter=FALSE) {
  control <- attr(robust,"control")
  if( is.logical(robust) ) robust <- if(robust) "mcd" else "pearson"
  if( has.missings(x) ||  has.missings(y) ) { 
    if( !(is.character(robust) && robust=="pearson" ))
      warning("var.*: Robust estimation with losts not yet implemented")
    if(is.null(y)){
      if(use=="pairwise.complete.obs"){
        return(gsi.varwithlosts(cdt(x),giveCenter=giveCenter) )
      }else{
        tk = as.logical( gsi.geometricmeanRow( is.NMV(x) ) )
        xaux = x[tk,]
          class(xaux) = class(x)
        return(var(cdt(xaux),giveCenter=giveCenter))
      }
    }else{
      warning("Covariance with losts not yet implemented. Omitting lost values.")
        tk = as.logical( gsi.geometricmeanRow( is.NMV(cbind(x,y)) ) )
        xaux = x[tk,]
          class(xaux) = class(x)
        yaux = y[tk,]
          class(yaux) = class(y)
        return(var(unclass(cdt(xaux)),unclass(cdt(yaux)),...))
    }
  } else {
    switch(robust,
           pearson={
             erg <- var(unclass(cdt(x)),unclass(cdt(y)),...)
             if( giveCenter) attr(erg,"center")<-mean(x,robust=FALSE)
             erg
           }
             ,
           mcd={
             #require("robustbase")
             if(is.null(y)) {
               erg <- if( is.null(control)) covMcd(unclass(idt(x)),...)$cov else covMcd(unclass(idt(x)),...,control=control)$cov
               if(giveCenter)
                 attr(erg,"center")<-mean(x,robust=FALSE)
               erg
             } else {
               Dx<- ncol(x)
               Dy<- ncol(y)
               x1 <- cdt(x)
               y1 <- cdt(y)
               erg <- if( is.null(control)) covMcd(cbind(x1,y1),...)$cov else covMcd(cbind(x1,y1),...,control=control)$cov
               m <- erg$center
               erg <- erg$cov
               erg <- erg[1:Dx,(Dx+1):ncol(erg)]
               row.names(erg) <- colnames(x)
               colnames(erg) <- colnames(y)
               if( giveCenter) attr(erg,"center")<-cdtInv(m,x)
               erg
             }
           },
           stop("var.*: unkown robust method",robust)
           )
  }
}
var.rplus <- var.aplus
var.rmult <- var.aplus

cov         <- function(x,y=x,...) UseMethod("cov",x)
cov.default <- function (x, y = NULL, use = "everything", method = c("pearson", 
    "kendall", "spearman"),...) stats::cov(x,y,use,method)

cov.acomp   <- var.acomp
cov.rcomp <- var.rcomp
cov.aplus <- var.aplus
cov.rplus <- var.rplus
cov.rmult <- var.rmult

cor <- function(x,y=NULL,...) UseMethod("cor",x)
cor.default <- function (x, y = NULL, use = "everything", method = c("pearson", 
    "kendall", "spearman"),...) stats::cor(x,y,use,method)




cor.acomp <- function(x,y=NULL,...,robust=getOption("robust")) {
  mat2cor <- function(x) {
    if( nrow(x) < 2 )
      return(x/x)
    sf<-diag(1/sqrt(diag(x)))
    gsi.mystructure( sf %*% x %*% sf ,dimnames=dimnames(x))
  }
  if( is.null(y) ) {
    mat2cor(var(x,y,...,robust=robust))
  } else {
    varX <- var(x,y=NULL,...,robust=robust)
    varY <- var(y,y=NULL,...,robust=robust)
    covXY<- var(x,y,...,robust=robust)
    sfX<-diag(1/sqrt(diag(varX)))
    sfY<-diag(1/sqrt(diag(varY)))
    gsi.mystructure( sfX %*% covXY %*% sfY, dimnames=list(colnames(x),colnames(y)))
  }
}

cor.rcomp <- cor.acomp 
cor.aplus <- cor.acomp
cor.rplus <- cor.acomp
cor.rmult <- cor.acomp

#  function(x,y=NULL,...) {
#  cor(unclass(x),unclass(cdt(y)),...)
#}


powerofpsdmatrix <- function(M,p,...) {
  s <- svd(M,...)
  d <- ifelse( abs(s$d)>max(abs(s$d))*1E-10, s$d^p,0)
  s$u %*% gsi.diagGenerate(d) %*% t(s$v)
}

mvar <- function(x,...) UseMethod("mvar",x)
mcov <- function(x,...) UseMethod("mcov",x)
mcor <- function(x,...) UseMethod("mcor",x)
msd  <- function(x,...) UseMethod("msd",x)

mvar.default <- function(x,y=NULL,...) {
  sum(gsi.diagExtract(var(x,y,...)))
}

mcov.default <- function(x,y=x,...) {
  sum(abs(svd(cov(idt(x),idt(y),...))$d))
}

msd.default <- function(x,y=NULL,...) {
  sqrt(mean(gsi.diagExtract(var(idt(x),y=NULL,...))))
}

mcor.default <- function(x,y,...) {
  ix <- scale(idt(x),center=TRUE,scale=FALSE)
  ix <- ix %*% powerofpsdmatrix(var(ix),-1/2)
  iy <- scale(idt(y),center=TRUE,scale=FALSE)
  iy <- iy %*% powerofpsdmatrix(var(iy),-1/2)
  mcov(ix,iy)
}



summary.acomp <- function( object,...,robust=getOption("robust") ) {
  W <- clo(gsi.plain(object))
  Wq <- apply(gsi.recodeM2C(W,BDL=NaN,SZ=NaN,MAR=NaN,MNAR=NaN),
              1,function(w) outer(w,w,"/"))
  dim(Wq)<-c(ncol(W),ncol(W),nrow(W))
  dimnames(Wq) <- list(colnames(W),colnames(W),NULL)
  vari <- if(is.null(robust) ) NULL else variation.acomp(acomp(W),robust=robust)
  narm <- function(x) x[is.finite(x)]
  gsi.mystructure(list(mean=if(is.null(robust)) NULL else mean(acomp(W),robust=robust),
       mean.ratio=apply(Wq,1:2,function(x) exp(mean(log(x[is.finite(x)])))),
       variation=vari,
       expsd=if( is.null(vari) ) NULL else exp(sqrt(vari)),
       invexpsd=if( is.null(vari) ) NULL else exp(-sqrt(vari)),
       min=apply(Wq,1:2,function(x) min(narm(x))),
       q1 =apply(Wq,1:2,function(x,...) quantile(narm(x),...),probs=0.25),
       med=apply(Wq,1:2,function(x,...) median(narm(x),...)),
       q3 =apply(Wq,1:2,function(x,...) quantile(narm(x),...),probs=0.75),
       max=apply(Wq,1:2,function(x,...) max(narm(x),...)),
       missingness=missingSummary(object)  
       ),class="summary.acomp")
       
}

summary.aplus <- function( object,...,digits=max(3, getOption("digits")-3),robust=NULL  ) {
  if( !missing(robust) )
    if( if(is.logical(robust)) robust else robust!="pearson" )
      warning("robustness currently not supported in summary.aplus")
  object <- ilt(object)
  erg <- sapply(data.frame(object),summary,...,digits=18)
  erg <- apply(erg,1:2,exp)
  erg <- apply(erg,1:2,signif,digits=digits)
  if( any( !is.NMV(object)) ) {
    attr(erg,"missingness")<-missingSummary(object)  
  }
  class(erg) <- c("summary.aplus",class(erg))
  erg       
}

summary.rplus <- function( object,... ,robust=NULL  ) {
  if( !missing(robust) )
    if( if(is.logical(robust)) robust else robust!="pearson" )
      warning("robustness currently not supported in summary.rplus")
  object <- iit(object)
  erg <- sapply(data.frame(object),summary,...)
  if( any( !is.NMV(object)) ) {
    attr(erg,"missingness")<-missingSummary(object)  
  }
  class(erg) <- c("summary.rplus",class(erg))
  erg       
}

summary.rmult <- function( object,...  ,robust=NULL ) {
  if( !missing(robust) )
    if( if(is.logical(robust)) robust else robust!="pearson" )
      warning("robustness currently not supported in summary.mult")
  object <- unclass(object)
  erg <- sapply(data.frame(object),summary,...)
  class(erg) <- c("summary.rmult",class(erg))
  erg       
}

summary.rcomp <- function( object,...,robust=NULL ) {
  # must support robust = NULL for no estimation with missing methods
  if( !missing(robust) )
    if( if(is.logical(robust)) robust else robust!="pearson" )
      warning("robustness currently not supported in summary.rcomp")
  object <- clo(gsi.plain(object)) 
  erg <- sapply(data.frame(object),function(x,...) summary(x[is.NMV(x)],...),...)
  if( has.missings(object) ) attr(erg,"missingness")<-missingSummary(object)
  class(erg) <- c("summary.rcomp",class(erg))
  erg       
}



vp.logboxplot <- function(x,y,...,dots=FALSE,boxes=TRUE,xlim=NULL,ylim=NULL,log=TRUE,notch=FALSE,plotMissings=TRUE,mp=~simpleMissingSubplot(missingPlotRect,
                                                                                         missingInfo,c("NM","TM",cn)),
         missingness=attr(y,"missingness")                                                                                ) {
  if(is.null(missingness))
    plotMissings <- FALSE
  fakMis <- FALSE
  if( any(is.na(x)) )  {
    fakMis<- TRUE
    levels(x) <- c(levels(x),"ERR")
    x[is.na(x)]<-"ERR"
  }
  nmv <- oneOrDataset(missingness=="NMV")
  nMis <- apply(!nmv,1,sum)
  nonmissing <- nMis==0
  lf <- length(levels(x))
  if( boxes ) {
    stats <- boxplot(split(log(ifelse(nonmissing,y,NA)),x),plot=FALSE)
    stats$stats <- exp(stats$stats)

    stats$conf  <- exp(stats$conf)
    stats$out   <- exp(stats$out)
    bxp(stats,add=TRUE,at=1:lf,width=rep(1,lf),notch=notch)
      
  }
  if( dots  ) points(x,y,...)
  if( plotMissings && !all(nmv)) {
    wM <- apply(!nmv,1,function(x) c(which(x),1)[1])
    missingTab <-  cbind(NotMissing=tapply(nonmissing,x,sum),
                     TotallyMissing=tapply(nMis>1,x,sum),
                     oneOrDataset(apply(nmv,2,function(w) tapply(nMis==1 & !w,x,sum))) 
                     )
    cn <- colnames(missingness)
    for( i in 1:length(levels(x))) {
      lev <- levels(x)[i]
      missingInfo <- missingTab[i,]
      if( sum(missingInfo[-1])>0 ) {
        usr <- par("usr")
        missingPlotRect <- c(i+0.45,i+0.5,usr[3],usr[4])
        eval(mp[[2]])
      }
    }
  }
}



#vp.boxplot <- function(x,y,...,dots=FALSE,boxes=TRUE,xlim,ylim,log,notch=FALSE,
#                       plotMissings=TRUE,
#                       mp=~simpleMissingSubplot(missingPlotRect,
#                                                missingInfo,c("NM","TM",cn)),
#                       missingness=attr(y,"missingness")) {
#    if( boxes ) boxplot(split(y,x),add=TRUE,notch=notch)
#    if( dots  ) points(x,y,...)
#}


vp.boxplot <- function(x,y,...,dots=FALSE,boxes=TRUE,xlim=NULL,ylim=NULL,log=FALSE,notch=FALSE,plotMissings=TRUE,mp=~simpleMissingSubplot(missingPlotRect,
                                                                                         missingInfo,c("NM","TM",cn)),
         missingness=attr(y,"missingness")                                                                                ) {
  if(is.null(missingness))
    plotMissings <- FALSE
  fakMis <- FALSE
  if( any(is.na(x)) )  {
    fakMis<- TRUE
    levels(x) <- c(levels(x),"ERR")
    x[is.na(x)]<-"ERR"
  }
  nmv <- oneOrDataset(missingness=="NMV")
  nMis <- apply(!nmv,1,sum)
  nonmissing <- nMis==0
  lf <- length(levels(x))
  if( boxes ) {
    stats <- boxplot(split(ifelse(nonmissing,y,NA),x),plot=FALSE)
    #stats$stats <- exp(stats$stats)

    #stats$conf  <- exp(stats$conf)
    #stats$out   <- exp(stats$out)
    bxp(stats,add=TRUE,at=1:lf,width=rep(1,lf),notch=notch)
      
  }
  if( dots  ) points(x,y,...)
  if( plotMissings && !all(nmv)) {
    wM <- apply(!nmv,1,function(x) c(which(x),1)[1])
    missingTab <-  cbind(NotMissing=tapply(nonmissing,x,sum),
                     TotallyMissing=tapply(nMis>1,x,sum),
                     oneOrDataset(apply(nmv,2,function(w) tapply(nMis==1 & !w,x,sum)) )
                     )
    cn <- colnames(missingness)
    for( i in 1:length(levels(x))) {
      lev <- levels(x)[i]
      missingInfo <- missingTab[i,]
      if( sum(missingInfo[-1])>0 ) {
        usr <- par("usr")
        missingPlotRect <- c(i+0.45,i+0.5,usr[3],usr[4])
        eval(mp[[2]])
      }
    }
  }
}



gsi.textpanel <- function(x,y,lab,...) {
  par(usr=c(0,1,0,1),xlog=FALSE,ylog=FALSE)
  text(0.5,0.5,lab,...)
}


# changed by Raimon on 2008-07-07
#   Now the verical scale of the plots has always the same length,
#   but each row of plots has its own ylim.
#   In this way, the boxplots are not too narrow, but
#   spread and location are still inter-comparable.
boxplot.acomp <- function(x,fak=NULL,...,
                          xlim=NULL,ylim=NULL,log=TRUE,
                          panel=vp.logboxplot,dots=!boxes,boxes=TRUE,
                          notch=FALSE,
                          plotMissings=TRUE,
                          mp=~simpleMissingSubplot(missingPlotRect,
                                                missingInfo,c("NM","TM",cn))) {
  X <- acomp(x)
  if( is.null(fak) )
    fak <- factor(rep("",nrow(X)))
  if( is.null(xlim)) {
    if( is.factor(fak) )
      xlim <- c(0,nlevels(fak)+1)
    else {
      xlim <- range(fak)
    }
  }
  if( !is.factor(fak) ) {
    boxes <- FALSE
    dots  <- TRUE
  }
  if( is.function(panel) )
    panel <- list(panel)
  ipanel <- function(x,y,...) {
    ic <- gsi.mapfrom01(log(x))
    jc <- gsi.mapfrom01(log(y))
    mis <- missingType(X[,c(ic,jc)])
    Y <- X[,c(jc)]/X[,c(ic)]
    attr(Y,"missingness") <- mis
    #a <- gsi.recodeM2Clean(unclass(X)[,gsi.mapfrom01(log(x))])
    #b <- gsi.recodeM2Clean(unclass(X)[,])
    for( thispanel in panel ) {
      thispanel(fak,Y,...,notch=notch,dots=dots,boxes=boxes,plotMissings=plotMissings,mp=mp)
    }
  }
  if( is.null(ylim) ) {
    a<-apply(x,1,function(x) {
      x <- x[is.finite(x)&x>0]
      if( length(x) > 0 ) {
        mi <- min(x)
        ma <- max(x)
        c(mi/ma,ma/mi)
      } else {
        c(1,1)
      }}
             )
    ylim <- range(a)
     nc = gsi.getD(X)
     ylims = sapply(1:nc, 
        function(i){
         aux = sapply(1:nc, function(j){
              aux = log(X[,i]/X[,j])
              aux = aux[is.finite(aux)]
              return( range(aux) )
        })
        return(c( min(aux[1,]), max(aux[2,]) ))
      })
     yrange = max(c(-1,1) %*% ylims )
     ylims = outer( c(0.5*c(1,1) %*% ylims), c(yrange*c(-1,1)/2), "+")
  }else{
     yrange = NULL
     ylims = NULL
  }

  #su <- summary.acomp(X,robust=NULL)
  #minq <- min(su$min)
  #maxq <- max(su$max)
  mm <- exp(sapply(1:NCOL(X),gsi.mapin01))
  colnames(mm) <- colnames(X)
  ipairs <- function (x, labels, panel = ipanel, ...,
                      font.main = par("font.main"),
                      cex.main = par("cex.main"), diag.panel = NULL, 
                      text.panel = textPanel,
                      label.pos = 0.5 , cex.labels = NULL, 
                      font.labels = 1, gap = 1,xlim, ylim, yrange, ylims, log) {
    textPanel <- function(x = 0.5, y = 0.5, txt, cex, font) text(x, 
                                     y, txt, cex = cex, font = font)
    localAxis <- function(side, xpd, bg, ...) axis(side, xpd = NA, 
                                                   ...)
    panel <- match.fun(panel)
    nc <- ncol(x)
    labels <- colnames(x)
    if (is.null(labels)) 
      labels <- paste("var", 1:nc)
    has.labs <- ! is.null(labels)
    oma <- c(4, 4, 4, 4)
    opar <- par(mfrow = c(nc, nc), mar = rep.int(gap/2, 4), oma = oma)
    on.exit(par(opar),add=TRUE)
    for (i in 1:nc ){
     for (j in 1:nc) {
      if(!is.null(yrange)){ylim=exp(ylims[i,])}
      plot(x[, j], x[, i], xlab = "", ylab = "", axes = FALSE, 
           type = "n", ...,xlim=xlim,ylim=ylim,log=log)
      box()
      mfg <- par("mfg")
      if (i == j) {
        if (has.labs) {
          par(usr = c(0, 1, 0, 1))
          if (is.null(cex.labels)) {
            l.wid <- strwidth(labels, "user")
            cex.labels <- max(0.8, min(2, 0.9/max(l.wid)))
          }
          text.panel(0.5, label.pos, labels[i], cex = cex.labels, 
                     font = font.labels)
        }
      }
      else  
       panel(as.vector(x[, j]), as.vector(x[, i]), ...)
      if (any(par("mfg") != mfg)) 
        stop("The panel function made a new plot")
     }
    }
    invisible(NULL)
  }
  ipairs(mm,labels=colnames(X),panel=ipanel,...,log=ifelse(log,"y",""),
             ylim=ylim, yrange=yrange, xlim=xlim, ylims=ylims, text.panel=gsi.textpanel)
  
  replot(plot=match.call())  
  
}


boxplot.rcomp <- function(x,fak=NULL,...,
                         xlim=NULL,ylim=NULL,log=FALSE,panel=vp.boxplot,
                          dots=!boxes,boxes=TRUE,notch=FALSE,
                          plotMissings=TRUE,
                          mp=~simpleMissingSubplot(missingPlotRect,
                                                missingInfo,c("NM","TM",cn))) {
  X <- acomp(x)
  if( is.null(fak) )
    fak <- factor(rep("",nrow(X)))
  if( is.null(xlim) ) {
    if( is.factor(fak) )
      xlim <- c(0,nlevels(fak)+1)
    else {
      xlim <- range(fak)
    }
  }
  if( !is.factor(fak) ) {
    boxes <- FALSE
    dots  <- TRUE
  }
  if( is.function(panel) )
    panel <- list(panel)
  
  if( is.null(ylim) ) {
    if( log ) {
      a<-apply(x,1,function(x) {
        x <- x[is.finite(x)&x>0]
        if( length(x) > 0 ) {
          mi <- min(x)
          ma <- max(x)
          c(mi/ma,ma/mi)
        } else {
          c(1,1)
        }}
               )
      ylim <- log(range(a))
    } else ylim<-c(0,1)
  }
  ipanel <- function(x,y,...) {
    a <- unclass(X)[,gsi.mapfrom01(log(x))]
    b <- unclass(X)[,gsi.mapfrom01(log(y))]
    Y <- if(log) log(ifelse(is.NMV(b)&is.NMV(a),b/a,NA)) else ifelse(is.NMV(b)&is.NMV(a),b/(a+b),NA)
    attr(Y,"missingness")<-missingType(X[,c(gsi.mapfrom01(log(x)),gsi.mapfrom01(log(y)))])
    for( thispanel in panel ) 
      thispanel(fak,Y,
                ...,notch=notch,dots=dots,boxes=boxes,plotMissings=plotMissings,mp=mp)
  }


  #su <- summary.rcomp(X) ## Must be changed when robustness in rcomp arises
  #minq <- log(min(su[,"min"])/(min(su[,"min"])+max(su[,"max"])))
  #maxq <- log(max(su[,"max"])/(min(su[,"min"])+max(su[,"max"])))
  
  ipairs <- function (x, labels, panel = points, ..., 
                      font.main = par("font.main"),
                      cex.main = par("cex.main"), diag.panel = NULL, 
                      text.panel = textPanel,
                      label.pos = 0.5 , cex.labels = NULL, 
                      font.labels = 1, gap = 1,xlim,ylim,log="") {
    textPanel <- function(x = 0.5, y = 0.5, txt, cex, font) text(x, 
                                     y, txt, cex = cex, font = font)
    localAxis <- function(side, xpd, bg, ...) axis(side, xpd = NA, 
                                                   ...)
    panel <- match.fun(panel)
    nc <- ncol(x)
    #labels <- colnames(x)
    if (is.null(labels)) 
      labels <- paste("var", 1:nc)
    has.labs <- ! is.null(labels)
    oma <- c(4, 4, 4, 4)
    opar <- par(mfrow = c(nc, nc), mar = rep.int(gap/2, 4), oma = oma)
    on.exit(par(opar),add=TRUE)
    for (i in 1:nc ) for (j in 1:nc) {
      plot(x[, j], x[, i], xlab = "", ylab = "", axes = FALSE, 
           type = "n", ...,xlim=xlim,ylim=ylim,log=log)
      box()
      mfg <- par("mfg")
      if (i == j) {
        if (has.labs) {
          par(usr = c(0, 1, 0, 1))
          if (is.null(cex.labels)) {
            l.wid <- strwidth(labels, "user")
            cex.labels <- max(0.8, min(2, 0.9/max(l.wid)))
          }
          text.panel(0.5, label.pos, labels[i], cex = cex.labels, 
                     font = font.labels)
        }
      }
      else  
        panel(as.vector(x[, j]), as.vector(x[, i]), ...)
      if (any(par("mfg") != mfg)) 
        stop("The panel function made a new plot")
    }
    invisible(NULL)
  }


  ipairs(exp(sapply(1:NCOL(X),gsi.mapin01)),labels=colnames(X),panel=ipanel,...,ylim=ylim,xlim=xlim)
  
  replot(plot=match.call())  

}

boxplot.rplus <- function(x,fak=NULL,...,ylim=NULL,log=FALSE,
                          plotMissings=TRUE,
                          mp=~simpleMissingSubplot(missingPlotRect,
                                                   missingInfo,
                                                   names(missingInfo))
                          ) {
  if( !is.null(fak) )
    warning("Spliting not yet implemente in boxplot.rplus")
  nmv <- oneOrDataset((is.NMV(x) ))
  xx <- ifelse(is.BDL(x),if(log) NA else 0,ifelse(nmv,x,NA))
  if( is.null(ylim) ) {
      ylim <- range(xx[nmv])
      if( !log )
        ylim[1]<-0
  }
  erg<-boxplot(as.data.frame(xx),...,ylim=ylim,log=if(log) "y" else "")
  if( plotMissings && !is.null(mp) &&
     !all(nmv)) {
    su <- missingSummary(x)
    for(i in 1:ncol(x)) {
      if(any(nmv[,i])) {
        usr <- par("usr")
        missingPlotRect <- c(i+0.45,i+0.5,usr[3],usr[4])
        cn <- colnames(x)[i]
        X<-x[,i]
        missingInfo <- su[i,]
        eval(mp[[2]])
      }
    }
  }
  replot(plot=match.call())  

  invisible(erg)
}

boxplot.aplus <- function(x,fak=NULL,...,log=TRUE,
                          plotMissings=TRUE,
                          mp=~simpleMissingSubplot(missingPlotRect,
                                                   missingInfo,
                                                   names(missingInfo))
) {
  if( !is.null(fak) )
    warning("Spliting not yet implemente in boxplot.aplus")
  
  stats <- boxplot(as.data.frame(ifelse(nmv<-is.NMV(x),ilt(x),NA)),plot=FALSE)
  delog <- function(x) {if(is.list(x)) lapply(x,delog) else exp(x)}
  stats$stats <- exp(stats$stats)
  stats$conf <- exp(stats$conf)
  stats$out <- exp(stats$out)
  erg<-bxp(stats,...,at=1:ncol(x),width=rep(1,ncol(x)),log=if(log) "y" else "")
  if( plotMissings && !is.null(mp) && !all(nmv) ) {
    su <- missingSummary(x)
    for(i in 1:ncol(x)) {
      if(any(nmv[,i])) {
        usr <- par("usr")
        missingPlotRect <- c(i+0.45,i+0.5,usr[3],usr[4])
        cn <- colnames(x)[i]
        X<-x[,i]
        missingInfo <- su[i,]
        eval(mp[[2]])
      }
    }
  }
  replot(plot=match.call())  

  invisible(erg)
}



vp.qqnorm <- function(x,y,...,alpha=NULL) {
  usr <- par("usr")
  usr[1:2] <- range(qnorm(ppoints(length(y))))
  usr[3:4] <- range(y)
  par( usr=usr )
  if( !is.null(alpha) && is.factor(x) ) 
    alpha <- alpha/nlevels(x)
  reject <- FALSE
  if( is.factor(x)) {
    for( k in split(y,x) ) {
      if( !is.null(alpha) && shapiro.test(k)$p < alpha )
        reject<-TRUE
      lines(qnorm(ppoints(length(k))),sort(k),...)
    }
  } else { 
    if( !is.null(alpha) && shapiro.test(y)$p < alpha )
        reject<-TRUE
    points(qnorm(ppoints(length(y))),sort(y),...)
  }
  qqline(y)
  if( reject )
    title(main="!",col.main="red")
    
}

qqnorm.acomp <- function(y,fak=NULL,...,panel=vp.qqnorm,alpha=NULL) {
  X <- acomp(y)
  if( !is.null(alpha) )
    alpha <- alpha/((nrow(X)*(nrow(X)-1)/2))
  if( is.function(panel) )
    panel <- list(panel)
  ipanel <- function(x,y,...) {
    a <- unclass(X)[,gsi.mapfrom01(x)]
    b <- unclass(X)[,gsi.mapfrom01(y)]
    v <- log(b/a)
    for( thispanel in panel )
      thispanel(fak,v,...,alpha=alpha)
  }
  pairs(sapply(1:NCOL(X),gsi.mapin01),labels=colnames(X),panel=ipanel,...)
  replot(plot=match.call())  

}

qqnorm.aplus <- function(y,fak=NULL,...,panel=vp.qqnorm,alpha=NULL) {
  X <- aplus(y)
  if( is.function(panel) )
    panel <- list(panel)
  if( !is.null(alpha) )
    alpha <- alpha/(nrow(X)^2)
  ipanelupper <- function(x,y,...) {
    a <- unclass(X)[,gsi.mapfrom01(x)]
    b <- unclass(X)[,gsi.mapfrom01(y)]
    for( thispanel in panel )
      thispanel(fak,log(b/a),...,alpha=alpha)
  }
  ipanellower <- function(x,y,...) {
    a <- unclass(X)[,gsi.mapfrom01(x)]
    b <- unclass(X)[,gsi.mapfrom01(y)]
    for( thispanel in panel )
      thispanel(fak,log(b*a),...,alpha=alpha)
  }
  ipaneldiag <- function(x,...) {
    a <- unclass(X)[,gsi.mapfrom01(x)]
    for( thispanel in panel )
      thispanel(fak,log(a),...,alpha=alpha)
  }
  itextpanel <- function(x,y,lab,...) {
    par(usr=c(0,1,0,1),xlog=FALSE,ylog=FALSE)
    text(0.1,0.9,lab,adj=c(0,1),...)
  }

  pairs(sapply(1:NCOL(X),gsi.mapin01),labels=colnames(X),lower.panel=ipanellower,upper.panel=ipanelupper,diag.panel=ipaneldiag,text.panel=itextpanel,...)
  replot(plot=match.call())  

}



qqnorm.rcomp <- function(y,fak=NULL,...,panel=vp.qqnorm,alpha=NULL) {
  X <- rcomp(y)
  if( is.function(panel) )
    panel <- list(panel)
  if( !is.null(alpha) )
    alpha <- alpha/(nrow(X)^2)
  ipanelupper <- function(x,y,...) {
    a <- unclass(X)[,gsi.mapfrom01(x)]
    b <- unclass(X)[,gsi.mapfrom01(y)]
    for( thispanel in panel )
      thispanel(fak,b-a,...,alpha=alpha)
  }
  ipanellower <- function(x,y,...) {
    a <- unclass(X)[,gsi.mapfrom01(x)]
    b <- unclass(X)[,gsi.mapfrom01(y)]
    for( thispanel in panel )
      thispanel(fak,b+a,...,alpha=alpha)
  }
  ipaneldiag <- function(x,...) {
    a <- unclass(X)[,gsi.mapfrom01(x)]
    for( thispanel in panel )
      thispanel(fak,a,...,alpha=alpha)
  }
  itextpanel <- function(x,y,lab,...) {
    par(usr=c(0,1,0,1),xlog=FALSE,ylog=FALSE)
    text(0.1,0.9,lab,adj=c(0,1),...)
  }

  pairs(sapply(1:NCOL(X),gsi.mapin01),labels=colnames(X),lower.panel=ipanellower,upper.panel=ipanelupper,diag.panel=ipaneldiag,text.panel=itextpanel,...)
  replot(plot=match.call())  

}

qqnorm.rplus <- function(y,fak=NULL,...,panel=vp.qqnorm,alpha=NULL) {
  X <- rplus(y)
  if( is.function(panel) )
    panel <- list(panel)
  if( !is.null(alpha) )
    alpha <- alpha/(nrow(X)^2)
  ipanelupper <- function(x,y,...) {
    a <- unclass(X)[,gsi.mapfrom01(x)]
    b <- unclass(X)[,gsi.mapfrom01(y)]
    for( thispanel in panel )
      thispanel(fak,b-a,...,alpha=alpha)
  }
  ipanellower <- function(x,y,...) {
    a <- unclass(X)[,gsi.mapfrom01(x)]
    b <- unclass(X)[,gsi.mapfrom01(y)]
    for( thispanel in panel )
      thispanel(fak,b+a,...,alpha=alpha)
  }
  ipaneldiag <- function(x,...) {
    a <- unclass(X)[,gsi.mapfrom01(x)]
    for( thispanel in panel )
      thispanel(fak,a,...,alpha=alpha)
  }
  itextpanel <- function(x,y,lab,...) {
    par(usr=c(0,1,0,1),xlog=FALSE,ylog=FALSE)
    text(0.1,0.9,lab,adj=c(0,1),...)
  }

  pairs(sapply(1:NCOL(X),gsi.mapin01),labels=colnames(X),lower.panel=ipanellower,upper.panel=ipanelupper,diag.panel=ipaneldiag,text.panel=itextpanel,...)
  replot(plot=match.call())  

}



gsi.drop  <-function(X,drop) if( drop ) drop(X) else X

is.acomp <- function(x) inherits(x,"acomp")

is.rcomp <- function(x) inherits(x,"rcomp")

is.aplus <- function(x) inherits(x,"aplus")

is.rplus <- function(x) inherits(x,"rplus")
   
is.rmult <- function(x) inherits(x,"rmult")

is.ccomp <- function(x) inherits(x,"ccomp")

perturbe <- function( x,y ) {
  acomp(gsi.mul(x,y))
}

perturbe.aplus <- function(x,y) {
  aplus(gsi.mul(x,y))
}


gsi.add <- function(x, y) {
  if( gsi.ANDsequentially(length(dim(x)) == 2, nrow(x)>1 )){
    if( gsi.ANDsequentially(length(dim(y)) == 2, nrow(y)>1 )){
      unclass(x)+unclass(y)
    }else{
      unclass(x)+rep(c(y),rep(NROW(x),length(y)))
    }
  }else if( gsi.ANDsequentially(length(dim(y)) == 2, nrow(y)>1)){
     unclass(y)+rep(c(x),rep(NROW(y),length(x)))
  }else{
    unclass(x)+unclass(y)
    }
}


gsi.sub <- function(x, y) {
  if( gsi.ANDsequentially(length(dim(x)) == 2, nrow(x)>1 )){
    if( gsi.ANDsequentially(length(dim(y)) == 2, nrow(y)>1 )){
      unclass(x)-unclass(y)
    }else{
      unclass(x)-rep(c(y),rep(NROW(x),length(y)))
    }
  }else if( gsi.ANDsequentially(length(dim(y)) == 2, nrow(y)>1)){
    unclass(y)-rep(c(x),rep(NROW(y),length(x)))
  }else{
    unclass(x)-unclass(y)
  }
}


gsi.mul <- function( x,y ) {
  if( gsi.ANDsequentially(length(dim(x)) == 2 & nrow(x)>1 ))
    if( gsi.ANDsequentially(length(dim(y)) == 2 & nrow(y)>1 ))
      unclass(x)*unclass(y)
    else
      unclass(x)*rep(c(y),rep(NROW(x),length(y)))
  else if( gsi.ANDsequentially(length(dim(y)) == 2 & nrow(y)>1 ))
      unclass(y)*rep(c(x),rep(NROW(y),length(x)))
  else
    unclass(x)*unclass(y)
}

gsi.div <- function( x,y ) {
  if( gsi.ANDsequentially(length(dim(x)) == 2 & nrow(x)>1 ))
    if( gsi.ANDsequentially(length(dim(y)) == 2 & nrow(y)>1 ))
      unclass(x)/unclass(y)
    else
      unclass(x)/rep(c(y),rep(NROW(x),length(y)))
  else if( gsi.ANDsequentially(length(dim(y)) == 2 & nrow(y)>1 ))
      # unclass(y)/rep(c(x),rep(NROW(y),length(x))) ## BUG!!
      rep(c(x),rep(NROW(y),length(x)))/unclass(y)
  else
    unclass(x)/unclass(y)
}


power.acomp <- function(x,s) {
  if( is.acomp(s) || is.rcomp(s))
    stop("power.acomp is scalar multiplication only")
  if( !is.matrix(x) || nrow(x) ==1 ) {
    if( length(s)>1 )
      x <- matrix(x,byrow=TRUE,ncol=length(x),nrow=length(s))
  } else {
    if( length(s) > 1 && length(s)!= nrow(x) )
      warning("lengths do not match in power.acomp")
  }
  acomp(unclass(x)^c(s)) 
}


"+.acomp" <- function(x,y) {
  acomp(gsi.mul(x,y))
}

"-.acomp" <- function(x,y) {
  if( missing(y) )
    acomp(1/unclass(x))
  else 
    acomp(gsi.div(x,y))
}

"*.acomp" <- function(x,y) {
  if( is.acomp(x) && !is.acomp(y) )
    power.acomp(x,y)
  else if( is.acomp(y)&& !is.acomp(x) )
    power.acomp(y,x)
  else
    stop("the powertransform performed in *.acomp only operates on acomps and scalar")
}

"/.acomp" <- function(x,y) {
  if( is.acomp(x) && !is.acomp(y) )
    power.acomp(x,1/unclass(y))
  else
    stop("/.acomp only operates on acomp / numeric")
}

"+.aplus" <- function(x,y) {
    aplus(gsi.mul(x,y))
}

"-.aplus" <- function(x,y) {
  if( missing(y) )
    return(aplus(1/unclass(y)))
  else
    aplus( gsi.div(x,y) )
}

"*.aplus" <- function(x,y) {
  if( is.aplus(x)&& !is.aplus(y) )
    power.aplus(x,y)
  else if( is.aplus(y)&& !is.aplus(x) )
    power.aplus(y,x)
  else
    stop("*.aplus only operates on aplus and scalar")
}

"/.aplus" <- function(x,y) {
  if( is.aplus(x) && !is.aplus(y) )
    power.aplus(x,1/unclass(y))
  else
    stop("/.aplus only operates on aplus and scalar")
}


"+.rcomp" <- function(x,y) {
#  warning("+ is meaningless for rcomp")
  if( is.rcomp(x) )
    if( is.rcomp(y) ) {
      stop("+ is meaningless for two rcomp objects")
   } else if( is.rcomp(x)) {
      erg=rmult(clo(x))+rmult(y)
    } else if( is.rcomp(y) ) {
      erg=rmult(x)+rmult(clo(y))
    } else
      stop("Why are we here in +.rcomp without rcomp?")
  #rcomp(gsi.add(x,y))
  return(erg)
}

"-.rcomp" <- function(x,y) {
  if( missing(y) )
    rmult(-unclass(x), orig=x)
  else
    rmult(gsi.sub(x,y))
}

"*.rcomp" <- function(x,y) {
  if( is.rcomp(x) && is.rcomp(y) )
    rcomp(gsi.mul(x,y))
  else if( is.rcomp(x) )
    rplus(x)*y
  else if( is.rcomp(y) )
    rplus(y)*x
  else
    stop("undefined combination of arguments for *.rcomp")
}

"/.rcomp" <- function(x,y) {
  if( is.rcomp(x) && is.rcomp(y) )
    rcomp(gsi.div(x,y))
  else if( is.rcomp(x) )
    rplus(x)/y
  else
    stop("undefined combination of arguments for /.rcomp")
}

"+.rplus" <- function(x,y) {
  if( is.rplus(x) && is.rplus(y) )
    rplus(gsi.add(x,y))
  else
    rmult(gsi.add(x,y))
}

"-.rplus" <- function(x,y) {
  if( missing(y) )
    rmult(-unclass(x))
  else
    rmult(gsi.sub(x,y))
}


"*.rplus" <- function(x,y) {
  if( is.rplus(x) && is.rplus(y) )
    rplus(gsi.mul(x,y))
  else if( is.rplus(x) )
    mul.rplus(x,y)
  else if( is.rplus(y) )
    mul.rplus(y,x)
  else
    stop("undefined combination of arguments for *.rplus")
}

"/.rplus" <- function(x,y) {
  if( is.rplus(x) && is.rplus(y) )
    rplus(gsi.div(x,y))
  else if( is.rcomp(x) )
    mul.rplus(rplus(x),1/unclass(y))
  else
    stop("undefined combination of arguments for /.rcomp")
}

"+.rmult" <- function(x,y) {
  rmult(gsi.add(x,y), orig=gsi.orig(x,y), V=gsi.getV(x,y))
}

"-.rmult" <- function(x,y) {
  if( missing(y) )
    rmult(-unclass(x), orig=gsi.orig(x,y), V=gsi.getV(x,y))
  else
    rmult(gsi.sub(x,y), orig=gsi.orig(x,y), V=gsi.getV(x,y))
}


"*.rmult" <- function(x,y) {
  if( is.rmult(x) && is.rmult(y) )
    rmult(gsi.mul(x,y), orig=gsi.orig(x,y), V=gsi.getV(x,y))
  else
    rmult(unclass(x)*unclass(y), orig=gsi.orig(x,y), V=gsi.getV(x,y))
}

"/.rmult" <- function(x,y) {
  if( is.rmult(x) && is.rmult(y) )
    rmult(gsi.div(x,y), orig=gsi.orig(x,y), V=gsi.getV(x,y))
  else 
    rmult(unclass(x)/unclass(y), orig=gsi.orig(x,y), V=gsi.getV(x,y))
}

"%*%" <- function(x,y) UseMethod("%*%",structure(c(unclass(x), unclass(y)),class=c(class(x),class(y))))


#gsi.internaltmp <- get("%*%",pos="package:base")
#formals(gsi.internaltmp) <- formals(get("%*%"))
#"%*%.default" <- gsi.internaltmp

"%*%.default" <- function(x,y) base::"%*%"(x,y)

"%*%.rmult" <- function(x,y) {
  if( is.rmult(y) )
    if( is.rmult(x) ) 
      c(gsi.mul(x,y) %*% rep(1,gsi.getD(x)))
    else if( is.matrix(x) ) 
      rmult(gsi.simshape(oneOrDataset(y) %*% t(x),y), orig=gsi.orig(x,y), V=gsi.getV(x,y))
    else
      c(oneOrDataset(y) %*% x) 
  else if( is.matrix(y) )
      rmult(gsi.simshape(oneOrDataset(x) %*% y,x), orig=gsi.orig(x,y), V=gsi.getV(x,y))
  else
      c(oneOrDataset(x) %*% y) 
  }

"%*%.acomp" <- function(x,y) {
  if( is.acomp(y) )
    if( is.acomp(x) ) 
      cdt(x) %*% cdt(y)
    else if( is.matrix(x) ) {
      if( nrow(x) == gsi.getD(y) )
        clrInv(x %*% clr(y))
      else
        ilrInv(x %*% ilr(y))
    }
    else
      stop( "%*%.acomp is only defined for special combinations I" )
  else if( is.acomp(x) ) {
    if( is.matrix(y) ) {
      if( ncol(y) == gsi.getD(x) )
        clrInv(clr(x) %*% y )
      else
        ilrInv(ilr(x) %*% y )
    }
  else
      stop( "%*%.acomp is only defined for special combinations II" )
  }
  else
      stop( "%*%.acomp is only defined for special combinations III" )
    
}

"%*%.aplus" <- function(x,y) {
  if( is.aplus(y) )
    if( is.aplus(x) ) 
      cdt(x) %*% cdt(y)
    else if( is.matrix(x) ) {
        iltInv(x %*% ilt(y))
    }
    else
      stop( "%*%.acomp is only defined for special combinations I" )
  else if( is.aplus(x) ) {
    if( is.matrix(y) ) {
        iltInv(ilt(x) %*% y )
    }
  else
      stop( "%*%.aplus is only defined for special combinations II" )
  }
  else
      stop( "%*%.aplus is only defined for special combinations III" )
    
}


convex.rcomp <- function(x,y,alpha=0.5) {
  rcomp( alpha*x + (1-alpha)*y )
}


mul.rplus <- function(x,r) {
  if( all(r>=0) )
    rplus(unclass(x)*r)
  else
    rmult(unclass(x)*r)
}

power.aplus <- function(x,r) {
  aplus(unclass(x)^r) 
}


gsi.expandrcomp <- function(x,alpha) {
  cptInv(cpt(x)*alpha)
}

endmemberCoordinates <- function(X,...) UseMethod("endmemberCoordinates")

endmemberCoordinates.default <- function(X,endmembers=diag(gsi.getD(X)),...) {
  class(endmembers) <- class(X)
  X <- oneOrDataset(idt(X))
  A <- t(unclass(idt(endmembers)))
  erg <- solve( rbind(cbind(t(A)%*%A,1),c(rep(1,ncol(A)),0)),
               rbind(t(A)%*%t(unclass(X)),1))
  erg <- rmult(t(erg[-nrow(erg),,drop=FALSE]))
  colnames(erg) <- rownames(endmembers)
  erg
}

endmemberCoordinates.acomp <- function(X,endmembers=clrInv(diag(gsi.getD(X))),...) {
  ep <- ilr(endmembers)
  rownames(ep) <- rownames(endmembers)
  endmemberCoordinates(idt(X),ep,...)
}

endmemberCoordinates.aplus <- function(X,endmembers,...) {
  ep <- ilt(endmembers)
  rownames(ep) <- rownames(endmembers)
  endmemberCoordinates(idt(X),ep,...)
}


endmemberCoordinates.rplus <- function(X,endmembers,...) {
  ep <- iit(endmembers)
  rownames(ep) <- rownames(endmembers)
  endmemberCoordinates(idt(X),ep,...)
}


endmemberCoordinatesInv <- function(K,endmembers,...) UseMethod("endmemberCoordinatesInv",endmembers)

endmemberCoordinatesInv.rmult <- function(K,endmembers,...) {
  rmult(t(t(unclass(endmembers)) %*% t(unclass(K))))
}

endmemberCoordinatesInv.acomp <- function(K,endmembers,...) {
  ilrInv(endmemberCoordinatesInv(K,ilr(endmembers)))
}

endmemberCoordinatesInv.rcomp <- function(K,endmembers,...) {
  iptInv(endmemberCoordinatesInv(K,ipt(endmembers)))
}


endmemberCoordinatesInv.aplus <- function(K,endmembers,...) {
  iltInv(endmemberCoordinatesInv(K,ilt(endmembers)))
}

endmemberCoordinatesInv.rplus <- function(K,endmembers,...) {
  iitInv(endmemberCoordinatesInv(K,iit(endmembers)))
}


formals(scale) <- c(formals(scale),alist(...= ))
formals(scale.default) <- c(formals(scale.default),alist(...= ))

scale.aplus  <- scale.acomp <- function( x,center=TRUE, scale=TRUE ,...,robust=getOption("robust")) {
  if(is.logical(center) & is.logical(scale)){
    if( ! (center || scale ) ) return(x)
  }
  va <- var(x,robust=robust,giveCenter=TRUE)
  ce <- attr(va,"center")
  if( is.logical(center) ) {
    if( center )
      x <- x-ce
  } else x <- x-center
  if( is.logical(scale) ) {
    if(scale)
      x <- (1/sqrt(mean(gsi.diagExtract(va))))*x
  } else x <- x*scale
  return(x)
#  W <- x
#  if( center ) {
#    W <- clrInv( scale(clr(W),center=center,scale=FALSE) )
#    if( scale )
#      W <- power.acomp(W,as.numeric(scale)/
#                       sqrt(sum(gsi.diagExtract(var(clr(W))))))
#  } else if( scale ) {
#    mean <- c(mean(acomp(W),robust=robust))
#    W <- perturbe(power.acomp(perturbe(W,1/mean),as.numeric(scale)/sqrt(sum(gsi.diagExtract(var(clr(W)))))),mean)
#  }
#  W
}

#scale.rcomp <- function( x,center=TRUE, scale=TRUE ) {
#  W <- x
#  if( center ) {
#    W <- cptInv( scale(cpt(W),center=center,scale=FALSE) )
#    if( scale )
#      W <- gsi.expandrcomp(W,as.numeric(scale)/sqrt(sum(gsi.diagExtract(var(cpt(W))))))
#  } else if( scale ) {
#    mean <- c(mean(rcomp(W)))
#    W <- gsi.add(mean,gsi.sub(W,mean)/sqrt(sum(gsi.diagExtract(var(cpt(W))))))
#  }
#  W
#}

#scale.aplus <- function( x,center=TRUE, scale=TRUE ) {
#  W <- x
#  if( center ) {
#    W <- iltInv( scale(ilt(W),center=center,scale=FALSE) )
#    if( scale )
#      W <- power.aplus(W,as.numeric(scale)/sqrt(sum(gsi.diagExtract(var(ilt(W))))))
#  } else if( scale ) {
#    mean <- c(mean(aplus(W)))
#    W <- perturbe.aplus(power.aplus(perturbe.aplus(W,1/mean),as.numeric(scale)/sqrt(sum(gsi.diagExtract(var(ilt(W)))))),mean)
#  }
#  W
#}

#scale.rplus <- function( x,center=TRUE, scale=TRUE ) {
#   rmult(scale(gsi.plain(x),center=center,scale=scale))
#}

scale.rcomp <- scale.rplus <- scale.rmult <- function( x,center=TRUE, scale=TRUE ,..., robust=getOption("robust")) {
  if(is.logical(center) & is.logical(scale)){
    if( ! (center || scale ) ) return(x)
  }
  var <- var(x,robust=robust,giveCenter=TRUE)
  ce <- attr(var,"center")
  if( is.logical(center) ) {
    if( center )
      x <- x-ce
  } else x <- x-center
  if( is.logical(scale) ){
    if(scale) {
      s <- gsi.diagGenerate(1/sqrt(gsi.diagExtract(var)))
      x <- s %*% x
    }
  } else if( is.matrix(scale) )
     x <- scale %*% x
  else if( length(scale)==1)
     x <- s * x
  else
     x <- gsi.diagGenerate(scale) %*% x
  return(x)
   #rmult(scale(gsi.plain(x),center=center,scale=scale))
}

normalize <- function(x,...) UseMethod("normalize",x)
normalize.default <- function(x,...) x/norm(x)

norm <- function(x,...) UseMethod("norm",x)

norm.default <- function(x,...) {
  sqrt( sum(x^2) )
}

norm.matrix <- function(x,...){
  base::norm(x=x, ...)
}

norm.acomp <- function(x,...) {
  norm.rmult(cdt(x),...)
}
norm.rcomp <- norm.acomp
norm.aplus <- norm.acomp
norm.rplus <- norm.acomp
norm.rmult <- function(x,...) {
   sqrt(x %*% x)
}

dist <- function(x,...) UseMethod("dist")
dist.default <- function(x,...) stats::dist(cdt(x),...)


scalar <- function(x,y) UseMethod("scalar")

scalar.default <- function(x,y) {
  x <- cdt(x)
  y <- cdt(y)
  tmp <- gsi.mul(oneOrDataset(x,y), oneOrDataset(y,x)) 
  c( tmp %*% rep(1,NCOL(tmp)))
}


clr <- function( x ,... ) {
  W <- oneOrDataset(x)
  nmv <- is.NMV(W)
  LOG <- unclass(log(ifelse(nmv,W,1)))
  erg <- ifelse(nmv,LOG-gsi.rsum(LOG)/gsi.rsum(nmv),0)
  #M   <- gsi.rsum(gsi.recodeM2C(W,LOG,BDL=0,SZ=0,MAR=0,MNAR=0))
  rmult(gsi.simshape(erg,x),orig=x) 
}

clrInv <- function( z,..., orig=gsi.orig(z) ) {
  res = acomp( gsi.recodeC2M(exp(z),ninf=BDLvalue,nan=MARvalue,na=MNARvalue) )
  if(!is.null(orig)){
    if(length(dim(res))>0)
      colnames(res) = colnames(oneOrDataset(orig))
    else
      names(res) = colnames(oneOrDataset(orig))
  }
  return(res)
}

ult <- function( x,... ) {
  ilt(clo(x),...)
}

ultInv <- clrInv

Kappa <- function( x, ...) {
  W <- oneOrDataset(x)
  (clr(W)-ult(W))[,1]
}

#gsi.ilrBase <- function(D) {
#  if( D==1 )
#    return(matrix(nrow=0,ncol=0))
#  tmp <- diag(D) - 1/(D)* matrix(1,ncol=D,nrow=D)
#  for( i in 1:(NCOL(tmp)-1)  ) {
#    tmp[,i] <- tmp[,i]/sqrt(sum(tmp[,i]^2))
#    rest <- (i+1):NCOL(tmp)
#    if( length(rest) != 1 ) {
#      tmp[,rest]  <-tmp[,rest,drop=FALSE] - tmp[,rep(i,length(rest)),drop=FALSE]%*%
#        gsi.diagGenerate( c(t(tmp[,i])%*%tmp[,rest,drop=FALSE] ) )
#    } 
#  }
#  tmp[,-NROW(tmp)]
#}

gsi.ilrBase <-function(D){
  if(D<=1)
    return(matrix(nrow=0,ncol=0))
  else if(D==2){
    return(t(t(unclass(normalize(rmult(t(contr.helmert(n=D))))))))
  } else
    t(unclass(normalize(rmult(t(contr.helmert(n=D))))))
}




                                        # Old ilrBase
#ilrBase <- function( x=NULL , z=NULL , D = NULL ) {
#  if( missing(D) )
#    D <- if(is.null(x))
#      NCOL(oneOrDataset(z))+1
#    else
#      NCOL(oneOrDataset(x))
#  while( D > length(ilrBaseList) )
#    ilrBaseList <<- c(ilrBaseList,gsi.ilrBase(length(ilrBaseList)+1))
#  ilrBaseList[[D]]gsi.OrderIlr
#}
# ilrBaseList <- lapply(1:20,gsi.ilrBase)


ilrBase <- function(x=NULL, z=NULL, D=NULL, method="basic"){
 if(!is.null(gsi.getV(z))) return(gsi.getV(z))
 if (method=="basic"){
    if (missing(D))
        D <- if (is.null(x))
            NCOL(oneOrDataset(z)) + 1
        else NCOL(oneOrDataset(x))
#     while (D > length(ilrBaseList)) ilrBaseList <<- c(ilrBaseList,
#         gsi.ilrBase(length(ilrBaseList) + 1))
#     V=ilrBaseList[[D]]
  V = gsi.ilrBase(D)
 } #end if basic
 if (method=="balanced"){
    # build the merge structure (as in hclust)
    if(is.null(D)==TRUE){D=max(ncol(x),ncol(z))}
    M = c(-c(1:D),c(floor(D/2):1),c((floor(D/2)+1):(D-2)))
    M = matrix(M, byrow=TRUE, nrow=D-1, ncol=2)
    V = gsi.merge2signary(M)
    V = gsi.buildilrBase(V)
 }#end if balanced
 if (method=="optimal"){
  if(length(dim(x))<2){
   warning("method 'optimal' requires a data set")
  }
  else{
    V = gsi.optimalilrBase(x)
    V = gsi.buildilrBase(V)

  }
 } #end if optimal
 if(length(grep(pattern="PB",x=method))!=0){
   if(length(dim(x))<2){
     stop("all 'Principal Balances' methods require a data set")
   }
   gsi.PrinBal(x, method)
 } # end methods of principal balances (all having string "PB" in their name)
 return(V)
}

gsi.buildilrBase <-function(W=c(1,-1)){
  # builds an ilr base from a matrix of 1, -1 and 0 (a partition)
  if(length(W)<2){
    return(ilrBase(D=1))
  }
if(length(dim(W))==0){
  return(ilrBase(D=2))
  }
  if(length(dim(W))>0){
   W = as.matrix(W)
   nc = ncol(W)
   D = nrow(W)
   isPos = (W>0)
   isNeg = (W<0)
   nPos = matrix(1,D,D) %*% isPos
   nNeg = matrix(1,D,D) %*% isNeg
   W = (isPos * nNeg - isNeg * nPos)
   nn = sapply(1:nc,function(i){1/norm.rmult(W[,i])})
   nn = matrix(nn, ncol=ncol(W), nrow=nrow(W), byrow=TRUE)
   W = W * nn
   return(W)
  }
}
gsi.signary2ilrBase <- gsi.buildilrBase


gsi.optimalilrBase <- function(x){
  # Takes as data a binary data frame: 0=case unobserved, 1=case observed
  # performs a cluster analysis of variables on it
  # and recodes the structure to a signary matrix (pre-ilr)
  if(is.null(attr(x,"Losts"))==TRUE){
    Ones = !oneOrDataset(is.infinite(log(as.matrix(x))),x) # find zeroes
  }
  if(is.null(attr(x,"Losts"))==FALSE){
    Ones = !attr(x,"Losts")
  }
  h= hclust(dist(t(Ones)))
  V = gsi.merge2signary(h$merge)
  return(V)
}


gsi.merge2signary <- function(M){
  # takes a merge structure (as explained in hclust) and converts it to a sign matrix (encoding the ilr partition: 0=no influence, 1=numerator, -1=denominator)
 V = matrix(0,ncol=nrow(M)+1,nrow=nrow(M))
  for(i in 1:nrow(M)){
   for(j in 1:2){
    weight = (-1)^j
    k = M[i,j]
    if(k<0){
      V[i,abs(k)] = weight
    } # for singletons
    if(k>0){ # for groups
      take = as.logical(V[k,])
      V[i,take] = rep(weight,sum(take))
    }
  }
 }
return(t(V))
}




ilr    <- function( x , V=ilrBase(x),... ){
  rmult(clr2ilr( clr(oneOrDataset(x)),V ), orig=acomp(x), V=t(gsi.svdinverse(V)))
}
  

ilrInv <- function( z, V=ilrBase(z=z),...,orig=gsi.orig(z)) {
  erg <- clrInv( ilr2clr(z,V) )
  if( ! is.null(orig) && gsi.getD(erg) == gsi.getD(orig) ) {
    names(erg)<-names(orig)
  }
  erg
}

alr <- function( x ,ivar=ncol(x),...) {
  # control of ivar, recast to number
  if(is.null(ivar)) ivar=length(x)
  if(is.character(ivar)) ivar = colnames(x)==ivar
  if(is.logical(ivar)) ivar = which(ivar)
  if(length(ivar)!=1) stop("alr: 'ivar' must identify a single variable")
  # store input, give colnames if necessary, close
  xo <- x
  x = oneOrDataset(x)
  cn = paste("v", 1:ncol(x), sep="")
    if(is.null(colnames(x))) colnames(x) = cn
  colnames(x)[colnames(x)==""] = cn[colnames(x)==""]
  W <- unclass(clo(x))
  # construct contrast matrix
  D <- ncol(W)
  Phi = rbind(diag(D-1),-1)
  rownames(Phi) = c(colnames(x)[-ivar], colnames(x)[ivar])
  colnames(Phi) = colnames(x)[-ivar]
  # recode missings and zeros
  x <- gsi.recodeM2C(W,log(W),BDL=-Inf,SZ=NaN,MAR=NaN,MNAR=NA)
  # produce output
  rmult(gsi.simshape( x[,-ivar,drop=FALSE] - c(x[,ivar]), xo), orig=acomp(xo),
        V = t(gsi.svdinverse(Phi[colnames(x),])))
}

alrInv <- function( z ,...,orig=gsi.orig(z)) {
  .V = gsi.getV(z)
  if(is.null(.V)){
    Z <- cbind(oneOrDataset(z),0)
  }else{
    Z <- cbind(oneOrDataset(z) %*% t(.V))
  }
  erg <- acomp(gsi.simshape( clo(gsi.recodeC2M(Z,exp(Z),
                                        ninf=BDLvalue,
                                        inf =MNARvalue,
                                        nan =MARvalue,
                                        na  =MNARvalue
                                        )) , z ))
  if( ! is.null(orig) && gsi.getD(erg) == gsi.getD(orig) ) {
    names(erg)<-names(orig)
  }
  erg
}


pwlr = function(x, as.rmult=FALSE, as.data.frame=!as.rmult, ...){
  if(!as.rmult & !as.data.frame) as.rmult=TRUE 
  # ensure input is taken as a matrix
  X = unclass(compositions::oneOrDataset(x))
  # extact column names or indices
  cn = colnames(X)
  if(is.null(cn)) cn = 1:ncol(X)
  # produce all combinations of 2 elements
  pw = combn(cn,2)
  # compute ratios and set names
  Y = log(X[,pw[2,], drop=F]/X[,pw[1,], drop=F])
  colnames(Y) = paste(pw[2,], pw[1,], sep=".")
  if(as.rmult){
    DD = length(cn)
    pw = combn(1:DD,2)
    W = apply(pw,2,function(i){
      aa = rep(0,DD)
      aa[i[1]]=-1
      aa[i[2]]=+1
      return(aa)
    })
    Winv = gsi.svdinverse(W) 
    colnames(Winv) = cn
    Y = rmult(Y, orig=acomp(x), V=t(Winv))
  }else{
    Y = as.data.frame(Y)
  }
  return(Y)
}

pwlrInv = function(z, orig = gsi.orig(z)){
  y = oneOrDataset(z)
  P = ncol(y)
  DD = 0.5*(1+sqrt(1+8*P))
  if(floor(DD)!=DD) stop("pwlrInv: z provided does not have a number of cols compatible with a pwlr") 
  if(!is.null(orig)){
    if(DD!=ncol(orig))
      stop("pwlrInv: orig and z do not have compatible ncols")
  }
  pw = combn(1:DD,2)
  W = apply(pw,2,function(i){
    aa = rep(0,DD)
    aa[i[1]]=-1
    aa[i[2]]=+1
    return(aa)
  })
  Winv = gsi.svdinverse(W)
  erg = clrInv(y %*% Winv)
  if(!is.null(orig))
    colnames(erg) = colnames(orig)
  return(erg)
}
  
  

apt <- function( x ,...) {
  W <- oneOrDataset(x)
  Dd <- ncol(W)
  V <- gsi.recodeM2C(W,gsi.plain(clo( W )),BDL=0.0,SZ=0.0,MAR=NaN,MNAR=NA)
  rmult(gsi.simshape(V[,-NCOL(W)],x), orig=rcomp(x), 
        V=t(gsi.svdinverse(rbind(diag(Dd-1),-1))))
}

aptInv <- function( z ,...,orig=gsi.orig(z)) {
  Z <- oneOrDataset(z)
  Z <- cbind(Z, 1 - gsi.recodeC2M(Z,na=0.0,nan=0.0) %*% rep(1,NCOL(Z)))
  erg <- rcomp(gsi.simshape( Z ,z ))
  if( ! is.null(orig) && gsi.getD(erg) == gsi.getD(orig) ) {
    names(erg)<-names(orig)
  }
  erg
}

cpt <- function( x ,...) {
  X <- oneOrDataset(x)
  rmult(clo(x) - 1/NCOL(X),orig=rcomp(x))
}

cptInv <- function( z ,..., orig=gsi.orig(z)) {
  if( abs(sum(z))>0.0001 )
    warning( "z not in cpt plane in cptInv")
  res = rcomp(z + 1/NCOL(oneOrDataset(z)))
  if(!is.null(orig)){
    if(length(dim(res))>1){
      colnames(res) = colnames(oneOrDataset(orig))
    }else{
      names(res) = colnames(oneOrDataset(orig))
    }
  }
  return(res)
}

ipt    <- function( x , V=ilrBase(x),...) {
  rmult(clr2ilr(cpt(x),V), orig=rcomp(x), V=t(gsi.svdinverse(V)) )
}

iptInv <- function( z, V=ilrBase(z=z) ,...,orig=gsi.orig(z)) {
  erg<-cptInv( ilr2clr(z,V) )
  if( ! is.null(orig) && gsi.getD(erg) == gsi.getD(orig) ) {
    names(erg)<-names(orig)
  }
  erg
}

uciptInv <- function( z, V=ilrBase(z=z) ,...,orig=gsi.orig(z)) {
  tmp <- ilr2clr(z,V) + 1/(gsi.getD(z)+1)
  tmp[tmp<0]<-MNARvalue
  erg<-rcomp(tmp)
  if( ! is.null(orig) && gsi.getD(erg) == gsi.getD(orig) ) {
    names(erg)<-names(orig)
  }
  erg
}


ilt <- function( x ,...) {
  W <- gsi.plain(x)
  ww = ifelse(is.NMV(W),W,1)
  res = rmult(log(ww),orig=aplus(x))
  return(res)
}

iltInv <- function( z ,...) {
  aplus(gsi.recodeC2M(z,exp(z),ninf=BDLvalue,nan=MARvalue,na=MNARvalue))
}

iit <- function( x ,...) {
  rmult( gsi.recodeM2C(x,BDL=0.0,SZ=0.0,MAR=0.0,MNAR=0.0 ) ,orig=rplus(x))
}

iitInv <- function(z,...) {
  rplus(gsi.recodeC2M(z,na=MNARvalue,nan=MARvalue))
}

idt         <- function(x,...) UseMethod("idt",x)
idt.default <- function(x,...) x
idt.acomp   <- function(x,...) ilr(x,...) 
idt.rcomp   <- function(x,...) ipt(x,...)
idt.ccomp   <- function(x,...) 
  rmult( gsi.recodeM2C(x,BDL=0.0,SZ=0.0,MAR=0.0,MNAR=0.0 ) ,orig=ccomp(x) )
idt.aplus   <- ilt 
idt.rplus   <- iit
idt.rmult   <- function(x,...) x
idt.factor  <- function(x,...){
  Vx = contrasts(x)
  rws = apply(Vx==0,1,all)
  if(any(rws)) Vx[rws,]=-1
  rmult(clr2ilr(cdt(x), V=Vx),orig=x, V=Vx)
} 


cdt         <- function(x,...) UseMethod("cdt",x)
cdt.default <- function(x,...) x
cdt.acomp   <- clr 
cdt.rcomp   <- cpt
cdt.ccomp   <- function(x,...) 
  rmult( gsi.recodeM2C(x,BDL=0.0,SZ=0.0,MAR=0.0,MNAR=0.0 ) ,orig=ccomp(x) )
cdt.aplus   <- ilt 
cdt.rplus   <- iit
cdt.rmult   <- function(x,...) x
cdt.factor  <- function(x,...) {
  #x <- matrix(0,nrow=length(x),ncol=nlevels(x),dimnames=list(names(x),levels(x)))
  #x[1:ncol(x)+unclass(x)] <- model.matrix(~-1+x)
  #rmult(matrix(x,nrow=nrow(x),dimnames=dimnames(x)))
  y = diag(length(levels(x)))
  colnames(y) <- rownames(y)<- levels(x)
  rmult(y[as.character(x),], orig=x)
}

cdtInv <- function(x,orig=gsi.orig(x),...) UseMethod("cdtInv",orig)
cdtInv.default <- function(x,orig=gsi.orig(x),...) x
cdtInv.acomp   <- function(x,orig=gsi.orig(x),...) clrInv(x,...,orig=orig)
cdtInv.rcomp   <- function(x,orig=gsi.orig(x),...) cptInv(x,...,orig=orig)
cdtInv.ccomp   <- function(x,orig=gsi.orig(x),...) iitInv(x,...,orig=orig)
cdtInv.aplus   <- function(x,orig=gsi.orig(x),...) iltInv(x,...,orig=orig)
cdtInv.rplus   <- function(x,orig=gsi.orig(x),...) iitInv(x,...,orig=orig)
cdtInv.rmult   <- function(x,orig=gsi.orig(x),...) x
cdtInv.factor   <- function(x,orig=gsi.orig(x),...){
  cn = colnames(x)
  if(length(levels(orig))>length(cn))cn=levels(orig)
  factor(cn[x %*% c(1:ncol(x))])
}

idtInv <- function(x,orig=gsi.orig(x), ...) UseMethod("idtInv",orig)
idtInv.default <- function(x,orig=gsi.orig(x), ...) x
idtInv.acomp   <- function(x,orig=gsi.orig(x), V=gsi.getV(x),...) ilrInv(x,...,orig=orig,V=V)
idtInv.rcomp   <- function(x,orig=gsi.orig(x), V=gsi.getV(x),...) iptInv(x,...,orig=orig,V=V)
idtInv.ccomp   <- function(x,orig=gsi.orig(x), ...) iitInv(x,...,orig=orig)
idtInv.aplus   <- function(x,orig=gsi.orig(x), ...) iltInv(x,...,orig=orig)
idtInv.rplus   <- function(x,orig=gsi.orig(x),...) iitInv(x,...,orig=orig)
idtInv.rmult   <- function(x,orig=gsi.orig(x), ...) x
idtInv.factor <- function(x,orig=gsi.orig(x),V=gsi.getV(x),...){
  cdtInv.factor(ilr2clr(x, V=V), orig=orig)
}

backtransform <- backtransform.rmult <- function(x, as=x){
  if(!is.rmult(x)) stop("backtransform only defined for rmult objects")
  if(!is.null(gsi.getV(as))){
    rs = idtInv(x, orig=gsi.orig(as), V=gsi.getV(as))
  }else{
    rs = cdtInv(x, orig=gsi.orig(as))
  }
  # keep extra attributes
  atr = attributes(x)
  keep = setdiff(names(atr), c("dim", "dimnames", "class" ))
  if(length(keep)!=0){
    attributes(rs) <- append(attributes(rs), atr[keep])
  }
  return(rs)
}


gsi.cdt2idt <- function(x, as){
  .V = gsi.getV(as)
  if(is.null(.V)) return(x)
  W = gsi.svdinverse(.V)
  clr2ilr(x, V=t(W))
}
gsi.cdtvar2idt <- function(x, as){
  .V = gsi.getV(as)
  if(is.null(.V)) return(x)
  W = gsi.svdinverse(.V)
  clrvar2ilr(x, V=t(W))
}



variation <- function( x, ... ) UseMethod("variation",x)

variation.acomp <- function( x,...,robust=getOption("robust") ) {
  co <-var(x,robust=robust)
  d <- NCOL(x)
  va <-gsi.diagExtract(co)
  co1 <- matrix(rep(va,each=d),ncol=d)
  co2 <- matrix(rep(va,d),ncol=d)
  -2*co+co1+co2
}

variation.rcomp <- function( x ,...,robust=getOption("robust")) {
  co <-var(x,robust=robust)
  d <- NCOL(x)
  va <-gsi.diagExtract(co)
  co1 <- matrix(rep(va,each=d),ncol=d)
  co2 <- matrix(rep(va,d),ncol=d)
  -2*co+co1+co2
  
}


variation.aplus <- function( x ,...,robust=getOption("robust")) {
  co <-var(x,robust=robust)
  d <- NCOL(x)
  va <-gsi.diagExtract(co)
  co1 <- matrix(rep(va,each=d),ncol=d)
  co2 <- matrix(rep(va,d),ncol=d)
  -2*co+co1+co2
  
}

variation.rmult <- function( x ,...,robust=getOption("robust")) {
  co <-var(x,robust=robust)
  d <- NCOL(x)
  va <-gsi.diagExtract(co)
  co1 <- matrix(rep(va,each=d),ncol=d)
  co2 <- matrix(rep(va,d),ncol=d)
  -2*co+co1+co2
  
}
variation.rplus <- variation.rmult


gsi.mapin01 <- function(i,min=0,max=1) {c(min,min+(max-min)/i,max)}
gsi.mapfrom01 <- function(x) {(x[3]-x[1])/(x[2]-x[1])}
gsi.mapmin <- function(x) {x[1]}
gsi.mapmax <- function(x) {x[3]}

#gsi.plots <- list()
#gsi.setPlot <- function(x) {
#  gsi.setPlot[[dev.cur()]]<-x
#}
#gsi.getPlot <- function() {
#  gsi,plots[[dev.cur()]]
#}

gsi.plots <- new.env()

gsi.setPlot <- function(x,what="XXXplots",dev=dev.cur()) {
  y<-NULL
  try(
  y <- get(what,gsi.plots),silent=TRUE
      )
  if( is.null(y))
    y <- list()
  y[[dev]]<-x
  assign(what,y,gsi.plots)
}

gsi.getPlot <- function(what="XXXplots",dev=dev.cur()) {
  y<-NULL
  try(
      y <- get(what,gsi.plots),silent=TRUE
      )
  if( is.null(y))
    y <- list()
  
  #x <- get(what,gsi.plots)
  if( dev <= length(y) )
     y[[dev]]
  else
     NULL
}

#gsi.coorInfo <- list()
#gsi.setCoorInfo <- function(...) {
#  par()
#  gsi.coorInfo[[dev.cur()]] <<- list(...)
#}
#gsi.getCoorInfo <- function() {
#  if( dev.cur() <= length(gsi.coorInfo))
#    gsi.coorInfo[[dev.cur()]]
#  else
#    NULL
#}

gsi.setCoorInfo <- function(...,all=list(...)) {
  par()
  gsi.setPlot(all,what="gsi.coorInfo")
  #gsi.coorInfo[[dev.cur()]] <<- list(...)
}
gsi.addCoorInfo <- function(...,all=list(...)) {
  coorinfo <- gsi.getPlot(what="gsi.coorInfo")
  coorinfo[names(all)]<-all
  gsi.setCoorInfo(all=coorinfo)
#  if( dev.cur() <= length(gsi.coorInfo))
#    gsi.coorInfo[[dev.cur()]]
#  else
#    NULL
}


gsi.getCoorInfo <- function() {
  gsi.getPlot(what="gsi.coorInfo")
#  if( dev.cur() <= length(gsi.coorInfo))
#    gsi.coorInfo[[dev.cur()]]
#  else
#    NULL
}


gsi.call  <- function(fkt,...) {
  if( is.character(fkt) )
    do.call(fkt,list(...))
  else
    fkt(...)
}

gsi.add2pairs <- function(x,panel,...,noplot=FALSE) {
#  if( dev.cur() <= length(gsi.plots) )
#    curplot <- gsi.plots[[dev.cur()]]
#  else
#    curplot <- NULL
  curplot <- gsi.getPlot()
  if( is.null(curplot) ) {
    panel(x[,1],x[,2],...)
  } else {
    if( !missing(panel) )
      curplot$add <- c(curplot$add,list(list(x=x,panel=panel,args=list(...))))
    gsi.setPlot(curplot)
    if(!noplot) do.call("gsi.pairs",curplot)
  }
}



##### OldVersion
#gsi.pairs <- function (x, labels, panel = points, ..., main = NULL, oma = NULL, 
#    font.main = par("font.main"), cex.main = par("cex.main"), 
#    lower.panel = panel, upper.panel = panel, diag.panel = NULL, 
#    text.panel = textPanel, label.pos = 0.5 + has.diag/3, cex.labels = NULL, 
#    font.labels = 1, row1attop = TRUE, gap = 1,add=list(),xlim=apply(x,2,range),ylim=apply(x,2,range),log="",noplot=FALSE) 
#{
#    textPanel <- function(x = 0.5, y = 0.5, txt, cex, font) text(x, 
#        y, txt, cex = cex, font = font)
#    localAxis <- function(side, xpd, bg, ...) axis(side, xpd = NA, 
#        ...)
#    if (!is.matrix(x)) 
#        x <- data.matrix(x)
#    if (!is.numeric(x)) 
#        stop("non-numeric argument to pairs")
#    panel <- match.fun(panel)
#    if ((has.lower <- !is.null(lower.panel)) && !missing(lower.panel)) 
#        lower.panel <- match.fun(lower.panel)
#    if ((has.upper <- !is.null(upper.panel)) && !missing(upper.panel)) 
#        upper.panel <- match.fun(upper.panel)
#    if ((has.diag <- !is.null(diag.panel)) && !missing(diag.panel)) 
#        diag.panel <- match.fun(diag.panel)
#    if (row1attop) {
#        tmp <- lower.panel
#        lower.panel <- upper.panel
#        upper.panel <- tmp
#        tmp <- has.lower
#        has.lower <- has.upper
#        has.upper <- tmp
#    }
#    nc <- ncol(x)
#    if (nc < 2) 
#        stop("only one column in the argument to gsi.pairs")
#    has.labs <- TRUE
#    if (missing(labels)) {
#        labels <- colnames(x)
#        if (is.null(labels)) 
#            labels <- paste("var", 1:nc)
#    }
#    else if (is.null(labels)) 
#        has.labs <- FALSE
#    if( length(dim(xlim)) < 2 ) xlim <- matrix(rep(xlim,ncol(x)),nrow=2)  
#    if( length(dim(ylim)) < 2 ) ylim <- matrix(rep(ylim,ncol(x)),nrow=2)  
#    if (is.null(oma)) {
#        oma <- c(4, 4, 4, 4)
#        if (!is.null(main)) 
#            oma[3] <- 6
#    }

#    mycall <- list(x=x,labels=labels,panel=panel,...,main=main,oma=oma,
#                   font.main=font.main,cex.main=cex.main,
#                   lower.panel=lower.panel, upper.panel=upper.panel,
#                   diag.panel=diag.panel,text.panel=text.panel,
#                   label.pos=label.pos,cex.labels=cex.labels,
#                   font.labels=font.labels,row1attop=row1attop,gap=gap,add=add,
#                   xlim=xlim,ylim=ylim,log=log)
#    if( noplot ) {
#      gsi.plots[[dev.cur()]] <<- mycall
#      return(invisible(NULL))
#    }
#    opar <- par(mfrow = c(nc, nc), mar = rep.int(gap/2, 4), oma = oma)
#    on.exit(par(opar))
#    for (i in if (row1attop) 
#        1:nc
#    else nc:1) for (j in 1:nc) {
#        plot(x[, j], x[, i], xlab = "", ylab = "", axes = FALSE, 
#            type = "n", ...,log=ifelse(i==j,"",log),xlim=xlim[,j],ylim=ylim[,i])
#        if (i == j || (i < j && has.lower) || (i > j && has.upper)) {
#            box()
#            if (i == 1 && (!(j%%2) || !has.upper || !has.lower)) 
#                localAxis(1 + 2 * row1attop, ...)
#            if (i == nc && (j%%2 || !has.upper || !has.lower)) 
#                localAxis(3 - 2 * row1attop, ...)
#            if (j == 1 && (!(i%%2) || !has.upper || !has.lower)) 
#                localAxis(2, ...)
#            if (j == nc && (i%%2 || !has.upper || !has.lower)) 
#                localAxis(4, ...)
#            mfg <- par("mfg")
#            if (i == j) {
#                if (has.diag) 
#                  diag.panel(as.vector(x[, i]))
#                if (has.labs) {
#                  par(usr = c(0, 1, 0, 1))
#                  if (is.null(cex.labels)) {
#                    l.wid <- strwidth(labels, "user")
#                    cex.labels <- max(0.8, min(2, 0.9/max(l.wid)))
#                  }
#                  text.panel(0.5, label.pos, labels[i], cex = cex.labels, 
#                    font = font.labels)
#                }
#            }
#            else if (i < j) 
#                lower.panel(as.vector(x[, j]), as.vector(x[, 
#                  i]), ...)
#           else upper.panel(as.vector(x[, j]), as.vector(x[, 
#                i]), ...)
#            if( i!=j ) for( p in add ) {
#              arg <- c(list(p$panel,as.vector(p$x[,j]), as.vector(p$x[,i])),p$args)
#              do.call("gsi.call",arg)
#            }
#            if (any(par("mfg") != mfg)) 
#                stop("The panel function made a new plot")
#        }
#        else par(new = FALSE)
#    }
#    if (!is.null(main)) 
#        mtext(main, 3, 3, TRUE, 0.5, cex = cex.main, font = font.main)
#    gsi.plots[[dev.cur()]] <<- mycall
#    invisible(NULL)
#}

noreplot <- function(expr,dev=dev.cur()) {
  curplot  <- gsi.getPlot(what="...replot",dev=dev)
  if( is.null(curplot) )
    gsi.setPlot(quote(list()),what="...replot",dev=dev)
  on.exit(gsi.setPlot(curplot,what="...replot",dev=dev),add=TRUE)
  is.null(erg <- expr)
  invisible(erg)
}

replot <- function(...,dev=dev.cur(),plot=TRUE,envir=NULL,add=FALSE) {
  if( !is.logical(plot) ) {
    if( !is.list(plot)) {
      if( !is.null(envir) )
        environment(plot)<-envir
      if( is.null(environment(plot)) )
        environment(plot)<- parent.frame(2)
    }
    if( is.logical(add) & !add ) {
      if( is.call(plot) )
        gsi.setPlot(list(main=plot),what="...replot",dev=dev)
      else 
        gsi.setPlot(plot,what="...replot",dev=dev)
      curplot <- gsi.getPlot(what="...replot",dev=dev)
    } else {
      curplot <- gsi.getPlot(what="...replot",dev=dev)
      if( is.logical(add) )
        add=length(curplot)+1
      curplot[[add]]<-plot
      gsi.setPlot(curplot,what="...replot",dev=dev)
    }
    return(invisible(curplot))
  } 
  lm <- list(...)
  if( is.logical(add) )
    if( !add ) add <- 1 else stop("Add needs to specify an additional plot") 
  curplot <- gsi.getPlot(what="...replot",dev=dev)
  if( is.null(curplot) ) {
    if( plot==FALSE && length(lm)==0 )
      return(curplot)
    stop("showOnlyPanel: The active plot does not support replot")
  }
  if(!is.null(envir))
    envir <- environment(curplot[[add]])
  if( length(lm) > 0 ) 
    curplot[[add]][names(lm)]<-lm
  if(!is.null(envir))
    environment(curplot[[add]])<-envir
  gsi.setPlot(curplot,what="...replot",dev=dev)
  if( plot ) {
    lapply(curplot,function(e) eval(e,environment(e)))
  }
  return(invisible(curplot))
}

replotable <- function(expr,add=FALSE) {
  replot(plot=substitute(expr),add=add)
  invisible(noreplot(expr))
}


#### New version.
#### New version.
# modified by Raimon on 2008-05-23:, and again on 2008-06-23
#    when margin = part, the diagonal name panel were not responding adequately
#    see lines added after "if (i == j)"
gsi.pairs <- function (x, labels, panel = points, ..., main = NULL, oma = NULL, 
    font.main = par("font.main"), cex.main = par("cex.main"), 
    lower.panel = panel, upper.panel = panel, diag.panel = NULL, 
    text.panel = textPanel, label.pos = 0.5 + has.diag/3, cex.labels = NULL, 
    font.labels = 1, row1attop = TRUE, gap = 1,add=list(),xlim=apply(x,2,range),ylim=apply(x,2,range),log="",onlyPanel=NULL,noplot=FALSE,trimode=FALSE) 
{
    textPanel <- function(x = 0.5, y = 0.5, txt, cex, font) {
      x<-0.5
      y<-0.5
      usr <- par("usr")
      if( par("xlog") )
        X <- 10^(usr[1]*(1-x)+usr[2]*x)
      else
        X <- usr[1]*(1-x)+usr[2]*x
      if( par("ylog") )
        Y <- 10^(usr[3]*(1-y)+usr[4]*y)
      else  
        Y <- usr[3]*(1-y)+usr[4]*y
      text(X,Y, txt, cex = cex, font = font)
    }
    localAxis <- function(side, xpd, bg, ...) axis(side, xpd = NA, 
        ...)
    if (!is.matrix(x)) 
        x <- data.matrix(x)
    if (!is.numeric(x)) 
        stop("non-numeric argument to pairs")
    panel <- match.fun(panel)
    if ((has.lower <- !is.null(lower.panel)) && !missing(lower.panel)) 
        lower.panel <- match.fun(lower.panel)
    if ((has.upper <- !is.null(upper.panel)) && !missing(upper.panel)) 
        upper.panel <- match.fun(upper.panel)
    if ((has.diag <- !is.null(diag.panel)) && !missing(diag.panel)) 
        diag.panel <- match.fun(diag.panel)
    if (row1attop) {
        tmp <- lower.panel
        lower.panel <- upper.panel
        upper.panel <- tmp
        tmp <- has.lower
        has.lower <- has.upper
        has.upper <- tmp
    }
    nc <- ncol(x)
    if (nc < 2) 
        stop("only one column in the argument to gsi.pairs")
    has.labs <- TRUE
    if (missing(labels)) {
        labels <- colnames(x)
        if (is.null(labels)) 
            labels <- paste("var", 1:nc)
    }
    else if (is.null(labels)) 
        has.labs <- FALSE
    if( length(dim(xlim)) < 2 ) xlim <- matrix(rep(xlim,ncol(x)),nrow=2)  
    if( length(dim(ylim)) < 2 ) ylim <- matrix(rep(ylim,ncol(x)),nrow=2)  
    if (is.null(oma)) {
      if( trimode ) {
        oma <- c(3, 3, 3, 3)
        if (!is.null(main)) 
          oma[3] <- 5
      } else {
        oma <- c(4, 4, 4, 4)
        if (!is.null(main)) 
          oma[3] <- 6
      }
    }

    mycall <- list(x=x,labels=labels,panel=panel,...,main=main,oma=oma,
                   font.main=font.main,cex.main=cex.main,
                   lower.panel=lower.panel, upper.panel=upper.panel,
                   diag.panel=diag.panel,text.panel=text.panel,
                   label.pos=label.pos,cex.labels=cex.labels,
                   font.labels=font.labels,row1attop=row1attop,gap=gap,add=add,
                   xlim=xlim,ylim=ylim,log=log,onlyPanel=onlyPanel,
                   trimode=trimode)
    if( noplot ) {
      gsi.setPlot(mycall)
      #gsi.plots[[dev.cur()]] <<- mycall
      return(invisible(NULL))
    }
    
    if( is.null(onlyPanel) )
      onlyPanel <- list(1:nc,1:nc)
    if( length(onlyPanel)!=2)
        stop("onlyPanel must be a list of two")
    if( trimode ) {
      opar <- par(mfrow = c(length(onlyPanel[[1]]), length(onlyPanel[[2]])),
                  mar = rep.int(gap/2, 4)+c(1,0,0,0), oma = oma,pty="s",xaxs="i",yaxs="i")
    } else {
      opar <- par(mfrow = c(length(onlyPanel[[1]]), length(onlyPanel[[2]])),
                  mar = rep.int(gap/2, 4), oma = oma)
    }
#    opar <- par(mfrow = c(nc, nc), mar = rep.int(gap/2, 4), oma = oma)
    on.exit({par(opar);gsi.addCoorInfo(d=NULL)},add=TRUE)
    for (iP in if (row1attop) 
        1:length(onlyPanel[[1]])
    else length(onlyPanel[[1]]):1) for (jP in 1:length(onlyPanel[[2]])) {
      i <- onlyPanel[[1]][iP]
      j <- onlyPanel[[2]][jP]
      gsi.addCoorInfo(d=c(i,j))
      if( trimode ){
        plot(x[, j], x[, i], xlab = "", ylab = "", axes = FALSE, 
            type = "n", ...,log=log,xlim=c(0,1),ylim=c(0,1),usr=c(0,1,0,1))
      } else {
        plot(x[, j], x[, i], xlab = "", ylab = "", axes = FALSE, 
            type = "n", ...,log=log,xlim=xlim[,j],ylim=ylim[,i])
      }
        if (i == j || (i < j && has.lower) || (i > j && has.upper)) {
            if(trimode) {
              if(i!=j) {
                #localAxis(1, ...)
              }
            } else {
              box()
              if (i == 1 && (!(j%%2) || !has.upper || !has.lower)) 
                localAxis(1 + 2 * row1attop, ...)
              if (i == nc && (j%%2 || !has.upper || !has.lower)) 
                localAxis(3 - 2 * row1attop, ...)
              if (j == 1 && (!(i%%2) || !has.upper || !has.lower)) 
                localAxis(2, ...)
              if (j == nc && (i%%2 || !has.upper || !has.lower)) 
                localAxis(4, ...)
            }
            mfg <- par("mfg")
            if (i == j) {
                if (has.diag) 
                  diag.panel(as.vector(x[, i]))
                if (has.labs) {
 #                 par(usr = c(0, 1, 0, 1))
                  if (is.null(cex.labels)) {
                    l.wid <- strwidth(labels, "user")
 #                   cex.labels <- max(0.8, min(2, 0.9/max(l.wid)))
                    cex.labels <- max(1, min(2, 0.9/max(l.wid)))
                  }
                  # to ensure that diagonal panels respond when margin=part
                  if(trimode){
                   mrg = gsi.getCoorInfo()$margin
                   classes = c("acomp","rcomp")
                   k = i + ifelse(mrg %in% classes, 0, ifelse( i< match(mrg,labels),0,1))
                   text.panel(0.5, label.pos, labels[k], cex = cex.labels, 
                     font = font.labels)
                  }else{
                   text.panel(0.5, label.pos, labels[i], cex = cex.labels, 
                    font = font.labels)
                  }
                }
            }
            else if (i < j) 
                lower.panel(as.vector(x[, j]), as.vector(x[, 
                  i]), ...)
            else upper.panel(as.vector(x[, j]), as.vector(x[, 
                i]), ...)
            if( i!=j ) for( p in add ) {
              arg <- c(list(p$panel,as.vector(p$x[,j]), as.vector(p$x[,i])),p$args)
              do.call("gsi.call",arg)
            }
            if (any(par("mfg") != mfg)) 
                stop("The panel function made a new plot")
        }
        else par(new = FALSE)
    }
    if (!is.null(main)) 
        mtext(main, 3, 3, TRUE, 0.5, cex = cex.main, font = font.main)
    #gsi.plots[[dev.cur()]] <<- mycall
    gsi.setPlot(mycall)
    invisible(NULL)
}






simpleMissingSubplot <- function(loc,
                            portions,labels=NULL,
                            col=c("white","yellow","red","green","blue"),
                                 ...,border="gray60",vertical=NULL,xpd=NA) {
  x1<-loc[1]
  x2<-loc[2]
  y1<-loc[3]
  y2<-loc[4]
  opar <- par(list("xlog","ylog","xpd","pin","plt"))
  usr<-par("usr")
  #par(opar[c("xlog","ylog","xpd","pin","plt")])
  on.exit(par(opar),add=TRUE)
  par(xlog=FALSE,ylog=FALSE,xpd=xpd,par(),opar)
  if( is.null(vertical) ) {
    vertical <- opar$pin[1]*abs(x2-x1)/abs(usr[2]-usr[1]) < 
      opar$pin[2]*abs(y2-y1)/abs(usr[4]-usr[3])
    if( is.na(vertical) ) {
      print(list(opar=opar,usr=usr,args=match.call(),loc=loc))
    }
  }
  if( length(col)<length(portions) ) col <- rep(col,length(portions))
  col <- col[1:length(portions)]
  col <- col[portions>0]
  labels <- labels[1:length(portions)]
  labels<- labels[portions>0]
  portions<-portions[portions>0]
  portions <- portions/sum(portions)  
  p <- cumsum(c(0,portions))
  mp <- (p[-1]+p[-length(p)])/2
  xd <- x2-x1
  yd <- y2-y1
  if( vertical ) {
    xs <- (x2+x1)/2
    for(i in 1:length(portions))
      rect(x1,y1+yd*p[i],x2,y1+yd*p[i+1],col=col[i],border=border)
    if(!is.null(labels) ) text(xs,y1+mp*yd,labels,...,xpd=xpd)
  } else {
    ys <- (y2+y1)/2
    for(i in 1:length(portions))
      rect(x1+xd*p[i],y1,x1+xd*p[i+1],y2,col=col[i],border=border)
    if(!is.null(labels) ) text(x1+mp*xd,ys,labels,...,xpd=xpd)
  }
  invisible(mp)
}


ternaryAxis <- function(side=1:3,at=seq(0.2,0.8,by=0.2),
                        labels=if(is.list(at)) lapply(at,format) else format(at),
                        ...,
                        tick=TRUE,pos=0,
                        font.axis=par("font.axis"),
                        font.lab=par("font.lab"),
                        lty="solid",lwd=1,
                        len.tck=0.025,dist.lab=0.03,
                        dist.axis=0.03,
                        lty.tck="solid",
                        col.axis=par("col.axis"),
                        col.lab=par("col.lab"),
                        cex.axis=par("cex.axis"),
                        cex.lab=par("cex.lab"),
                        Xlab=NULL,Ylab=NULL,Zlab=NULL,small=TRUE,
                        xpd=NA,aspanel=FALSE){
  #print(match.call())
  nr <-1
  it <- function(x,Nr=nr) {
    if( length(x) == 0 )
      return(x)
    x[[((Nr-1)%%length(x))+1]]
  }
  itl <- function(x,Nr=nr) {
    if( length(x) == 0 )
      return(x)
    if( is.list(x) ) 
      x[[((Nr-1)%%length(x))+1]]
    else
      x
  }
  if( ! aspanel ) {
    axes <- match.call()
    axes$aspanel=TRUE
    environment(axes) <- parent.frame()
    replot(axes=substitute(quote(axes),list(axes=axes)))
    return(invisible(NULL))
  }
  #if (is.null(col) && length(list(...)) && !is.null(fg <- list(...)$fg)) 
  #  col <- fg
  s60 <- sin(pi/3)
  c60 <- cos(pi/3)
  s30 <- sin(pi/6)
  c30 <- cos(pi/6)
  if( small ) {
    if( !is.null(Xlab) )
      text(0,-it(dist.lab,1),Xlab,adj=c(0.5,1),font=it(font.lab,1),col=it(col.lab,1),cex=it(cex.lab,1),xpd=xpd)
    if( !is.null(Ylab) )
      text(1,-it(dist.lab,2),Ylab,adj=c(0.5,1),font=it(font.lab,2),col=it(col.lab,2),cex=it(cex.lab,2),xpd=xpd)
    if( !is.null(Zlab) )
      text(0.5,s60+it(dist.lab,3),Zlab,adj=c(0.5,0),font=it(font.lab,3),col=it(col.lab,3),cex=it(cex.lab,3),xpd=xpd)
  } else {
    if( !is.null(Xlab) )
      text(-c30*it(dist.lab,1),-s30*it(dist.lab,1),
           Xlab,adj=c(1,1),font=it(font.lab,1),col=it(col.lab,1),cex=it(cex.lab,1),xpd=xpd)
    if( !is.null(Ylab) )
      text(1+c30*it(dist.lab,2),
           -s30*it(dist.lab,2),Ylab,adj=c(0,1),font=it(font.lab,2),col=it(col.lab,2),cex=it(cex.lab,2),xpd=xpd)
    if( !is.null(Zlab) )
      text(c60,s60+it(dist.lab,3),Zlab,
           adj=c(0.5,0),font=it(font.lab,3),col=it(col.lab,3),cex=it(cex.lab,3),xpd=xpd)
  }
  if(length(side)>0) for( nr in  1:length(side) ) {
    b <- it(pos)
    a <- 1-b
    if( is.list(at) ) {
      att<-at[[nr]]
    } else {
      att<-at
    }
    switch(as.character(side[nr]),
           "0"={},
           "1"={
             if( !is.na(it(lty)) )
               segments(0*a+c60*b,
                        0*a+s60*b,
                        1*a+c60*b,
                        0*a+s60*b,lwd=it(lwd),lty=it(lty),
                        col=it(col.axis),
                        xpd=xpd)
             if( !is.na(it(lty.tck)) && it(tick))
               segments(att*a+c60*b,
                        0*a+s60*b,
                        att*a+c60*b,
                 0*a+s60*b-it(len.tck),
                        lwd=it(lwd),lty=it(lty.tck),
                        col=it(col.axis),
                        xpd=xpd)
             if( length(itl(labels))>0 )
               text(att*a+c60*b,
                    0*a+s60*b-it(dist.axis),
                    as.graphicsAnnot(itl(labels)),adj=c(0.5,1),
                    font=it(font.axis),col=it(col.axis),
                    cex=it(cex.axis),xpd=xpd)
           },
           "2"={
             if( !is.na(it(lty)) )
               segments(1*a,
                        0*a,
                        c60*a,
                        s60*a,lwd=it(lwd),lty=it(lty),
                        col=it(col.axis),
                        xpd=xpd)
             if( !is.na(it(lty.tck)) && it(tick))
               segments((1+att*(c60-1))*a,
                        (0+att*(s60-0))*a,
                        (1+att*(c60-1))*a+it(len.tck)*c30,
                        (0+att*(s60-0))*a+it(len.tck)*s30,
                        lwd=it(lwd),lty=it(lty),
                        col=it(col.axis)
                        ,xpd=xpd)
             if( length(itl(labels))>0 )
               text((1+att*(c60-1))*a+it(dist.axis)*c30,
                    (0+att*(s60-0))*a+it(dist.axis)*s30,
                    adj=c(0,0),
                    as.graphicsAnnot(itl(labels)),
                    font=it(font.axis),
                    col=it(col.axis),
                    cex=it(cex.axis),
                    xpd=xpd)
           },
           "3"={
             if( !is.na(it(lty)) )
               segments(c60*a+1*b,
                        s60*a+0*b,
                        0*a+1*b,
                        0*a+0*b,lwd=it(lwd),lty=it(lty),
                        col=it(col.axis),
                        xpd=xpd)
             if( !is.na(lty.tck) && it(tick))
               segments((c60+att*-c60)*a+1*b,
                        (s60+att*-s60)*a+0*b,
                        (c60+att*-c60)*a+1*b+it(len.tck)*-c30,
                        (s60+att*-s60)*a+0*b+it(len.tck)*s30,
                        lwd=it(lwd),lty=it(lty.tck),
                        col=it(col.axis),
                        xpd=xpd)
             if( length(itl(labels))>0 )
               text((c60+att*-c60)*a+1*b+it(len.tck)*-c30,
                    (s60+att*-s60)*a+0*b+it(len.tck)*s30,
                    as.graphicsAnnot(itl(labels)),
                    adj=c(1,0),
                    font=it(font.axis),
                    col=it(col.axis),
                    cex=it(cex.axis),
                    xpd=xpd)
           },
           "-1"={
             if( !is.na(it(lty)) )
               segments(1*a+c60*b,
                        0*a+s60*b,
                        (1-c30*s60)*a+(c60-c30*s60)*b,
                        (0-s30*s60)*a+(s60-s30*s60)*b,lwd=it(lwd),lty=it(lty),
                        col=it(col.axis),
                        xpd=xpd)
             if( !is.na(it(lty.tck)) && it(tick))
               segments(1*a+c60*b-att*c30*s60,
                        0*a+s60*b-att*s30*s60,
                        1*a+c60*b-att*c30*s60-c60*it(len.tck),
                        0*a+s60*b-att*s30*s60+s60*it(len.tck),
                        lwd=it(lwd),lty=it(lty.tck),
                        col=it(col.axis),
                        xpd=xpd)
             if( length(itl(labels))>0 )
               text(1*a+c60*b-att*c30*s60-c60*it(dist.axis),
                    0*a+s60*b-att*s30*s60+s60*it(dist.axis),
                    as.graphicsAnnot(itl(labels)),adj=c(1,0),
                    font=it(font.axis),col=it(col.axis),
                    cex=it(cex.axis),xpd=xpd)
           },
           "-2"={
             if( !is.na(it(lty)) )
               segments(c60*a+0*b,
                        s60*a+0*b,
                        (c60+c30*s60)*a+(0+c30*s60)*b,
                        (s60-s30*s60)*a+(0-s30*s60)*b,lwd=it(lwd),lty=it(lty),
                        col=it(col.axis),
                        xpd=xpd)
             if( !is.na(it(lty.tck)) && it(tick))
               segments(c60*a+0*b+att*c30*s60,
                        s60*a+0*b-att*s30*s60,
                        c60*a+0*b+att*c30*s60+c60*it(len.tck),
                        s60*a+0*b-att*s30*s60+s60*it(len.tck),
                        lwd=it(lwd),lty=it(lty.tck),
                        col=it(col.axis),
                        xpd=xpd)
             if( length(itl(labels))>0 )
               text(c60*a+0*b+att*c30*s60+c30*it(dist.axis),
                    s60*a+0*b-att*s30*s60+s30*it(dist.axis),
                    as.graphicsAnnot(itl(labels)),adj=c(0,0),
                    font=it(font.axis),col=it(col.axis),
                    cex=it(cex.axis),xpd=xpd)
           },
           "-3"={
             if( !is.na(it(lty)) )
               segments(0*a+1*b,
                        0*a+0*b,
                        (0-0*s60)*a+(1-0*s60)*b,
                        (0+1*s60)*a+(0+1*s60)*b,lwd=it(lwd),lty=it(lty),
                        col=it(col.axis),
                        xpd=xpd)
             if( !is.na(it(lty.tck)) && it(tick))
               segments(0*a+1*b-att*0*s60,
                        0*a+0*b+att*1*s60,
                        0*a+1*b-att*0*s60-1*it(len.tck),
                        0*a+0*b+att*1*s60+0*it(len.tck),
                        lwd=it(lwd),lty=it(lty.tck),
                        col=it(col.axis),
                        xpd=xpd)
             if( length(itl(labels))>0 )
               text(0*a+1*b-att*0*s60-1*it(dist.axis),
                    0*a+0*b+att*1*s60+0*it(dist.axis),
                    as.graphicsAnnot(itl(labels)),adj=c(1,0.5),
                    font=it(font.axis),col=it(col.axis),
                    cex=it(cex.axis),xpd=xpd)
           },

           warning("Unkown axis side",side[nr])
           )
  }
}

## Paradigma:
#
# 1) Prepare the parameters
# 2) (if !add and !aspanel) Set Up Coordinate system
# 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
# 3a) Set up gsi.pairs
# 3a.1) Store original data in environment 
# 3a.2) Define an infkt
# 3a.3) Call gsi.add2pairs or gsi.pairs
# 3b) Plot directly
# 3b.1) if( newPlot ) gsi.setPlot(NULL)
# 3b.2) Transform data
# 3b.3) prepare plotting
# 3b.4) Eventually create the plot
# 3b.5) plot coordinate System
# 3b.6) Analyse Missings
# 3b.7) Plot Nonmissings
# 3b.8) Plot Missings
# 4) Postprocessing: create dependent subplotting
# 5) if( ! aspanel ) replot(plot=match.call(),add=add)
# 7) return(invisible(replot(plot=FALSE))) 
plot.acomp <- function(x,...,labels=names(x),aspanel=FALSE,id=FALSE,idlabs=NULL,idcol=2,center=FALSE,scale=FALSE,pca=FALSE,col.pca=par("col"),margin="acomp",add=FALSE,triangle=!add,col=par("col"),axes=FALSE,plotMissings=TRUE,lenMissingTck=0.05,colMissingTck="red",mp=~simpleMissingSubplot(c(0,1,0.95,1),missingInfo,c("NM","TM",cn)),robust=getOption("robust"))
 {
   ## Prepare the parameters
   va <- NULL
   col <- unclass(col)
   if( is.null(colMissingTck) ) colMissingTck<-col
   if( is.null(labels) ) labels <- paste("var",1:gsi.getD(x))
   #colnames(x) <- labels
   newPlot <- ! aspanel && !add
   ## oX <- X
   ## Setting up the coordinate system
   if( newPlot ) {
     D  <- gsi.getD(x)
     ce <- acomp(gsi.mystructure(rep(1,D),names=names(x)))
     ms <- 1
     va <- NULL
     if( is.logical(center) && is.logical(scale) ) {
       if( center || scale ) {
         if( is.null(va) )
           va <- var(x,robust=robust,giveCenter=TRUE)
         if( center )
           ce <- attr(va,"center")
         if( scale ) {
           ms <- (1/sqrt(mean(gsi.diagExtract(va))))
         }
       }
     } else {
       if( !is.logical(center) )
         ce <- center
       if( !is.logical(scale) )
         ms <- scale
     }
     if( gsi.getD(x) > 3 ){
       nc <- gsi.getD(x) - if( margin %in% c("acomp","rcomp") ) 0 else 1
     }else{
       nc <- 1}
     gsi.setCoorInfo(mean=ce,
                     scale=ms,
   #                  var=va,
                     geo="acomp",
                     margin=margin,nc=nc)
     ## Set up panels
   }
   ## Setting up a gsi.pairs or plotting directly?
#   if( newPlot && gsi.getD(x) > 3 ) {
   if( !aspanel && gsi.getD(x) > 3 ) {
     ## Set up gsi.pairs
     X <- x # Store the dataset for later use in panel.
     infkt <- function(x,y,...) {
       plot.acomp(x=X,aspanel=TRUE,labels=labels,center=center,scale=scale,col=col,plotMissings=plotMissings,lenMissingTck=lenMissingTck,colMissingTck=colMissingTck,mp=mp,robust=robust,axes=axes,...)
     }
# ##    if( margin=="rcomp" )
# ##      infkt <- function(x,y,...) {
# ##        plot.acomp(rcompmargin(X,d=c(gsi.mapfrom01(x),gsi.mapfrom01(y)),pos=3),...,aspanel=TRUE,center=center,scale=scale,col=col,plotMissings=plotMissings,lenMissingTck=lenMissingTck,colMissingTck=colMissingTck,mp=mp,robust=robust,axes=axes)
# ##      }
# ##    else if(margin=="acomp") {
# ##      infkt <- function(x,y,...) {
# ##        plot.acomp(acompmargin(X,d=c(gsi.mapfrom01(x),gsi.mapfrom01(y)),pos=3),...,aspanel=TRUE,center=center,scale=scale,col=col,plotMissings=plotMissings,lenMissingTck=lenMissingTck,colMissingTck=colMissingTck,mp=mp,robust=robust,axes=axes)
# ##      }
# ##      
# ##    } else {
# ##      if( !is.numeric(margin))
# ##        margin <- match(margin,colnames(X))
# ##      fest <- X[,margin,drop=FALSE]
# ##      X    <- X[,-margin]
# ##      infkt <- function(x,y,...) {
# ##        plot.acomp(acomp(cbind(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],fest)),...,aspanel=TRUE,center=center,scale=scale,col=col,plotMissings=plotMissings,lenMissingTck=lenMissingTck,colMissingTck=colMissingTck,mp=mp,robust=robust,axes=axes)
# ##      }
# ##    }
     nc <- gsi.getCoorInfo()$nc
     if( add )
       noreplot(gsi.add2pairs(sapply(1:nc,gsi.mapin01),infkt,...))
     else
       noreplot(gsi.pairs(sapply(1:nc,gsi.mapin01),labels=labels,panel=infkt,...,trimode=TRUE))
   } else {
     ## Dont set up gsi.pairs, but plot directly
     if( newPlot )
       gsi.setPlot(NULL) ## not a gsi.pairs plot
     ## From here on we have a single ternary diagram
     ## and a coorInfo set up
     ## in this else part we are actually plotting
     
     ## Transform into local system
#     coorInfo <- gsi.getCoorInfo()
     Y <- oneOrDataset(gsi.pltTrafo(x,what="data"))
     cn<- gsi.pltTrafo(labels,what="names")
     if( is.null(cn) ) {
       cn <- c("x","y","z")
     }
     ## Prepare plotting
     s60 <- sin(pi/3)
     c60 <- cos(pi/3)
     s30 <- sin(pi/6)
     c30 <- cos(pi/6)
     
     ## Create the plot
     if( newPlot ) {
       usr <- par(list("pty")); on.exit(par(usr),add=TRUE)
       par( pty="s" )
       plot(x=c(0,c60,1,0),y=c(0,s60,0,0),
            xlim=c(0,1),ylim=c(0,1),type="n",xlab="",ylab="",
            axes=FALSE)
     }
     ## Plot triangle, axes and annotations
     if( triangle ) {
       lines(x=c(0,c60,1,0),y=c(0,s60,0,0))
     }
     if( is.logical(axes) ) {
       if( axes ) 
         ternaryAxis(1:3,Xlab=cn[1],Ylab=cn[2],Zlab=cn[3],aspanel=TRUE,small=aspanel)
       else if( !add )
         ternaryAxis(0,Xlab=cn[1],Ylab=cn[2],Zlab=cn[3],aspanel=TRUE,small=aspanel)
     } else {
       if( is.null(axes$Xlab) ) axes$Xlab<- cn[1]
       if( is.null(axes$Ylab) ) axes$Ylab<- cn[2]
       if( is.null(axes$Zlab) ) axes$Zlab<- cn[3]
       if( is.null(axes$small) )
         axes$small <- aspanel
       if( is.call(axes) ) {
         env <- environment(axes)
         if( is.null(env) )
           eval(axes)
         else
           eval(axes,env)
       } else {
         axes$aspanel<-TRUE
         do.call("ternaryAxis",as.list(axes))
       }
     }
     ## Analyse Missingness
     nmv <- is.NMV(Y)
     bdl <- is.BDL(Y)
     nMis <- apply(if( plotMissings ) !nmv else !(nmv | bdl),1,sum)
     nonmissing   <- nMis == 0
     Y<-oneOrDataset(clo(gsi.mystructure(c(ifelse(nmv,Y,0)),dim=dim(Y))))
     ## plot  Nonmissings
     x1 <- Y[,2]+Y[,3]*c60
     y1 <- Y[,3]*s60
     points(ifelse(nonmissing,x1,NA),ifelse(nonmissing,y1,NA),...,col=col)
     ## plot Missings
     if( plotMissings && !all(nonmissing) ) {
       ## Missing ticks
       totallyMissing   <- nMis > 1
       partiallyMissing <- nMis == 1
       wM <- apply(!nmv,1,function(x) c(which(x),0)[1])
       if( lenMissingTck != 0 && any(partiallyMissing) ) {
         xD <- -(x1-c(NA,0,1,c60)[wM+1])*lenMissingTck
         yD <- -(y1-c(NA,0,0,s60)[wM+1])*lenMissingTck
         segments(x1,y1,x1+xD,y1+yD,col=colMissingTck,...,xpd=TRUE)
       }
       ## Missing-Panel-Plot
       missingInfo <-  c(NotMissing=sum(nonmissing),
                         TotallyMissing=sum(totallyMissing),
                         Missing1=sum(partiallyMissing&!nmv[,1]),
                         Missing2=sum(partiallyMissing&!nmv[,2]),
                         Missing3=sum(partiallyMissing&!nmv[,3]))
       eval(mp[[2]])
     }
     ## Id 
     if( id ) {
       if( is.null(idlabs) )
         nam <- names(x)
       idlabs <- apply(x,1,function(k) paste(names(x),k,sep="=",col="\n"))
                                        #paste(cn[1],"=",round(Y[,1],2),",\n",
                                        #              cn[2],"=",round(Y[,2],2),",\n",
                                        #              cn[3],"=",round(Y[,3],2))
       return( identify(x1,y1,idlabs,col=idcol,xpd=NA))
     }
   }
### After the actual plot:
   ## Create PCA
  if( pca && ! aspanel) {
       if( is.null(va) ) va <- var(acomp(x),robust=robust,giveCenter=TRUE)
       pca.d <- acomp(princomp(acomp(x),robust=robust,covmat=va)$Loadings[1,])
       pca.c <- attr(va,"center")
       noreplot(straight.acomp(pca.c,pca.d,col=col.pca))
   }
   ## Set up replotting information:
   if( !aspanel )
     replot(plot=match.call(),add=add)
   return(invisible(replot(plot=FALSE)))
}

plot.ccomp <- function(x,...) {
  x<-unclass(x)
  x<-rcomp(gsi.mystructure(abs(x+runif(length(x),-0.3,0.3)),dim=dim(x)))
  plot(x,...)
}


# modified by Raimon in May 2008
# more modifications by Gerald
### plot.rcomp
### Differences
###  a) Scaling equals Acomp centering, no mean shift. *
###  b) Uses rcomp geometry in finding the centering mean *
###      but not in doing it !!!
###  c) Principal Components are in rcomp geometry
###  d) default margin is acomp
###  e) BDL is not treated as nonmissing if missings are not plotted

plot.rcomp <- function(x,...,labels=names(x),aspanel=FALSE,id=FALSE,idlabs=NULL,idcol=2,center=FALSE,scale=FALSE,pca=FALSE,col.pca=par("col"),margin="rcomp",add=FALSE,triangle=!add,col=par("col"),axes=FALSE,plotMissings=TRUE,lenMissingTck=0.05,colMissingTck="red",mp=~simpleMissingSubplot(c(0,1,0.95,1),missingInfo,c("NM","TM",cn)),robust=getOption("robust"))
{
# 1) Prepare the parameters
  col <-unclass(col)
  if( is.null(colMissingTck) ) colMissingTck<-col
  if( !is.logical(center) || !is.logical(scale) || center || scale )
    warning("Scaling and centering meaningless for rcomp-compositions");
# 2) (if !add and !aspanel) Set Up Coordinate system
   newPlot <- ! aspanel && !add
   ## oX <- X
   ## Setting up the coordinate system
   if( newPlot ) {
     D  <- gsi.getD(x)
     ce <- rcomp(gsi.mystructure(rep(1,D),names=names(x)))
     ms <- 1
     #va <- NULL
     #if( is.logical(center) && is.logical(scale) ) {
     #  if( center || scale ) {
     #    if( is.null(va) )
     #      va <- var(x,robust=robust,giveCenter=TRUE)
     #    if( scale )
     #      ce <- attr(va,"center")
     #    if( center ) {
     #      warning("Centering not supported for rcomp-compositions")
     #      ms <- 1 # (1/sqrt(mean(gsi.diagExtract(va))))
     #    }
     #  }
     #} else {
     #  if( !is.logical(center) )
     #    ce <- center ## Both are the same thing
     #  if( !is.logical(scale) )
     #    ce <- scale  ## Both are the same thing
     #}
     if( gsi.getD(x) > 3){
       nc <- gsi.getD(x) - if( margin %in% c("acomp","rcomp") ) 0 else 1
     }else{
       nc <- 1
     }
     gsi.setCoorInfo(mean=ce,scale=ms,geo="rcomp", margin=margin,nc=nc)
   }
# 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
  #X <- oneOrDataset(x)
  #oX<-X
  if( !aspanel && gsi.getD(x) > 3 ) {
# 3a) Set up gsi.pairs
# 3a.1) Store original data in environment
    X<-x
# 3a.2) Define an infkt
    infkt <- function(x,y,...) {
      plot.rcomp(x=X,aspanel=TRUE,labels=labels,center=center,scale=scale,col=col,plotMissings=plotMissings,lenMissingTck=lenMissingTck,colMissingTck=colMissingTck,mp=mp,robust=robust,axes=axes,...)
     }
# 3a.3) Call gsi.add2pairs or gsi.pairs
#    if( margin=="rcomp" )
#      infkt <- function(x,y,...) {
#        plot.rcomp(rcompmargin(X,d=c(gsi.mapfrom01(x),gsi.mapfrom01(y)),pos=3),...,aspanel=TRUE,col=col,plotMissings=plotMissings,lenMissingTck=lenMissingTck,colMissingTck=colMissingTck,mp=mp,robust=robust,axes=axes)
#      }
#  else if(margin=="acomp") {
#    infkt <- function(x,y,...) {
#      plot.rcomp(acompmargin(X,d=c(gsi.mapfrom01(x),gsi.mapfrom01(y)),pos=3),...,aspanel=TRUE,col=col,plotMissings=plotMissings,lenMissingTck=lenMissingTck,colMissingTck=colMissingTck,mp=mp,robust=robust,axes=axes)
#    }
#    
#  } else {
#    if( !is.numeric(margin))
#      margin <- match(margin,colnames(X))
#    fest <- X[,margin,drop=FALSE]
#    X    <- X[,-margin]
#    infkt <- function(x,y,...) {
#                                        # plot.rcomp(acomp(cbind(X[,c(gsi.mapfrom01(y),gsi.mapfrom01(x))],fest)),...,aspanel=TRUE)
#      plot.rcomp(rcomp(cbind(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],fest)),...,aspanel=TRUE, col=col,plotMissings=plotMissings,lenMissingTck=lenMissingTck,colMissingTck=colMissingTck,mp=mp,robust=robust,axes=axes)
#    }
#  }
    nc <- gsi.getCoorInfo()$nc 
     if( add ){
       noreplot(gsi.add2pairs(sapply(1:nc,gsi.mapin01),infkt,...))
     }else{
       noreplot(gsi.pairs(sapply(1:nc,gsi.mapin01),labels=labels,panel=infkt,...,trimode=TRUE))
     }
#    if( add )
#      gsi.add2pairs(sapply(1:nc,gsi.mapin01),infkt,...)
#    else
#      gsi.pairs(sapply(1:NCOL(X),gsi.mapin01),labels=labels,panel=infkt,...,
#              trimode=TRUE)
  } else {
### 3b) Plot directly
### 3b.1) if( newPlot ) gsi.setPlot(NULL)
    if( newPlot ) gsi.setPlot(NULL)
### 3b.2) Transform data
    Y <- oneOrDataset(gsi.pltTrafo(x,what="data"))
    cn<- gsi.pltTrafo(labels,what="names")
    if( is.null(cn) ) {
      cn <- c("x","y","z")
    }
    
### 3b.3) prepare plotting
    s60 <- sin(pi/3)
    c60 <- cos(pi/3)
    s30 <- sin(pi/6)
    c30 <- cos(pi/6)
### 3b.4) Eventually create the plot
    if( newPlot ) {
      usr <- par(list("pty")); on.exit(par(usr),add=TRUE)
      par( pty="s" )
      plot(x=c(0,c60,1,0),y=c(0,s60,0,0),
           xlim=c(0,1),   #c(min(c(0,x)),max(c(1,x))),
           ylim=c(0,1),   #c(min(c(0,y)),max(c(1,y))),
           type="n",xlab="",ylab="",
           axes=FALSE)
     # gsi.setPlot(NULL)
    }
  
### 3b.5) plot coordinate System
    if( triangle ) {
      segments(x0=c(0,1,c60),y0=c(0,0,s60),x1=c(1,c60,0),y1=c(0,s60,0))
    }
    if( is.logical(axes) ) {
      if( axes ) 
        ternaryAxis(1:3,Xlab=cn[1],Ylab=cn[2],Zlab=cn[3],aspanel=TRUE)
      else
        ternaryAxis(0,Xlab=cn[1],Ylab=cn[2],Zlab=cn[3],aspanel=TRUE)
    } else {
      if( is.null(axes$Xlab) )  axes$Xlab<- cn[1]
      if( is.null(axes$Ylab) ) axes$Ylab<- cn[2]
      if( is.null(axes$Zlab) ) axes$Zlab<- cn[3]
      if( is.null(axes$small) )
        axes$small <- aspanel
      if( is.call(axes) )
        eval(axes)
      else {
        axes$aspanel<-TRUE
        do.call("ternaryAxis",as.list(axes))
      }
    }
    
### 3b.6) Analyse Missings
 
#    X <- rcomp(oneOrDataset(X),c(1,2,3))
#    Y <- X
#    ce <- acomp(c(1,1,1))
#    ms <- 1
#    va <- 1 ## Vorsicht!!!!!
#    gsi.setCoorInfo(mean=ce,scale=ms)
    nmv <- is.NMV(Y) | (is.finite(Y) & Y==0)
    bdl <- is.BDL(Y)
    nMis <- apply(if( plotMissings ) !nmv else !(nmv | is.BDL(Y)),1,sum)
    nonmissing   <- nMis == 0
    Y<-oneOrDataset(clo(gsi.mystructure(c(ifelse(nmv,Y,0)),dim=dim(Y))))
  #  names(Y) <- cn
### 3b.7) Plot Nonmissings
    x1 <- Y[,2]+Y[,3]*c60
    y1 <- Y[,3]*s60
    points(ifelse(nonmissing,x1,NA),ifelse(nonmissing,y1,NA),...,col=col)
### 3b.8) Plot Missings
    if( plotMissings && !all(nonmissing) ) {
      ## Missing ticks
      totallyMissing   <- nMis > 1
      partiallyMissing <- nMis == 1
      wM <- apply(!nmv,1,function(x) c(which(x),0)[1])
      if( lenMissingTck != 0 && any(partiallyMissing) ) {
        xD <- -c(NA,c30,-c30,0)[wM+1]*lenMissingTck*s60
        yD <- -c(NA,s30,s30,-1)[wM+1]*lenMissingTck*s60
        segments(x1,y1,x1+xD,y1+yD,col=colMissingTck,...,xpd=TRUE)
      }
      ## equal area plot
      missingInfo <-  c(NotMissing=sum(nonmissing),
                        TotallyMissing=sum(totallyMissing),
                        Missing1=sum(partiallyMissing&!nmv[,1]),
                        Missing2=sum(partiallyMissing&!nmv[,2]),
                        Missing3=sum(partiallyMissing&!nmv[,3]))
      eval(mp[[2]])
    }
    ##### !!! Special activity
    if( id ) {
      if( is.null(idlabs) )
        idlabs <- paste(cn[1],"=",round(Y[,1],2),",\n",
                        cn[2],"=",round(Y[,2],2),",\n",
                        cn[3],"=",round(Y[,3],2))
      if( !aspanel ) replot(plot=match.call(),add=add)  
      return( identify(x1,y1,idlabs,col=idcol,xpd=NA))
    }
  }
## 4) Postprocessing: create dependent subplotting
  if( pca && ! aspanel) {
    va <- var(rcomp(x),robust=robust,giveCenter=TRUE)
    pca.d <- rcomp(princomp(rcomp(x),covmat=va,robust=robust)$Loadings[1,])
    pca.c <- attr(va,"center")
    straight.rcomp(pca.c,pca.d,col=col.pca)
  }
# 5) if( ! aspanel ) replot(plot=match.call(),add=add)
  if( !aspanel ) replot(plot=match.call(),add=add)  
# 7) return(invisible(replot(plot=FALSE)))   
  return(invisible(replot(plot=FALSE)))
}



isoPortionLines <- function(...) {
  UseMethod("isoPortionLines",gsi.getCoorInfo()$mean)
}

isoProportionLines <- function(...) {
  UseMethod("isoProportionLines",gsi.getCoorInfo()$mean)
}

####  simplified for pure adding (with panels):
### 1) Prepare the parameters
### 2) -
### 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
### 3a) Set up gsi.pairs
### 3a.1) Store original data in environment 
### 3a.2) Define an infkt
### 3a.3) gsi.add2pairs
### 3b) Plot directly
### 3b.1) --
### 3b.2) Transform data
### 3b.3) prepare plotting
### 3b.4) --
### 3b.5) -- 
### 3b.6) Analyse Missings 
### 3b.7) Plot Nonmissings
### 3b.8) Plot Missings    # only with data-type plotting
### 4) Postprocessing: create dependent subplotting
### 5) if( ! aspanel ) replot(plot=match.call(),add=TRUE)
### 7) return(invisible(replot(plot=FALSE))) 

isoPortionLines.acomp <- function(by=0.2,at=seq(0,1,by=by),...,parts=1:3,total=1,labs=TRUE,lines=TRUE,unit="") {
  coor <- gsi.getCoorInfo()
  if( coor$scale != 1 )
    stop("Scaling not implemented  in isoPortionLines.acomp")
  for(k in parts) {
    isoCollaps <- function(kkw,k) {
      s <- sum(kkw[-k])
      rcomp(switch(k,c(kkw[k],0,s),c(s,kkw[k],0),c(0,s,kkw[k])))
    }
    dir   <- rep(0,3)
    dir[k]<- 0
    dir[-k]<-c(1,-1)
    dirt = rmult(rcomp(dir/unclass(coor$mean))) # directions must be also perturbed!
    diru = rmult(rcomp(dir)) # directions must be also per
    for(p in at) {
      start <- rep((1-p)/2,3)
      start[k] <- p
      tx <- rep(0,3)    # to p,center=TRUElace the text, it is easy to...
      tx[k] <- p         # ... take points on the sides of the diagram
      tx[c(3,1,2)[k]] <- 1-p
      if( p>0 && p<1 ) {
        #kwt <- clo(start/unclass(coor$mean)) # perturbation must be positive
        kwu <- clo(start)#/unclass(coor$mean)) # perturbation must be positive
        tx <- clo(tx/unclass(coor$mean))
        if(lines) noreplot(straight.rcomp(kwu,diru,...))
        kwt <- isoCollaps(tx,k)
        if( labs ){
            text(kwt[2]+cos(60*pi/180)*kwt[3],kwt[3]*sin(60*pi/180),
            paste(p*total,unit[(k-1)%%length(unit)+1]),pos=c(2,1,4)[k],...,xpd=TRUE)
           }
      }
    }
  }
  replot(plot=match.call(),add=TRUE)  

  invisible(NULL)
}

#isoPortionLines.acomp <- function(by=0.2,at=seq(0,1,by=by),...,parts=1:3,total=1,labs=TRUE,lines=TRUE,unit="") {
#  coor <- gsi.getCoorInfo()
#  if( coor$scale != 1 )
#    stop("Scaling not implemented  in isoPortionLines.acomp")
#  for(k in parts) {
#    isoCollaps <- function(kw,k) {
#      s <- sum(kw[-k])
#      rcomp(switch(k,c(kw[k],0,s),c(s,kw[k],0),c(0,s,kw[k])))
#    }
#    dir   <- rep(0,3)
#    dir[k]<- 0
#    dir[-k]<-c(1,-1)
#    for(p in at) {
#      start <- rep((1-p)/2,3)
#      start[k] <- p
#      if( p>0 && p<1 ) {
#        kw<-rcomp(acomp(start)-coor$mean)
#        if(lines) straight(kw,rmult(dir),...)
#        kw <- isoCollaps(kw,k)
#        if( labs ) text(kw[2]+cos(60*pi/180)*kw[3],kw[3]*sin(60*pi/180),
#             paste(p*total,unit[(k-1)%%length(unit)+1]),...,pos=c(2,1,4)[k],xpd=TRUE)
#      }
#    }
#  }
#  invisible(NULL)
#}

isoProportionLines.acomp <- function(by=0.2,at=seq(0,1,by=by),...,parts=1:3,labs=TRUE,lines=TRUE) {
  coor <- gsi.getCoorInfo()
  for(k in parts) {
    dir   <- rep(0.25,3)
    dir[k]<- 0.5
    dir = acomp(dir) # * coor$scale # not needed
    for(p in at) {
      if( p>0 && p<1) {
        start <- acomp(switch(k,c(1,1-p,p),c(p,1,1-p),c(1-p,p,1)))
#        start <- acomp(switch(k,c(1E-17,1-p,p),c(p,1E-17,1-p),c(1-p,p,1E-17)))
        kw<-(start+coor$mean)*(coor$scale)  # perturbation must be positive
        if(lines) noreplot(straight(kw,dir,...))
        kw[k]<- 1E-17
        kw <- acomp(kw)
        if( labs ) text(kw[2]+cos(60*pi/180)*kw[3],kw[3]*sin(60*pi/180),
             paste(p),...,pos=c(4,2,1)[k],xpd=TRUE)
      }
    }
  }
  replot(plot=match.call(),add=TRUE)  
  invisible(NULL)
}

#isoProportionLines.acomp <- function(by=0.2,at=seq(0,1,by=by),...,parts=1:3,labs=TRUE,lines=TRUE) {
#  coor <- gsi.getCoorInfo()
#  for(k in parts) {
#    dir   <- rep(0.25,3)
#    dir[k]<- 0.5
#    for(p in at) {
#      if( p>0 && p<1) {
#        start <- acomp(switch(k,c(1,1-p,p),c(p,1,1-p),c(1-p,p,1)))
#        kw<-(start-coor$mean)*coor$scale
#        if(lines) straight(kw,acomp(dir),...)
#        kw[k]<- 1E-17
#        kw <- acomp(kw)
#        if( labs ) text(kw[2]+cos(60*pi/180)*kw[3],kw[3]*sin(60*pi/180),
#             paste(p),...,pos=c(4,2,1)[k],xpd=TRUE)
#      }
#    }
#  }
#  invisible(NULL)
#}


isoPortionLines.rcomp <- function(by=0.2,at=seq(0,1,by=by),...,parts=1:3,total=1,labs=TRUE,lines=TRUE,unit="") {
  coor <- gsi.getCoorInfo()
  if( coor$scale != 1 || norm(acomp(coor$mean))>0.001 )
    stop("Scaling and centering not implemented  in isoPortionLines.rcomp")
  for(k in parts) {
    isoCollaps <- function(kw,k) {
      s <- sum(kw[-k])
      rcomp(switch(k,c(kw[k],0,s),c(s,kw[k],0),c(0,s,kw[k])))
    }
    dir   <- rep(0,3)
    dir[k]<- 0
    dir[-k]<-c(1,-1)
    for(p in at) {
      start <- rep((1-p)/2,3)
      start[k] <- p
      if( p>0 && p<1 ) {
        try({
        kw <- rcomp(start) # isoCollaps(rcomp(start)-coor$mean)
        if(lines ) noreplot(straight(kw,rmult(dir),...))
        kw <- isoCollaps(kw,k)
        if( labs ) text(kw[2]+cos(60*pi/180)*kw[3],kw[3]*sin(60*pi/180),
             paste(p*total,unit[(k-1)%%length(unit)+1]),...,pos=c(2,1,4)[k],xpd=TRUE)
      },silent=FALSE)
      }
    }
  }
  replot(plot=match.call(),add=TRUE)  
  invisible(NULL)
}


isoProportionLines.rcomp <- function(by=0.2,at=seq(0,1,by=by),...,parts=1:3,labs=TRUE,lines=TRUE) {
  coor <- gsi.getCoorInfo()
  if( coor$scale != 1 || norm(acomp(coor$mean))>0.001)
    stop("Scaling not implemented  in isoPortionLines.rcomp")
  for(k in parts) {
    dir   <- rep(0.25,3)
    dir[k]<- 0.5
    for(p in at) {
      if( p>0 && p<1) {
        start <- acomp(switch(k,c(1,1-p,p),c(p,1,1-p),c(1-p,p,1)))
        kw<-start
        if(lines) noreplot(straight(kw,acomp(dir),...))
        kw[k]<- 1E-17
        kw <- acomp(kw)
        if( labs ) text(kw[2]+cos(60*pi/180)*kw[3],kw[3]*sin(60*pi/180),
             paste(p),...,pos=c(4,2,1)[k],xpd=TRUE)
      }
    }
  }
  replot(plot=match.call(),add=TRUE)  
  invisible(NULL)
}

#plot.aplus <- function (x, ..., labels = colnames(x), cn = colnames(x), aspanel = FALSE,
# The X not x is here to apply that to the dataset if only a single point is given.
# Is there any situation in which this is a problem?
plot.aplus <- function (x, ..., labels = colnames(X), cn = colnames(X), aspanel = FALSE,
    id = FALSE, idlabs = NULL, idcol = 2, center = FALSE, scale = FALSE,
    pca = FALSE, col.pca = par("col"), add = FALSE, logscale = TRUE,
    xlim = NULL, ylim = xlim, col = par("col"), plotMissings = TRUE,
    lenMissingTck = 0.05, colMissingTck = "red", mp = ~simpleMissingSubplot(missingPlotRect,
        missingInfo, c("NM", "TM", cn)), robust = getOption("robust")){
    col <- unclass(col)
    if (is.null(colMissingTck))
        colMissingTck <- col
    if (!aspanel && (center || scale))
        x <- scale(x, center = center, scale = scale, robust = robust)
    if (!aspanel && !add) {
        if (is.null(xlim))
            xlim <- if (logscale)
                apply(ifelse(is.NMV(x), x, NA), 2, function(x) {
                  erg <- range(x, na.rm = TRUE)
                  if (erg[1] == erg[2])
                    erg <- erg * c(1/1.1, 1.1)
                  erg
                })
            else apply(ifelse(is.NMV(x), x, 0), 2, function(x) c(0,
                max(x)))
        if (is.null(ylim))
            ylim <- xlim
    }
    X <- oneOrDataset(x)
    oX <- X
    if (NCOL(X) > 2) {
        infkt <- function(x, y, ...) {
            plot.aplus(X[, c(x[1], y[1]), drop = FALSE], ...,
                aspanel = TRUE, center = center, scale = scale,
                logscale = logscale, add = add, col = col, plotMissings = plotMissings,
                lenMissingTck = lenMissingTck, colMissingTck = colMissingTck,
                mp = mp, robust = robust)
        }
        usr <- par(list("xlog", "ylog"))
        on.exit(par(usr), add = TRUE)
        if (add)
            gsi.add2pairs(matrix(1:NCOL(X), nrow = 1), panel = infkt,
                ...)
        else {
            gsi.pairs(matrix(1:NCOL(X), nrow = 1), labels = labels,
                panel = infkt, ..., log = ifelse(logscale, "xy",
                  ""), xlim = xlim, ylim = ylim)
        }
    }
    else {
        if (is.null(cn)) {
            cn <- c("x", "y")
        }
        if (!add && !aspanel) {
            plot(x = c(1), y = c(1), ..., xlim = xlim[, 1], ylim = ylim[,
                2], type = "n", log = ifelse(logscale, "xy",
                ""), xlab = cn[1], ylab = cn[2])
            gsi.setPlot(NULL)
        }
        nmv <- is.NMV(X)
        nMis <- apply(if (plotMissings || logscale)
            !nmv
        else !(nmv | is.BDL(x)), 1, sum)
        nonmissing <- nMis == 0
        Y <- oneOrDataset(gsi.mystructure(c(ifelse(nmv, X, 0)), dim = dim(x)))
        x1 <- ifelse(nmv[, 1], Y[, 1], if (par("xlog"))
            10^par("usr")[1]
        else par("usr")[1])
        y1 <- ifelse(nmv[, 2], Y[, 2], if (par("ylog"))
            10^par("usr")[3]
        else par("usr")[3])
        points(ifelse(nonmissing, x1, NA), ifelse(nonmissing,
            y1, NA), ..., col = col)
        if (plotMissings && !all(nmv)) {
            opar <- par(list("xlog", "ylog", "pin", "plt"))
            usr <- par("usr")
            try({
                if (lenMissingTck != 0) {
                  yH <- nmv[, 2] & !nmv[, 1]
                  if (any(yH)) {
                    par(xlog = FALSE)
                    segments(usr[1], ifelse(yH, y1, NA), usr[1] -
                      (usr[1] - usr[2]) * lenMissingTck, ifelse(yH,
                      y1, NA), ..., col = colMissingTck, xpd = TRUE)
                    par(xlog = opar$xlog)
                  }
                  xH <- nmv[, 1] & !nmv[, 2]
                  if (any(xH)) {
                    par(ylog = FALSE)
                    segments(ifelse(xH, x1, NA), usr[3], ifelse(xH,
                      x1, NA), usr[3] - (usr[3] - usr[4]) * lenMissingTck,
                      ..., col = colMissingTck, xpd = TRUE)
                    par(ylog = opar$ylog)
                  }
                }
                if (!is.null(mp)) {
                  missingPlotRect <- c(usr[2], usr[2] + (usr[2] -
                    usr[1]) * (1 - opar$plt[2])/(opar$plt[2] -
                    opar$plt[1]), usr[3], usr[4])
                  missingInfo <- c(NotMissing = sum(nonmissing),
                    TotallyMissing = sum(nMis == 2), Missing1 = sum(nMis ==
                      1 & !nmv[, 1]), Missing2 = sum(nMis ==
                      1 & !nmv[, 2]))
                  eval(mp[[2]])
                }
            }, silent = FALSE)
            par(opar)
        }
        if (id) {
            if (is.null(idlabs))
                idlabs <- paste(cn[1], "=", round(X[, 1], 2),
                  ",\n", cn[2], "=", round(X[, 2], 2))
            if (!aspanel)
                replot(plot = match.call(), add = add)
            return(identify(x1, y1, idlabs, col = idcol, xpd = NA))
        }
    }
    if (pca && !aspanel) {
        pca.d <- iltInv(princomp(ilt(oX), robust = robust)$loadings[,
            1])
        pca.c <- mean(aplus(oX), robust = robust)
        straight.aplus(pca.c, pca.d, col = col.pca)
    }
    if (!aspanel)
        replot(plot = match.call(), add = add)
    return(invisible(NULL))
}


plot.rplus <- function (x, ..., labels = colnames(X), cn = colnames(X), aspanel = FALSE,
    id = FALSE, idlabs = NULL, idcol = 2, center = FALSE, scale = FALSE,
    pca = FALSE, col.pca = par("col"), add = FALSE, logscale = FALSE,
    xlim = NULL, ylim = xlim, col = par("col"), plotMissings = TRUE,
    lenMissingTck = 0.05, colMissingTck = "red", mp = ~simpleMissingSubplot(missingPlotRect,
        missingInfo, c("NM", "TM", cn)), robust = getOption("robust"))
{
    col <- unclass(col)
    if (is.null(colMissingTck))
        colMissingTck <- col
    if (!aspanel && !add) {
        if (is.null(xlim))
            xlim <- if (logscale)
                apply(ifelse(is.NMV(x), x, NA), 2, function(x) {
                  erg <- range(x, na.rm = TRUE)
                  if (erg[1] == erg[2])
                    erg <- erg * c(1/1.1, 1.1)
                })
            else apply(ifelse(is.NMV(x), x, 0), 2, function(x) c(0,
                max(x)))
        if (is.null(ylim))
            ylim <- xlim
    }
    if (scale)
        warning("Scaling has no graphical effect in rplus-amounts")
    X <- oneOrDataset(x)
    oX <- X
    if (NCOL(X) > 2) {
        if (!is.matrix(xlim))
            xlim <- replicate(ncol(oneOrDataset(x)), xlim)
        if (!is.matrix(xlim))
            ylim <- replicate(ncol(oneOrDataset(x)), xlim)
        infkt <- function(x, y, ...) {
            plot.rplus(X[, c(x[1], y[1]), drop = FALSE], ...,
                aspanel = TRUE, center = center, scale = scale,
                logscale = logscale, plotMissings = plotMissings,
                lenMissingTck = lenMissingTck, colMissingTck = colMissingTck,
                mp = mp, col = col)
        }
        if (add)
            gsi.add2pairs(matrix(1:NCOL(X), nrow = 1), infkt,
                ...)
        else {
            gsi.pairs(matrix(1:NCOL(X), nrow = 1), labels = labels,
                panel = infkt, ..., xlim = xlim, ylim = ylim,
                log = if (logscale)
                  "xy"
                else "")
        }
    }
    else {
        if (is.null(cn)) {
            cn <- c("x", "y")
        }
        if (!add && !aspanel) {
            plot(x = c(1), y = c(1), ..., xlim = xlim[, 1], ylim = ylim[,
                2], type = "n", log = ifelse(logscale, "xy",
                ""), xlab = cn[1], ylab = cn[2])
            gsi.setPlot(NULL)
        }
        nmv <- is.NMV(X) | (is.finite(X) & X == 0)
        nMis <- apply(if (plotMissings || logscale)
            !nmv
        else !(nmv | is.BDL(x)), 1, sum)
        nonmissing <- nMis == 0
        x1 <- ifelse(nmv[, 1], X[, 1], if (par("xlog"))
            10^par("usr")[1]
        else par("usr")[1])
        y1 <- ifelse(nmv[, 2], X[, 2], if (par("ylog"))
            10^par("usr")[3]
        else par("usr")[3])
        points(ifelse(nonmissing, x1, NA), ifelse(nonmissing,
            y1, NA), ..., col = col)
        if (plotMissings && !all(nmv)) {
            opar <- par(list("xlog", "ylog", "pin", "plt"))
            usr <- par("usr")
            try({
                if (lenMissingTck != 0) {
                  yH <- nmv[, 2] & !nmv[, 1]
                  if (any(yH)) {
                    par(xlog = FALSE)
                    segments(usr[1], ifelse(yH, y1, NA), usr[1] -
                      (usr[1] - usr[2]) * lenMissingTck, ifelse(yH,
                      y1, NA), ..., col = colMissingTck, xpd = TRUE)
                    par(xlog = opar$xlog)
                  }
                  xH <- nmv[, 1] & !nmv[, 2]
                  if (any(xH)) {
                    par(ylog = FALSE)
                    segments(ifelse(xH, x1, NA), usr[3], ifelse(xH,
                      x1, NA), usr[3] - (usr[3] - usr[4]) * lenMissingTck,
                      ..., col = colMissingTck, xpd = TRUE)
                    par(ylog = opar$ylog)
                  }
                }
                if (!is.null(mp)) {
                  missingPlotRect <- c(usr[2], usr[2] + (usr[2] -
                    usr[1]) * (1 - opar$plt[2])/(opar$plt[2] -
                    opar$plt[1]), usr[3], usr[4])
                  missingInfo <- c(NotMissing = sum(nonmissing),
                    TotallyMissing = sum(nMis == 2), Missing1 = sum(nMis ==
                      1 & !nmv[, 1]), Missing2 = sum(nMis ==
                      1 & !nmv[, 2]))
                  eval(mp[[2]])
                }
            }, silent = FALSE)
            par(opar)
        }
        if (id) {
            if (is.null(idlabs))
                idlabs <- paste(cn[1], "=", round(X[, 1], 2),
                  ",\n", cn[2], "=", round(X[, 2], 2))
            if (!aspanel)
                replot(plot = match.call(), add = add)
            return(identify(x1, y1, idlabs, col = idcol, xpd = NA))
        }
    }
    if (pca && !aspanel) {
        pca.d <- princomp(iit(oX), robust = robust)$loadings[,
            1]
        pca.c <- mean(rplus(oX), robust = robust)
        straight.rplus(pca.c, pca.d, col = col.pca)
    }
    if (!aspanel)
        replot(plot = match.call(), add = add)
    return(invisible(NULL))
}


plot.rmult <- function(x,...,labels=colnames(X),cn=colnames(X),aspanel=FALSE,id=FALSE,idlabs=NULL,idcol=2,center=FALSE,scale=FALSE,pca=FALSE,col.pca=par("col"),add=FALSE,logscale=FALSE,col=par("col"),robust=getOption("robust")) {
X <- oneOrDataset(x)
oX <- X
if( NCOL(X) > 2 ) {
    infkt <- function(x,y,...) {
      plot.rmult(X[,c(x[1],y[1]),drop=FALSE],...,aspanel=TRUE,center=center,scale=scale,pca=pca,col.pca=col.pca,logscale=logscale,col=col)
    }
    if( add )
      gsi.add2pairs(matrix(1:NCOL(X),nrow=1),infkt,...)
    else
      gsi.pairs(matrix(1:NCOL(X),nrow=1),labels=labels,panel=infkt,...,xlim=apply(x,2,range),ylim=apply(x,2,range),log=if(logscale) "xy" else "")
  } else {
    if( is.null(cn) ) {
      cn <- c("x","y")
    }
    x <- X[,1]
    y <- X[,2]
    if( aspanel && ! add ) {
      usr <- par(list("usr")); on.exit(par(usr),add=TRUE)
      #if( logscale )
       # par( xlog=TRUE,ylog=TRUE,usr=c(log10(min(x)),log10(max(x)),log10(min(y)),log10(max(y))))
      #else
      #  par( usr=c(min(x),max(x),min(y),max(y)) )
                                        #axis(1)
                                        #axis(2)
    } else {
      if( !add ) {
        plot(x=c(1),y=c(1),...,
             xlim=range(x),ylim=range(y),type="n",
             log=ifelse(logscale,"xy",""),xlab=cn[1],ylab=cn[2])
        #gsi.plots[[dev.cur()]]<<-NULL
        gsi.setPlot(NULL)
      }
    }
    points(x,y,...,col=col)
    if( id ) {
      if( is.null(idlabs) )
        idlabs <- paste(cn[1],"=",round(X[,1],2),",\n",
                        cn[2],"=",round(X[,2],2))
      if( !aspanel ) replot(plot=match.call(),add=add)  
      return( identify(x,y,idlabs,col=idcol,xpd=NA))
    }
  }
if( pca && ! aspanel ) {
  pca.d <- iitInv(princomp(iit(oX),robust=robust)$loadings[,1])
  pca.c <- mean(oX,robust=robust)
  straight.rmult(pca.c,pca.d,col=col.pca)
}
    if( !aspanel ) replot(plot=match.call(),add=add)  

return( invisible(NULL))
}



#### Plot Function Paradigma
####  simplified for pure adding (with panels):
### 1) Prepare the parameters
### 2) -
### 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
### 3a) Set up gsi.pairs
### 3a.1) Store original data in environment 
### 3a.2) Define an infkt
### 3a.3) gsi.add2pairs
### 3b) Plot directly
### 3b.1) --
### 3b.2) Transform data
### 3b.3) prepare plotting
### 3b.4) --
### 3b.5) -- 
### 3b.6) Analyse Missings 
### 3b.7) Plot Nonmissings
### 3b.8) Plot Missings    # only with data-type plotting
### 4) Postprocessing: create dependent subplotting
### 5) if( ! aspanel ) replot(plot=match.call(),add=TRUE)
### 7) return(invisible(replot(plot=FALSE))) 

### Called in three modes:
### a) User Mode: Add lines to plot
### b) internal panel mode: Draws lines in global coordinates
### c) external panel mode: Draws lines in local coordinates

lines.acomp <- function(x,...,steps=30,aspanel=FALSE) {
### 1) Prepare the parameters
### 2) -
### 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
  if( !aspanel && gsi.getD(x) > 3 ) {
### 3a) Set up gsi.pairs
### 3a.1) Store original data in environment 
    X <- oneOrDataset(x)
### 3a.2) Define an infkt
    infkt <- function(x,y,...) {
      lines.acomp(x=X,...,steps=steps,aspanel=TRUE)
    }
### 3a.3) gsi.add2pairs
    nc <- gsi.pltTrafo(x,"mfrow")[1]
    gsi.add2pairs(sapply(1:nc[1],gsi.mapin01),infkt,...)
  } else {
### 3b) Plot directly
### 3b.1) --
### 3b.2) Transform data
    Xt <- oneOrDataset(gsi.pltTrafo(gsi.mystructure(acomp(x),trafoed=attr(x,"trafoed")),"data"))
### 3b.3) prepare plotting
    s60 <- sin(pi/3)
    c60 <- cos(pi/3)
### 3b.4) --
### 3b.5) -- 
### 3b.6) Analyse Missings
    nmv <-is.NMV(Xt)
    NNN <- apply(nmv,1,all)
    if(!all(NNN))
       Xt[!NNN,]<-NA
### --- 
### 3b.7) Plot Nonmissings
    nx <- NROW(Xt)
    Xe <- Xt[-1,,drop=FALSE]
    Xs <- Xt[-nx,,drop=FALSE]
    nx <- NROW(Xs)
    l   <- rep((0:steps)/steps,nx)
    i   <- rep(1:nx,each=steps+1)
    XP  <- unclass(ilrInv((1-l)*ilr(Xs[i,,drop=FALSE]) +
                           l*ilr(Xe[i,,drop=FALSE])))
    x1 <- XP[,2]+XP[,3]*c60
    y1 <- XP[,3]*s60
    lines(x1,y1,...)

### 3b.8) Plot Missings    # only with data-type plotting
### --- is geometry type plotting    
  }
### 4) Postprocessing: create dependent subplotting
### ---
### 5) if( ! aspanel ) replot(plot=match.call(),add=TRUE)
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  
### 7) return(invisible(replot(plot=FALSE))) 
return(invisible(replot(plot=FALSE)))
}


lines.rcomp <- function(x,...,steps=30,aspanel=FALSE) {
#### Plot Function Paradigma
####  simplified for pure adding (with panels):
### 1) Prepare the parameters
  X <- oneOrDataset(clo(x))
  trafoed <- attr(x,"trafoed")
  if(is.null(trafoed)){trafoed=FALSE}
  if( (!aspanel||trafoed) && any( !is.finite(X)|x<0) ) {
    # Remove out of box problems
    X[is.BDL(x)]<-0.00000000001
    Xa <- X[-nrow(X),,drop=FALSE]
    Xb <- X[-1,,drop=FALSE]
    Xd <- Xb-Xa
    nm <- apply(is.NMV(Xa),1,all)&apply(is.NMV(Xb),1,all) 
    XaOk <-nm & apply(Xa>=0,1,all)
    XbOk <-nm & apply(Xb>=0,1,all)
    nm <- nm | (!XaOk & !XbOk)
    if( any(ra <- !XaOk & nm ) ) {
      delta <- apply(Xb[ra,,drop=FALSE]/-Xd[ra,,drop=FALSE],2,function(x) min(x[x>0]))
      Xa[ra,] <- Xb[ra,]-Xd[ra,]*delta
    }
    if( any(rb <- !XbOk & nm ) ) {
      delta <- apply(Xa[rb,,drop=FALSE]/Xd[rb,,drop=FALSE],2,function(x) min(x[x>0]))
      Xb[rb,] <- Xb[rb,]-Xd[rb,]*delta
    }
    Xa[!nm,]<-NA
    Xb[!nm,]<-NA
    LNK <- apply(Xa[-1,]==Xb[-nrow(Xb),],1,all)
    PAD <- !is.finite(LNK)
    LNK <- ifelse(is.finite(LNK),LNK,FALSE)
    padLNK <- apply(!is.finite(Xa[-1,])&!is.finite(Xb[-nrow(Xb),]),1,all)
    Redundant <- LNK | padLNK
    # Problem: Not LNK and NOT PAD would require extra pad
    gp <- rbind(c(TRUE,!Redundant),TRUE,
                c(!LNK & apply(is.finite(Xb[-nrow(Xb),])&is.finite(Xb[-nrow(Xb),]),1,all) ,FALSE))
    X<-t(gsi.mystructure(gsi.mystructure(t(cbind(Xa,Xb,Xb*NA)),dimnames=NULL),dim=c(ncol(Xb),3*nrow(Xb))))[c(gp),,drop=FALSE]
  }
### 2) -
### 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
  if( !aspanel && gsi.getD(X) > 3 ) {
### 3a) Set up gsi.pairs
### 3a.1) Store original data in environment
    #X<-X
### 3a.2) Define an infkt
    infkt <- function(x,y,...) {
      lines.rcomp(x=X,...,steps=steps,aspanel=TRUE)
    }
### 3a.3) gsi.add2pairs
    nc <- gsi.pltTrafo(X,"mfrow")
    gsi.add2pairs(sapply(1:nc[1],gsi.mapin01),infkt,...)
  } else {
### 3b) Plot directly
### 3b.1) --
### 3b.2) Transform data
#    Xt <- oneOrDataset(gsi.pltTrafo(gsi.mystructure(rcomp(X),trafoed=attr(X,"trafoed")),"data"))
    Xt <- oneOrDataset(gsi.pltTrafo(gsi.mystructure(rcomp(X),trafoed=trafoed),"data"))
#    Xt <- gsi.pltTrafo(gsi.mystructure(rcomp(X),trafoed=trafoed),"data")
### 3b.3) prepare plotting
    s60 <- sin(pi/3)
    c60 <- cos(pi/3)
### 3b.4) --
### 3b.5) -- 
### 3b.6) Analyse Missings
###   --- predone    
### 3b.7) Plot Nonmissings
    Xe <- Xt[-1,,drop=FALSE]
    Xs <- Xt[-nrow(X),,drop=FALSE]
    l   <- rep(c((0:steps)/steps),NROW(Xs))
    i   <- rep(1:NROW(Xs),each=steps+1)
    XP  <- unclass(convex.rcomp(Xs[i,,drop=FALSE],Xe[i,,drop=FALSE],l))
    x <- XP[,2]+XP[,3]*c60
    y <- XP[,3]*s60
    lines(x,y,...)
### 3b.8) Plot Missings    # only with data-type plotting
### ----
  }
### 4) Postprocessing: create dependent subplotting
### 5) if( ! aspanel ) replot(plot=match.call(),add=TRUE)
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  
### 7) return(invisible(replot(plot=FALSE))) 
  return(invisible(replot(plot=FALSE)))
}




lines.aplus <- function(x,...,steps=30,aspanel=FALSE) {
  X <- oneOrDataset(x)
  if( ncol(X) > 2 ) {
    infkt <- function(x,y,...) {
      lines.aplus(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],...,aspanel=TRUE)
    }
    gsi.add2pairs(sapply(1:NCOL(X),gsi.mapin01),infkt,...)
  } else {
    Y <- X[-1,,drop=FALSE]
    X <- X[-nrow(X),,drop=FALSE]
    l   <- rep((0:steps)/steps,NROW(X))
    i   <- rep(1:NROW(X),each=steps+1)
    XP  <- unclass(iltInv((1-l)*ilt(X[i,,drop=FALSE]) + l*ilt(Y[i,,drop=FALSE])))
    x <- XP[,1]
    y <- XP[,2]
    lines(x,y,...)
  }
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  
}

lines.rplus <- function(x,...,steps=30,aspanel=FALSE) {
  X <- oneOrDataset(x)
  if( !aspanel && any( !is.finite(X)|x<0) ) {
    # Remove out of box problems
    X[is.BDL(x)]<-0.00000000001
    Xa <- X[-nrow(X),,drop=FALSE]
    Xb <- X[-1,,drop=FALSE]
    Xd <- Xb-Xa
    nm <- apply(is.NMV(Xa),1,all)&apply(is.NMV(Xb),1,all) 
    XaOk <-nm & apply(Xa>=0,1,all)
    XbOk <-nm & apply(Xb>=0,1,all)
    nm <- nm | (!XaOk & !XbOk)
    if( any(ra <- !XaOk & nm ) ) {
      delta <- apply(Xb[ra,,drop=FALSE]/-Xd[ra,,drop=FALSE],2,function(x) min(x[x>0]))
      Xa[ra,] <- Xb[ra,]-Xd[ra,]*delta
    }
    if( any(rb <- !XbOk & nm ) ) {
      delta <- apply(Xa[rb,,drop=FALSE]/Xd[rb,,drop=FALSE],2,function(x) min(x[x>0]))
      Xb[rb,] <- Xb[rb,]-Xd[rb,]*delta
    }
    Xa[!nm,]<-NA
    Xb[!nm,]<-NA
    LNK <- apply(Xa[-1,]==Xb[-nrow(Xb),],1,all)
    PAD <- !is.finite(LNK)
    LNK <- ifelse(is.finite(LNK),LNK,FALSE)
    padLNK <- apply(!is.finite(Xa[-1,])&!is.finite(Xb[-nrow(Xb),]),1,all)
    Redundant <- LNK | padLNK
    # Problem: Not LNK and NOT PAD would require extra pad
    gp <- rbind(c(TRUE,!Redundant),TRUE,
                c(!LNK & apply(is.finite(Xb[-nrow(Xb),])&is.finite(Xb[-nrow(Xb),]),1,all) ,FALSE))
    X<-t(gsi.mystructure(t(cbind(Xa,Xb,Xb*NA)),dim=c(ncol(Xb),3*nrow(Xb))))[c(gp),,drop=FALSE]
  }
  if( ncol(X) > 2 ) {
    infkt <- function(x,y,...) {
      lines.rplus(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],...,aspanel=TRUE)
    }
    gsi.add2pairs(sapply(1:NCOL(X),gsi.mapin01),infkt,...)
  } else {
    Y <- X[-1,,drop=FALSE]
    X <- X[-nrow(X),,drop=FALSE]
    l   <- rep((0:steps)/steps,NROW(X))
    i   <- rep(1:NROW(X),each=steps+1)
    XP  <- unclass(iitInv((1-l)*iit(X[i,,drop=FALSE]) + l*iit(Y[i,,drop=FALSE])))
    x <- XP[,1]
    y <- XP[,2]
    lines(x,y,...)
  }
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  
}

lines.rmult <- function(x,...,steps=30,aspanel=FALSE) {
  X <- oneOrDataset(x)
  if( ncol(X) > 2 ) {
    infkt <- function(x,y,...) {
      lines.rmult(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],...,aspanel=TRUE)
    }
    gsi.add2pairs(sapply(1:NCOL(X),gsi.mapin01),infkt,...)
  } else {
    Y <- X[-1,,drop=FALSE]
    X <- X[-nrow(X),,drop=FALSE]
    l   <- rep((0:steps)/steps,NROW(X))
    i   <- rep(1:NROW(X),each=steps+1)
    XP  <- (1-l)*unclass(X)[i,,drop=FALSE] + l*unclass(Y)[i,,drop=FALSE]
    x <- XP[,1]
    y <- XP[,2]
    lines(x,y,...)
  }
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  
}

segments <- function(x0,...) UseMethod("segments",x0)
segments.default <- function(x0, ...) graphics::segments(x0, ...) 

segments.acomp <- function(x0,y1,...,steps=30,aspanel=FALSE) {
  y = y1
#### Plot Function Paradigma
####  simplified for pure adding (with panels):
### 1) Prepare the parameters
### 2) -
### 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
  if( !aspanel && gsi.getD(x0) > 3 ) {
### 3a) Set up gsi.pairs
### 3a.1) Store original data in environment
    x0Store<-x0
    yStore <-y
### 3a.2) Define an infkt
    infkt <- function(x,y,...) {
      segments.acomp(x0=x0Store,y1=yStore,...,steps=steps,aspanel=TRUE)
    }
### 3a.3) gsi.add2pairs
    nc <- gsi.getCoorInfo()$nc 
    gsi.add2pairs(sapply(1:nc,gsi.mapin01),infkt,...) 
   } else {
### 3b) Plot directly
### 3b.1) --
### 3b.2) Transform data
    Xs <- oneOrDataset(gsi.pltTrafo(x0,"data"))
    Xe <- oneOrDataset(gsi.pltTrafo(y,"data"))
### 3b.3) prepare plotting
    s60 <- sin(pi/3)
    c60 <- cos(pi/3)
### 3b.4) --
### 3b.5) -- 
### 3b.6) Analyse Missings
    ## Unclear
    Xsm <- !apply(is.NMV(Xs),1,all)
    Xem <- !apply(is.NMV(Xe),1,all)
    if(any(Xsm)) Xs[Xsm,]<-NA
    if(any(Xem)) Xe[Xem,]<-NA
### 3b.7) Plot Nonmissings
    l   <- rep(c((0:steps)/steps,NA),NROW(Xs))
    i   <- rep(1:NROW(Xs),each=steps+2)
    XP  <- unclass(ilrInv((1-l)*ilr(Xs[i,]) + l*ilr(Xe[i,])))
    #print(XP)
    x <- XP[,2]+XP[,3]*c60
    y <- XP[,3]*s60
    lines(x,y,...)
### 3b.8) Plot Missings    # only with data-type plotting
    ## geometry type plotting
  }
### 4) Postprocessing: create dependent subplotting
  ## --
### 5) if( ! aspanel ) replot(plot=match.call(),add=TRUE)
  if( ! aspanel ) replot(plot=match.call(),add=TRUE)
### 7) return(invisible(replot(plot=FALSE))) 
  return(invisible(replot(plot=FALSE)))
}


segments.rcomp <- function(x0,y1,...,steps=30,aspanel=FALSE) {
  y = y1
### 1) Prepare the parameters
### 2) -
### 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
  if( !aspanel && gsi.getD(x0) > 3 ) {
### 3a) Set up gsi.pairs
### 3a.1) Store original data in environment
    x0Store<-x0
    yStore <-y
### 3a.2) Define an infkt
    infkt <- function(x,y,...) {
      segments.rcomp(
                     x0=x0Store,y1=yStore,
                                 ...,steps=steps,aspanel=TRUE)
    }
### 3a.3) gsi.add2pairs
    nc <- gsi.getCoorInfo()$nc
    gsi.add2pairs(sapply(1:nc,gsi.mapin01),infkt,...)
  } else {
### 3b) Plot directly
### 3b.1) --
### 3b.2) Transform data
    Xs <- oneOrDataset(gsi.pltTrafo(x0,"data"))
    Xe <- oneOrDataset(gsi.pltTrafo(y,"data"))
### 3b.3) prepare plotting
    s60 <- sin(pi/3)
    c60 <- cos(pi/3)
### 3b.4) --
### 3b.5) -- 
### 3b.6) Analyse Missings
    ## remove those data points with BDL (in the future, maybe a flag allows to zeroreplace them)
    Xsm <- !apply(!is.BDL(Xs),1,all)
    Xem <- !apply(!is.BDL(Xe),1,all)
    if(any(Xsm)) Xs[Xsm,]<-0
    if(any(Xem)) Xe[Xem,]<-0
    ## remove those data points with Missings
    Xsm <- !apply(is.NMV(Xs)|is.BDL(Xs),1,all)
    Xem <- !apply(is.NMV(Xe)|is.BDL(Xe),1,all)
    if(any(Xsm)) Xs[Xsm,]<-NA
    if(any(Xem)) Xe[Xem,]<-NA
### 3b.7) Plot Nonmissings
    l   <- rep(c((0:steps)/steps,NA),NROW(Xs))
    i   <- rep(1:NROW(Xs),each=steps+2)
    XP  <- unclass(convex.rcomp(Xs[i,],Xe[i,],l))
    x <- XP[,2]+XP[,3]*c60
    y <- XP[,3]*s60
    lines(x,y,...)
### 3b.8) Plot Missings    # only with data-type plotting
    ## -- geometry type plot
  }
### 4) Postprocessing: create dependent subplotting
  ##--
### 5) if( ! aspanel ) replot(plot=match.call(),add=TRUE)
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  
### 7) return(invisible(replot(plot=FALSE))) 
  return(invisible(replot(plot=FALSE)))
}





segments.aplus <- function(x0,y1,...,steps=30,aspanel=FALSE) {
  y = y1
  X <- oneOrDataset(x0,y)
  Y <- oneOrDataset(y,x0)
  if( ncol(X) > 2 ) {
    infkt <- function(x,y,...) {
      segments.aplus(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],
                     Y[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],...,aspanel=TRUE)
    }
    gsi.add2pairs(sapply(1:NCOL(X),gsi.mapin01),infkt,...)
  } else {
    l   <- rep(c((0:steps)/steps,NA),NROW(X))
    i   <- rep(1:NROW(X),each=steps+2)
    XP  <- unclass(iltInv((1-l)*ilt(X[i,]) + l*ilt(Y[i,])))
    x <- XP[,1]
    y <- XP[,2]
    lines(x,y,...)
  }
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  
}

segments.rplus <- function(x0,y1,...,steps=30,aspanel=FALSE) {
  y = y1
  X <- oneOrDataset(x0,y)
  Y <- oneOrDataset(y,x0)
  if( ncol(X) > 2 ) {
    infkt <- function(x,y,...) {
      segments.rplus(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],
                     Y[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],...,aspanel=TRUE)
    }
    gsi.add2pairs(sapply(1:NCOL(X),gsi.mapin01),infkt,...)
  } else {
    l   <- rep(c((0:steps)/steps,NA),NROW(X))
    i   <- rep(1:NROW(X),each=steps+2)
    XP  <- unclass(iitInv((1-l)*iit(X[i,]) + l*iit(Y[i,])))
    x <- XP[,1]
    y <- XP[,2]
    lines(x,y,...)
  }
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  

}

segments.rmult <- function(x0,y1,...,steps=30,aspanel=FALSE) {
  y = y1
  X <- oneOrDataset(x0,y)
  Y <- oneOrDataset(y,x0)
  if( ncol(X) > 2 ) {
    infkt <- function(x,y,...) {
      segments.rmult(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],
                     Y[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))],...,aspanel=TRUE)
    }
    gsi.add2pairs(sapply(1:NCOL(X),gsi.mapin01),infkt,...)
  } else {
    l   <- rep(c((0:steps)/steps,NA),NROW(X))
    i   <- rep(1:NROW(X),each=steps+2)
    XP  <- (1-l)*unclass(X)[i,] + l*unclass(Y)[i,]
    x <- XP[,1]
    y <- XP[,2]
    lines(x,y,...)
  }
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  

}



gsi.closespread <- function(spread) {
  if(length(dim(spread))>3) {
    return(apply(spread,1,gsi.closespread))
  }
  d <- nrow(spread)
  Pmat <- diag(d)-1/d
  row.names(Pmat)<-row.names(spread)
  Pmat %*% spread %*% t(Pmat)
}

gsi.spreadToIsoSpace <- function(spread) {
  if(length(dim(spread))>3) {
    return(apply(spread,1,gsi.closespread))
  }
  d <- nrow(spread)
  V <- ilrBase(D=d)
  t(V) %*% spread %*% V
}

ellipses <- function(mean,...) UseMethod("ellipses",mean)



#ellipses.rcomp <- function(mean,var,r=1,...,steps=360,thinRatio=1/100) {
#mean <- oneOrDataset(ipt(mean))
#sp <- var
#w  <- seq(0,2*pi,length.out=steps)
#for(i in 1:nrow(mean)) {
#    if( length(dim(var))==3 )
#      sp<-var[i,,]
#    isp <- gsi.spreadToIsoSpace(sp)
#    mi <- mean[i,]
#    eisp <- eigen(isp,TRUE)
#    MEV <- eisp$values[1]
#    NE  <- max(sum(eisp$values>MEV*thinRatio),2)
#    X<-NULL
#    for(r1 in 1:(NE-1))
#      for(r2 in (r1+1):NE) {
#        X <- rbind(X,t(mi+ t(sqrt(eisp$values[1])*r*cos(w) %o% eisp$vectors[,1] +
#             sqrt(eisp$values[2])*r*sin(w) %o% eisp$vectors[,2])),NA)
#      }
#    lines.rcomp(uciptInv(X),...)
#  }
#}

#ellipses.rplus <- function(mean,var,r=1,...,steps=360,thinRatio=1/100) {
#mean <- oneOrDataset(iit(mean))
#sp <- var
#w  <- seq(0,2*pi,length.out=steps)
#for(i in 1:nrow(mean)) {
#    if( length(dim(var))==3 )
#      sp<-var[i,,]
##    isp <- gsi.spreadToIsoSpace(sp)
#    mi <- mean[i,]
#    eisp <- eigen(sp,TRUE)
#    MEV <- eisp$values[1]
#    NE  <- max(sum(eisp$values>MEV*thinRatio),2)
#    X<-NULL
#    for(r1 in 1:(NE-1))
#      for(r2 in (r1+1):NE) {
#        X <- rbind(X,t(mi+ t(sqrt(eisp$values[1])*r*cos(w) %o% eisp$vectors[,1] +
#                     sqrt(eisp$values[2])*r*sin(w) %o% eisp$vectors[,2])),NA)
#      }
#    lines.rmult(X,...)
#  }
#}



#ellipses.rmult <- function(mean,var,r=1,...,steps=360,thinRatio=1/100) {
#mean <- oneOrDataset(mean)
#sp <- var
#w  <- seq(0,2*pi,length.out=steps)
#for(i in 1:nrow(mean)) {
#  if( length(dim(var))==3 )
#    sp<-var[i,,]
#  mi <- mean[i,]
#  eisp <- eigen(sp,TRUE)
#  MEV <- eisp$values[1]
#  NE  <- max(sum(eisp$values>MEV*thinRatio),2)
#  X<-NULL
#  for(r1 in 1:(NE-1))
#    for(r2 in (r1+1):NE) {
#      X <- rbind(X,t(mi+ t(sqrt(eisp$values[r1])*r*cos(w) %o% eisp$vectors[,r1] +
#                           sqrt(eisp$values[r2])*r*sin(w) %o% eisp$vectors[,r2])),NA)
#    }
#  lines.rmult(X,...)
#}
#}
# var given as idt!!! --->>> This gives some failures: var given better as clr:
gsi.DrawCompEllipses = function(mean,var,r,steps=72,...) {
  # mean and variance in clr/cpt
  ei   <- eigen(clrvar2ilr(var),symmetric=TRUE)
  w <- seq(0,2*pi,length.out=steps+1)
  sw<-sin(w)
  cw<-cos(w)
  if( min(ei$values) / max(ei$values) < -1E-8) {
    warning("Non positive Semidefinite Matrix used in Ellipses")
    print(list(problem="Non positive Semidefinite Matrix used in Ellipses",var=var,eigen=ei))
  }
  rs <- sqrt(abs(ei$values))*r
 # Loop over ellipse centers
  meFull <- oneOrDataset(idt(mean))
  if(length(dim(meFull))==0) dim(meFull) = c(1, length(meFull))
  
  for(k in 1:nrow(meFull) ) {
    # me   <- gsi.mystructure(meFull[k,],class="rmult")
    me   <- meFull[k,]
    aux = cbind(me[1]+rs[1]*ei$vectors[1,1]*sw+rs[2]*ei$vectors[1,2]*cw,
                me[2]+rs[1]*ei$vectors[2,1]*sw+rs[2]*ei$vectors[2,2]*cw
    )
    X <- idtInv(aux, orig=mean, V=ilrBase(D=ncol(oneOrDataset(mean))))
    noreplot(lines(gsi.mystructure(X,trafoed=TRUE),...,aspanel=TRUE))
  }
}




gsi.ellipsesCompPanel <- function(i,j,margin,mean,var,r=1,...,steps=72) {
  va <- gsi.pltTrafo(var, what="var", geo=class(mean))
  me <- gsi.pltTrafo(mean, what="data", geo=class(mean))
  gsi.DrawCompEllipses(gsi.mystructure(me,class=class(mean)),va,r,steps=steps,...)
}


ellipses.rcomp <- ellipses.acomp <- function(mean,var,r=1,...,steps=72,thinRatio=NULL,aspanel=FALSE) {
### 1) Prepare the parameters
### 2) -
### 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
  if( !aspanel && gsi.getD(mean) > 3 ) {
    if( is.null(thinRatio) ) {
### 3a) Set up gsi.pairs
### 3a.1) Store original data in environment 
### 3a.2) Define an infkt
      infkt <- function(x,y,...) {
      gsi.ellipsesCompPanel(mean,var,r,...)
    }
### 3a.3) gsi.add2pairs
      nc <- gsi.getCoorInfo()$nc 
      gsi.add2pairs(sapply(1:nc,gsi.mapin01),infkt,...,mean=mean,var=var,r=r,steps=steps,thinRatio=thinRatio)
    }
  } else {
### 3b) Plot directly
    if( is.null(thinRatio) ) {
      gsi.DrawCompEllipses(mean,var,r=r,steps=steps,...)
### Includes:
### 3b.1) --
### 3b.2) Transform data
### 3b.3) prepare plotting
### 3b.4) --
### 3b.5) -- 
### 3b.6) Analyse Missings 
### 3b.7) Plot Nonmissings
### 3b.8) Plot Missings    # only with data-type plotting
    }
  }
### 4) Postprocessing: create dependent subplotting
  if( !is.null(thinRatio) ) {
    meFull <- oneOrDataset(idt(mean))
    if(length(dim(meFull))==0) dim(meFull) = c(1, length(meFull))
    
    sp <- var
    w  <- seq(0,2*pi,length.out=steps)
    for(i in 1:nrow(meFull)) {
      if( length(dim(var))==3 )
        sp<-var[i,,]
      isp <- gsi.spreadToIsoSpace(sp)
      mi <- meFull[i,]
      eisp <- eigen(isp,TRUE)
      MEV <- eisp$values[1]
      NE  <- max(sum(eisp$values>MEV*thinRatio),2)
      X<-mi
#      X<-mi
      for(r1 in 1:(NE-1))
        for(r2 in (r1+1):NE) {
#           X <- rbind(X,t(mi + t(sqrt(eisp$values[r1])*r*cos(w) %o% eisp$vectors[,r1] +
#                                 sqrt(eisp$values[r2])*r*sin(w) %o% eisp$vectors[,r2])),NA)
            X <- rbind(X,
                         t(mi + t(sqrt(eisp$values[r1])*r*cos(w) %o% eisp$vectors[,r1] +
                           sqrt(eisp$values[r2])*r*sin(w) %o% eisp$vectors[,r2])), mi)
        }
      if( inherits(mean, "rcomp"))
        noreplot(lines.rcomp(uciptInv(X),...))
      else
        noreplot(lines(ilrInv(X),...))
    }
  }
### 5) if( ! aspanel ) replot(plot=match.call(),add=TRUE)
  replot(plot=match.call(),add=TRUE)  
### 7) return(invisible(replot(plot=FALSE))) 
  return(invisible(replot(plot=FALSE)))
}



gsi.ellipsesRealPanel <- function(i,j,mean,var,r=1,...,steps=72) {
  # Preparation
  va   <- var[c(i,j),c(i,j)]
  ei   <- eigen(va)
  w <- seq(0,2*pi,length.out=steps+1)
  # Loop over ellipse centers
  meFull <- unclass(oneOrDataset(cdt(mean)))
  if(length(dim(meFull))==0) dim(meFull) = c(1, length(meFull))
  for(k in 1:nrow(meFull) ) {
    me   <- meFull[k,c(i,j)]
    rs <- sqrt(ei$values)*r
    X <- cdtInv(cbind(me[1]+rs[1]*ei$vectors[1,1]*sin(w)+rs[2]*ei$vectors[1,2]*cos(w),
                      me[2]+rs[1]*ei$vectors[2,1]*sin(w)+rs[2]*ei$vectors[2,2]*cos(w)
                      ),mean)
    if( inherits(mean, "rplus" )) {
      noreplot(lines(gsi.mystructure(X,class="rplus"),...))
    } else noreplot(lines(X,...))
  }
}



ellipses.rmult<-ellipses.rplus<-ellipses.aplus <- function(mean,var,r=1,...,steps=72,thinRatio=NULL) {
    if( is.null(thinRatio) ) {
      if( gsi.getD(mean) > 2 ) {
        # Plot BigEllipse via panel
        infkt <- function(x,y,...) {
          gsi.ellipsesRealPanel(gsi.mapfrom01(x),gsi.mapfrom01(y),...)
        }
        gsi.add2pairs(sapply(1:gsi.getD(mean),gsi.mapin01),infkt,...,mean=mean,var=var,r=r,steps=steps)
      } else {
        # Plot BigEllipse directly
        gsi.ellipsesRealPanel(1,2,mean=mean,var=var,r=r,steps=steps,...)
      }
    } else {
      # Plot SmallEllipses directly
      meFull <- oneOrDataset(idt(mean))
      if(length(dim(meFull))==0) dim(meFull) = c(1, length(meFull))
      sp <- var
      w  <- seq(0,2*pi,length.out=steps)
      for(i in 1:nrow(meFull)) {
        if( length(dim(var))==3 )
          sp<-var[i,,]
                                        # isp <- gsi.spreadToIsoSpace(sp)
        mi <-meFull[i,]
###############
        eisp <- eigen(sp,TRUE)
        MEV <- eisp$values[1]
        NE  <- max(sum(eisp$values>MEV*thinRatio),2)
        X<-NULL
        for(r1 in 1:(NE-1))
          for(r2 in (r1+1):NE) {
            X <- rbind(t(mi + t(sqrt(eisp$values[r1])*r*cos(w) %o% eisp$vectors[,r1] +
                                  sqrt(eisp$values[r2])*r*sin(w) %o% eisp$vectors[,r2])))
         #   X <- rbind(X,t(mi + t(sqrt(eisp$values[r1])*r*cos(w) %o% eisp$vectors[,r1] +
         #                    sqrt(eisp$values[r2])*r*sin(w) %o% eisp$vectors[,r2])),NA)
            noreplot(lines(idtInv(X,mean),...))
          }
         # noreplot(lines(idtInv(X,mean),...))
      }
    }
    replot(plot=match.call(),add=TRUE)  

}




straight  <- function(x,...) UseMethod("straight",x)

#
# straight.acomp deals with partially missing directions by using
# a early transformation scheme 
#

#
# straight.rcomp deals with incompatible projections by using a
# late projection scheme
#

straight.acomp <- function(x,d,...,steps=30,aspanel=FALSE) {
### 1) Prepare the parameters
### 2) -
### 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
  if( !aspanel && gsi.getD(x) > 3 ) {
### 3a) Set up gsi.pairs
### 3a.1) Store original data in environment
    X<-x
    D<-d
### 3a.2) Define an infkt
    infkt <- function(x,y,...) {
      straight.acomp(x=X,d=D,
                     ...,steps=steps,aspanel=TRUE)
    }
### 3a.3) gsi.add2pairs
    nc <- gsi.getCoorInfo()$nc 

    gsi.add2pairs(sapply(1:nc,gsi.mapin01),infkt,...)
  } else {
### 3b) Plot directly
### 3b.1) --
### 3b.2) Transform data
    X <- oneOrDataset(gsi.pltTrafo(x,"data"),d)
    D <- oneOrDataset(gsi.pltTrafo(d,"direction"),x)
### 3b.3) prepare plotting
    s60 <- sin(pi/3)
    c60 <- cos(pi/3)
### 3b.4) --
### 3b.5) -- 
### 3b.6) Analyse Missings
    Xm <- !apply(is.NMV(X),1,all)
    Dm <- !apply(is.NMV(D),1,all)
    if(any(Xm)) X[Xm,]<-NA
    if(any(Dm)) D[Dm,]<-NA
    
### 3b.7) Plot Nonmissings
    D <- normalize(acomp(D)) 
    X <- perturbe(X,power.acomp(D,-scalar(acomp(X),acomp(D)))) 
    l   <- rep(2*c((0:steps)/steps,NA)-1,NROW(X))
    i   <- rep(1:NROW(X),each=steps+2)
    XP  <- acomp(clrInv(clr(X[i,]) + (2*l)^3*clr(D[i,])))
    x <- XP[,2]+XP[,3]*c60
    y <- XP[,3]*s60
    lines(x,y,...)
### 3b.8) Plot Missings    # only with data-type plotting
  }
### 4) Postprocessing: create dependent subplotting
### 5) if( ! aspanel ) replot(plot=match.call(),add=TRUE)
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  
### 7) return(invisible(replot(plot=FALSE))) 
  return(invisible(replot(plot=FALSE)))
}

straight.aplus <- function(x,d,...,steps=30,aspanel=FALSE) {
  X <- oneOrDataset(x,d)
  d <- oneOrDataset(d,x)
  if( ncol(X) > 2 ) {
    infkt <- function(x,y,...) {
      straight.aplus(
                     aplus(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))]),
                     aplus(d[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))]),
                                 ...,steps=steps,aspanel=TRUE)
    }
    gsi.add2pairs(sapply(1:NCOL(X),gsi.mapin01),infkt,...)
  } else {
    s <- log(d[,2])/log(d[,1])
#  if( par("xlog") && par("ylog") )
#    abline(exp(log(x[,2])-log(x[,1])/s),s,untf=FALSE,...)
#  else {
    l   <- rep(2*c((0:steps)/steps,NA)-1,NROW(X))
    i   <- rep(1:NROW(X),each=steps+2)
    r   <- par("usr")
    if( ! par("xlog") ) r[1:2] <- log(c(r[2]/100,r[2]))
    if( ! par("ylog") ) r[3:4] <- log(c(r[4]/100,r[4]))
    r   <- abs(r[2]-r[1])+abs(r[4]-r[3])
    XP  <- aplus(X[i,]) + r*l*normalize(aplus(d[i,]))
    noreplot(lines.rmult(XP,...)) # lines.aplus(XP,...) produced double lines
                                        #    warning("straight.aplus not yet implemented in nonlog coordinates");
                                        #  }
  }
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  

}


straight.rcomp <- function(x,d,...,steps=30,aspanel=FALSE) {
### 1) Prepare the parameters
### 2) -
### 3) if( !aspanel && ncol>3 ) Set up gsi.pairs else plot directly
  if( !aspanel && gsi.getD(x) > 3 ) {
### 3a) Set up gsi.pairs
### 3a.1) Store original data in environment
    X<-x
    D<-d
### 3a.2) Define an infkt
    infkt <- function(x,y,...) {
      straight.rcomp(x=X,d=D,...,steps=steps,aspanel=TRUE)
    }
### 3a.3) gsi.add2pairs
    nc <- gsi.getCoorInfo()$nc 
    gsi.add2pairs(sapply(1:nc,gsi.mapin01),infkt,...)
  } else { 
### 3b) Plot directly
    X <- oneOrDataset(x,d)
    d <- oneOrDataset(d,x)
    l1 <- apply(-X/d,1,function(x) {max(x[x<=0])})*0.99999 
    l2 <- apply(-X/d,1,function(x) {min(x[x>=0])})*0.99999
    X1 <- rcomp(rmult(X)+(l1*rmult(d))) 
    X2 <- rcomp(rmult(X)+(l2*rmult(d)))
    segments.rcomp(X1,X2,...,aspanel=TRUE) ## noreplot < aspanel
### Includes:
### 3b.1) --
### 3b.2) Transform data
### 3b.3) prepare plotting
### 3b.4) --
### 3b.5) -- 
### 3b.6) Analyse Missings 
### 3b.7) Plot Nonmissings
### 3b.8) Plot Missings    # only with data-type plotting
  }
### 4) Postprocessing: create dependent subplotting
### 5) if( ! aspanel ) replot(plot=match.call(),add=TRUE)
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  
### 7) return(invisible(replot(plot=FALSE))) 
  return(invisible(replot(plot=FALSE)))
}




#straight.rplus <- function(x,d,...,steps=30) {
#  x <- oneOrDataset(x,d)
#  d <- oneOrDataset(d,x)
#  s <- d[,2]/d[,1]
#  abline(x[,2]-x[,1]/s,s,untf=TRUE)
#  l1 <- apply(-x/d,1,function(x) {max(c(-100,x[x<=0]))}) 
#  l2 <- apply(-x/d,1,function(x) {min(c(100,x[x>=0]))})
#  X1 <- rcomp(gsi.add(x,gsi.mul(l1,d))) 
#  X2 <- rcomp(gsi.add(x,gsi.mul(l2,d)))
#  segments.rplus(X1,X2,...)
#}

straight.rplus <- function(x,d,...,steps=30,aspanel=FALSE) {
  X <- oneOrDataset(x,d)
  d <- oneOrDataset(d,x)
  if( ncol(X) > 2 ) {
    infkt <- function(x,y,...) {
      straight.rplus(
                     rplus(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))]),
                     rmult(d[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))]),
                                 ...,steps=steps,aspanel=FALSE)
    }
    gsi.add2pairs(sapply(1:NCOL(X),gsi.mapin01),infkt,...)
  } else {  
    #s <- log(d[,2])/log(d[,1])
                                        #  if( par("xlog") && par("ylog") )
                                        #    abline(exp(log(x[,2])-log(x[,1])/s),s,untf=FALSE,...)
                                        #  else {
    l   <- rep(2*c((0:steps)/steps,NA)-1,NROW(X))
    i   <- rep(1:NROW(X),each=steps+2)
    r   <- par("usr")
    if( par("xlog") ) r[1:2] <- 10^(r[1:2])
    if( par("ylog") ) r[3:4] <- 10^(r[3:4])
    r   <- abs(r[2]-r[1])+abs(r[4]-r[3])
    XP  <- rmult(X[i,]) + r*l*normalize(rmult(d[i,]))
    noreplot(lines.rmult(XP,...))
  }
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  

}

straight.rmult <- function(x,d,...,steps=30,aspanel=FALSE) {
  X <- oneOrDataset(x,d)
  d <- oneOrDataset(d,x)
  if( ncol(X) > 2 ) {
    infkt <- function(x,y,...) {
      straight.rmult(
                     aplus(X[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))]),
                     aplus(d[,c(gsi.mapfrom01(x),gsi.mapfrom01(y))]),
                                 ...,steps=steps,aspanel=TRUE)
    }
    gsi.add2pairs(sapply(1:NCOL(X),gsi.mapin01),infkt,...)
  } else {  
    #s <- log(d[,2])/log(d[,1])
                                        #  if( par("xlog") && par("ylog") )
                                        #    abline(exp(log(x[,2])-log(x[,1])/s),s,untf=FALSE,...)
#  else {
    l   <- rep(2*c((0:steps)/steps,NA)-1,NROW(X))
    i   <- rep(1:NROW(X),each=steps+2)
    r   <- par("usr")
    if( par("xlog") ) r[1:2] <- 10^(r[1:2])
    if( par("ylog") ) r[3:4] <- 10^(r[3:4])
    r   <- abs(r[2]-r[1])+abs(r[4]-r[3])
    XP  <- rmult(X[i,]) + r*l*normalize(rmult(d[i,]))
    noreplot(lines.rmult(XP,...))
                                        #    warning("straight.aplus not yet implemented in nonlog coordinates");
                                        #  }
  }
  if( !aspanel ) replot(plot=match.call(),add=TRUE)  

}


#straight.panel.acomp <- function(x,d,...,steps=30) {
#  function(what,...) {
#    if( !is.null(colnames(what)) )
#      what <- colnames(what)
#    x <- margin(x,what)
#    d <- margin(d,what)
#    straight.acomp(x,d,...,steps=steps)
#  }
#}

#straight.panel.rcomp <- function(x,d,...,steps=30) {
#  function(what,...) {
#    if( !is.null(colnames(what)) )
#      what <- colnames(what)
#    x <- margin(x,what)
#    d <- margin(d,what)
#    straight.rcomp(x,d,...,steps=steps)
#  }
#}

dDirichlet <- function(x, alpha, log=FALSE, measure="Lebesgue"){
  # ensure the data are converted to (row)matrices
  alpha = unclass(oneOrDataset(alpha, B = if(length(x)>length(alpha)){x} ))
  x = unclass(oneOrDataset(x, B = if(length(x)<length(alpha)){alpha} ))
  if(is.null(dim(alpha))) dim(alpha) = dim(x)
  if(is.null(dim(x))) dim(x) = dim(alpha)
  # are the points within the simplex?
  x0 = rowSums(x)
  inside = abs(x0-1)<1e-12 & apply(x>=0,1,all)
  # compute closing constant
  a0 = rowSums(alpha)
  logmultibeta = rowSums(lgamma(alpha)) - lgamma(a0)
  # process reference measure
  if(is.character(measure)){
    k = pmatch(tolower(measure), c("aitchison","lebesgue"))-1
    if(is.na(k)) stop("dDirichlet: `measure` needs to be a string or a function, see ?dDirichlet")
  }else if(is.function(measure)){
    k = 0
    m = apply(x,1,measure)
    logmultibeta = logmultibeta + m
  }else stop("dDirichlet: `measure` needs to be a string or a function, see ?dDirichlet")
  # compute density
  # attention: here are x and alpha transposed so that recycling happens in the right way
  D = ncol(x)
  logdens = sapply(1:D, function(i) log(x[,i])*(alpha[,i]-k)) %*% rep(1,D) - logmultibeta
  logdens = ifelse(inside, logdens, -Inf)
  if(log) return(logdens)
  return(exp(logdens))
}

rDirichlet.acomp <- function(n,alpha) {
  acomp(sapply(alpha,rgamma,n=n))
}

rDirichlet.rcomp <- function(n,alpha) {
  rcomp(sapply(alpha,rgamma,n=n))
}

rpois.ccomp <- function(n,p,lambda) {
  if( missing(p) ) {
    L <- lambda
    if( missing(n) )
      n <- nrow(rplus(lambda))
  } else {
    L <- rplus(rcomp(p))*lambda
    if( missing(n) )
      n <- max(nrow(p),length(lambda))
  }
  if( length(dim(L)) == 2 ) 
    L <- L[ ((1:n)-1) %% nrow(L) +1,]
  else
    L <- t(gsi.mystructure(rep(L,n),dim=c(length(L),n)))
  ccomp(gsi.mystructure(rpois(length(L),c(L)),dim=dim(L)))
}

rmultinom.ccomp <- function(n,p,N) {
  if( missing(n) )
    n <- max(nrow(p),length(N))
  erg <- matrix(0,ncol=gsi.getD(p),nrow=n)
  if( length(dim(p))> 1) {
    for(i in 1:n) {
      erg[i,]<-rmultinom(1,N[(i-1)%%length(N)+1],p[i,])
    }
  } else {
    for(i in 1:n) {
      erg[i,]<-rmultinom(1,N[(i-1)%%length(N)+1],p)
    }
  }
  ccomp(erg)
}

runif.acomp <- function(n,D) rDirichlet.acomp(n,rep(1,D))
runif.rcomp <- function(n,D) rDirichlet.rcomp(n,rep(1,D))

rnorm.aplus <- function(n,mean,var) {
  D <- NCOL(oneOrDataset(mean))
  perturbe.aplus(iltInv(matrix(rnorm(n*length(mean)),ncol=D) %*% chol(var)),
                mean)
}

dnorm.aplus <- function(x,mean,var,withJacobian=FALSE) {
  x <- aplus(x)
  mean <- aplus(mean)
  w <- ilt(x-mean)
  D <- ncol(oneOrDataset(x))
  if( length(dim(w)) == 2 ) 
    u <- c(rep(1,ncol(w))%*%t((solve(var,t(w)))*t(w)))
  else
    u <- sum(solve(var,w)*w)
  k = 1
  if(withJacobian){
    warning("dnorm.aplus should be used for the multivariate normal in R+, that is without jacobian. For clarity, use better dlnorm.rplus if you are interested in the density of the lognormal model.")
    k = exp(-log(unclass(x)) %*% rep(1, D) ) 
  }
  k*exp(-u/2)/sqrt(2^D*pi^D*det(var))
}

dnorm.rmult <- function(x,mean,var) {
  w <- rmult(x)-rmult(mean)
  D <- gsi.getD(x)
  if( length(dim(w)) == 2 ) 
    u <- c(rep(1,ncol(w))%*%t((solve(var,t(w)))*t(w)))
  else
    u <- sum(solve(var,w)*w)
  exp(-u/2)/sqrt(2^D*pi^D*det(var))
}




#rnorm.acomp <- function(n,mean,var) {
#  D <- NCOL(oneOrDataset(mean))
#  perturbe(ilrInv(matrix(rnorm(n*(D-1)),ncol=D-1) %*%
#                         chol(clrvar2ilr(var))),
#                mean)
#}

rnorm.acomp <-function (n, mean, var){
    D <- gsi.getD(mean)-1
    erg <- perturbe(ilrInv(matrix(rnorm(n*D), ncol = D) %*% chol(clrvar2ilr(var))), mean)
    colnames(erg) <- colnames(oneOrDataset(mean))
    erg
}




dnorm.acomp <- function(x,mean,var,withJacobian=FALSE) {
  x <- acomp(x)
  mean <- acomp(mean)
  w <- ilr(x-mean)
  D <- ncol(oneOrDataset(x))
  if( length(dim(w)) == 2 ) 
    u <- c(rep(1,D-1)%*%t((solve(clrvar2ilr(var),t(w)))*t(w)))
  else
    u <- sum(solve(clrvar2ilr(var),w)*w)
  k = 1
  if(withJacobian){
    k = c(exp(-log(unclass(x)) %*% rep(1, D) ) )
  }
  k*exp(-u/2)/sqrt(2*pi*det(clrvar2ilr(var)))
}


rnorm.ccomp <- function(n,mean,var,lambda) {
  rpois.ccomp(n,rnorm.acomp(n,mean=mean,var=var),lambda)

}

rlnorm.rplus <- function(n,meanlog,varlog) {
  D <- NCOL(oneOrDataset(meanlog))
  erg<-rplus(perturbe.aplus(exp(matrix(rnorm(n*length(meanlog)),ncol=D) %*% chol(varlog)),
                exp(meanlog)))
  colnames(erg) <- colnames(oneOrDataset(mean))
  erg
}

dlnorm.rplus <- function(x,meanlog,varlog) {
  # 20161024: Bug in density (2*pi) -> (2*pi)^p corrected; 
  #  warning issued by Florian Pechon, florian.pechon@uclouvain.be
  xx <- oneOrDataset(x)
  w <- ilt(x)-meanlog
  if( length(dim(w)) == 2 ) {
    u <- c(rep(1,ncol(w))%*%t((solve(varlog,t(w)))*t(w)))
    v <- c(exp(log(xx) %*% rep(1,ncol(xx)))) 
    p <- ncol(w)
  }
  else {
    u <- solve(varlog,w)%*%w
    v <- prod(x)
    p <- length(w)
  }
  exp(-u/2)/sqrt((2*pi)^p*det(varlog))/v
}


rnorm.rplus <- function(n,mean,var) {
  D <- ncol(var)
  erg <- rplus(pmax(rmult(matrix(rnorm(n*D),ncol=D) %*% chol(var))+rmult(mean),0))
  colnames(erg) <- colnames(oneOrDataset(mean))
  erg
}

rnorm.rmult <- function(n,mean,var) {
  D <- ncol(var)
  erg<-rmult(matrix(rnorm(n*D),ncol=D) %*% chol(var))+rmult(mean)
  colnames(erg) <- colnames(oneOrDataset(mean))
  erg
}

rnorm.rcomp <- function(n,mean,var) {
  # 20161024: Bug in the dimensions of matrix(rnorm...), both must be ncol(var)-1
  #  warning issued by John Szumiloski <John.Szumiloski@bms.com>
  D <- ncol(var)-1
  erg<-rcomp(pmax(ilr2clr(matrix(rnorm(n*D),ncol=D) %*% chol(clrvar2ilr(var)))+rplus(rcomp(mean)),0))
  colnames(erg) <- colnames(oneOrDataset(mean))
  erg
}



gsi.plotmargin <- function(X,d,margin,what="data") {
  X <- oneOrDataset(X)
  if( margin=="rcomp" )
    rcompmargin(X,d=d,pos=3)
  else if( margin=="acomp" )
    acompmargin(X,d=d,pos=3)
  else {
    if( ! is.numeric(margin))
      margin <- match(margin,colnames(X))
    fest <- X[,margin,drop=FALSE]
    X    <- X[,-margin,drop=FALSE]
    acomp(cbind(X[,d,drop=FALSE],fest))
  }
}



gsi.pltTrafo <- function(X,what="data",coorinfo=gsi.getCoorInfo(),geo="acomp",...) {
  # Types: data, var, mfrow, names, mfrow, direction
  trafoed <- attr(X,"trafoed")
  if( !is.null(trafoed) && trafoed )
    return(X)
  d <- coorinfo$d             # what panel
  margin  <- coorinfo$margin   # margin type
  D       <- coorinfo$D        # Dimension from which to transform
  mean    <- coorinfo$mean     # mean 
  scale   <- coorinfo$scale    # scaling
  coorgeo <- coorinfo$geo      # The geometry of scaling
  if( coorgeo == "acomp")  {
    zeroCenter <- max(coorinfo$mean)==min(coorinfo$mean)
    noScale    <- scale==1
    noTrafo    <- noScale&& zeroCenter
  } else {noTrafo<-noScale<-zeroCenter<-TRUE}
  if( !(geo %in% c("acomp","rcomp") ))
    stop("gsi.pltTrafo: Unkown data geometry",geo)
  if( !(coorgeo %in% c("acomp","rcomp") ))
    stop("gsi.pltTrafo: Unkown plot geometry",coorgeo)
  if( !(what %in% c("data","var","direction","mfrow","names")))
    stop("gsi.pltTrafo: Unkown transformation type ",what)
    
  #if( class(geo)!= "acomp" ) return(UseMethod("gsi.pltTrafo",geo))
  ### Scaling and centering
  if( what== "mfrow") {
    if( coorgeo %in% c("acomp","rcomp") )
      return(rep(gsi.getD(X),2))
    else
      return(rep(gsi.getD(X)-1,2))
  }
  if( coorgeo == "acomp" ) {
    if( what == "data" ) {
      Xn <- scale*(acomp(X)-acomp(mean))
    } else if( what =="direction") {
      if( geo == "acomp") { 
        dir <- scale*acomp(X)
      } else if( geo =="rcomp" ) {
        if( ! noTrafo )
          warning("gsi.pltTrafo: rcomp direction in acomp geometry ")
        dir <- X
      }
    } else if( what=="var" ){
      if( geo=="acomp" )
        var <- scale^2*X
      else if( geo=="rcomp" ) {
        if( !noTrafo )
          warning("gsi.pltTrafo: ",geo," variance in acomp geometry ")
        var <- X
      } else stop("Unkown geometry",geo)
    } else if(what=="names") {
      nam <- X
    } else if(what=="info") {
      orig <- X
    } else stop("gsi.pltTrafo: unkown request")
  } else if( coorgeo == "rcomp" ) {
    if( what == "data" )
      Xn <- X # No centering or scaling !!!
    else if(what=="direction") {
      if( geo == "acomp") { 
        dir <- X
      } else if( geo =="rcomp" ) {
        dir <- X
      } else stop("unkown geometry of data")
    } else if( what == "var" ) {
      if( geo == "acomp" )
        var <- X
      else if( geo=="rcomp" ) {
        var <- X
      } else stop("unkown geometry of data")
    } else if(what=="names") {
      nam <- X
    } else stop("gsi.pltTrafo: unkown request")
  } else stop("gsi.pltTrafo: unkown geometry in plot")
  ####  Marginalisation
  # is marginalisation necessary? (are we in a panel?)
  if( is.null(d) ) {
    if( what == "data" ) {
      return(Xn)
    } else if( what == "var" ){
      return(var)
    } else if( what == "names"){
      return(nam)
    } else if( what=="direction") {
      return(dir)
    } else stop("gsi.pltTrafo: Unkown request")
  }
  # acomp margin
  if( margin == "acomp" ) {
    if( what == "data" ) {
      return(acompmargin(Xn,d=d,pos=3,what="data"))
    } else if(what == "direction") {
      if( geo == "acomp" )
        return(acompmargin(dir,d=d,pos=3,what="data"))
      else if( geo=="rcomp" ) {
        warning("Incompatible geometries in plot")
        return(unclass(dir)*NA)
      }
    } else if( what == "var" ) {
      if( geo!="acomp" )
        warning("pltTrafo: Can not correctly marginalise a rcomp-variance with acomp-margin")
      return(acompmargin(var,d=d,pos=3,what="var"))
    } else if(what =="names") {
      return( c(nam[d],"*") )
    } else stop("unkown transformation type")
  # rcomp margin
  } else if( margin== "rcomp" ) {
    if( what == "data" ) {
      return(rcompmargin(Xn,d=d,pos=3,what="data"))
    } else if( what=="direction") {
      if( geo=="rcomp" )
        return(cpt(rcompmargin(rcomp(unclass(dir)+1),d=d,pos=3)))
      else {
        warning("gsi.pltTrafo: Can not marginalise acomp direction with rcomp-marginals")
        return(rcompmargin(rcomp(dir*NA),d=d,pos=3))
      }
    } else if( what == "var" ) {
      if( geo!="rcomp" )
        warning("pltTrafo: Can not correctly marginalise an acomp-variance with rcomp-margins")
      return(rcompmargin(var,d=d,pos=3,what="var"))
    } else if(what =="names") {
      return( c(nam[d],"*") )
    } else stop("unkown transformation type")
  # single variable margin
  } else { 
    if( is.character(margin))
      margin <- match(margin,names(mean))
    if( what == "data" ) {
      Xn <- oneOrDataset(Xn)
      return( gsi.mystructure(clo(cbind(Xn[,-margin,drop=FALSE][,d,drop=FALSE],
                                  Xn[,margin])),class=class(X)))
    } else if(what=="direction") {
#      Xn <- oneOrDataset(Xn)
      Xn <- oneOrDataset(dir)
      return( cbind(Xn[,-margin,drop=FALSE][,d,drop=FALSE],Xn[,margin]))      
    } else if( what =="var" ) {
      if( geo=="rcomp")
        warning("Can not correctly marginalise a rcomp-variances to subcompositions")
      varmar = rbind(cbind(var[-margin,-margin][d,d],var[-margin,margin][d]),
                   cbind(t(var[margin,-margin][d]),var[margin,margin]))
      return(varmar)
    } else if(what =="names") {
      return( c(nam[-margin][d],nam[margin]) )
    } 
  }
}




gsi.isSingleRow <- function(X) {
  return( NROW(X) == 1 || NCOL(X) ==1 )
}




barplot.acomp <- function(height,...,legend.text=TRUE,beside=FALSE,total=1,plotMissings=TRUE,missingColor="red",missingPortion=0.01) {
  nmv <- is.NMV(oneOrDataset(height))
  if( is.null(total) ) {
    X <- oneOrDataset(gsi.plain(ifelse(nmv,height,0)))
  } else {
    X <- oneOrDataset(gsi.plain(rcomp(ifelse(nmv,height,0),total=total)))
  }
  if( plotMissings && missingPortion>0 ) {
    X <- oneOrDataset(ifelse(nmv,X,missingPortion))
  }
  if( !beside && gsi.isSingleRow(X) ) {
    erg <- barplot(t(rbind(X,0)),c(1,0),...,legend.text=legend.text,
            beside=beside)
    ht <- t(X)
    ergDelta <- (erg[2]-erg[1])
    erg <- erg[1]
  }
  else {
    erg <- barplot(ht<-t(X),rep(1,ncol(nmv)),...,legend.text=legend.text,beside=beside)
    ergDelta <- (erg[2]-erg[1])/2
    erg 
  }
  ergDelta<-0.5
  if( plotMissings && any(!nmv) ) {
    if( is.matrix(erg) ) {
      rect(erg[!nmv]-ergDelta,
           0,
           erg[!nmv]+ergDelta,
           t(ht)[!nmv],
           col=missingColor
           )
    } else {
      ergMat <- matrix(erg,nrow=nrow(X),ncol=ncol(X))
      htMat  <- t(apply(rbind(0,ht),2,cumsum))
                                        #recover()
      rect(ergMat[!nmv]-ergDelta,
           htMat[cbind(!nmv,FALSE)],
           ergMat[!nmv]+ergDelta,
           htMat[cbind(FALSE,!nmv)],
           col=missingColor
           )
    }                                  #segments(ergMat[!nmv]-ergDelta,
    #      htMat[!nmv],
    #      ergMat[!nmv]+ergDelta,
    #      htMat[!nmv],
    #      lwd=3,
    #      col=missingColor,pch="-")
  }
  replot(plot=match.call(),add=FALSE)  

  invisible(erg)
}
barplot.rcomp <- barplot.acomp
barplot.ccomp <- barplot.acomp
#barplot.rcomp <- function(height,...,legend.text=TRUE,beside=FALSE,total=1) {
#  X <- height
#  if( gsi.isSingleRow(X) )
#    barplot(t(rbind(gsi.plain(rcomp(X,total=total)),0)),c(1,0),...,legend.text=legend.text,beside=beside)
#  else
#    barplot(gsi.plain(t(rcomp(X,total=total))),...,legend.text=legend.text,beside=beside);
#}
barplot.aplus <- barplot.acomp
#formals(barplot.aplus)$beside <- TRUE
formals(barplot.aplus)[c("beside","total")]  <- list(beside=TRUE,total=NULL)

#barplot.aplus <- function(height,...,legend.text=TRUE,beside=TRUE) {
#  X <- height
#  if( gsi.isSingleRow(X) )
#    barplot(t(rbind(gsi.plain(aplus(X)),0)),c(1,0),...,legend.text=legend.text,
#            beside=beside)
#  else
#    barplot(gsi.plain(t(aplus(X))),...,legend.text=legend.text,beside=beside);
#}

barplot.rplus <- barplot.aplus
#barplot.rplus <- function(height,...,legend.text=TRUE,beside=TRUE) {
#  X <- height
#  if( gsi.isSingleRow(X) )
#    barplot(t(rbind(gsi.plain(rplus(X)),0)),c(1,0),...,
#            legend.text=legend.text,beside=beside)
#  else
#    barplot(gsi.plain(t(rplus(X))),...,legend.text=legend.text,beside=beside);
#}



split.acomp <- function(x,f,drop=FALSE,...) {
  oo <- no <- options()$compositions
  no$stickyClass = TRUE
  options(compositions=no)
  rs = lapply(split(1:NROW(x),f,...),function(i) x[i,rep(TRUE, ncol(x)),drop=drop])
  options(compositions=oo)
  return(rs)
}
split.rcomp <- split.acomp
split.aplus <- split.acomp
split.rplus <- split.acomp
split.ccomp <- split.acomp
split.rmult <- split.acomp


as.data.frame.acomp <- function(x,...) as.data.frame.matrix(unclass(x))
as.data.frame.rcomp <- function(x,...) as.data.frame.matrix(unclass(x))
as.data.frame.ccomp <- function(x,...) as.data.frame.matrix(unclass(x))
as.data.frame.aplus <- function(x,...) as.data.frame.matrix(unclass(x))
as.data.frame.rplus <- function(x,...) as.data.frame.matrix(unclass(x))
as.data.frame.rmult <- function(x,...) as.data.frame.matrix(unclass(x))

gsi.addclass <- function(x,cls) {
  class(x) <- unique(c(cls,attr(x,"class")))
  x
}


gsi <- new.env(hash=TRUE,emptyenv())




princomp.acomp <- function(x,...,scores=TRUE,center=attr(covmat,"center"),
                           covmat=var(x,robust=robust,giveCenter=TRUE),robust=getOption("robust")) {
  cl <- match.call()
  D <- gsi.getD(x)
  tmp <- princomp(clr(x),...,center=clr(center),covmat=covmat,scores=scores)
  tmp$sdev        <- tmp$sdev[-D]
  tmp$loadings    <- gsi.mystructure(tmp$loadings[,-D],class="loadings")
  tmp$Center      <- clrInv(tmp$center)
  tmp$Loadings  <- acomp(clrInv(t(tmp$loadings)),total=D)
  tmp$DownLoadings<- acomp(clrInv(t(-tmp$loadings)),total=D)
  tmp$call <- cl
  gsi.addclass(tmp,"princomp.acomp")
}

print.princomp.acomp <- function(x,...) {
  NextMethod("print",x,...)
  cat("Mean (compositional):\n")
  print(x$Center)
  cat("+Loadings (compositional):\n")
  print(x$Loadings)
  cat("-Loadings (compositional):\n")
  print(x$DownLoadings)
  invisible(x)
}

plot.princomp.acomp <- function(x,y=NULL,...,npcs=min(10,length(x$sdev)),
                                        type=c("screeplot","variance",
                                          "biplot","loadings","relative"),
                                main=NULL,scale.sdev=1) {
  if( missing(main) ) main <- deparse(substitute(x))
  type <- match.arg(type)
  if( type=="biplot" )
    biplot(x,...,main=main)
  else if( type=="loadings" ) {
    if( is.na(scale.sdev) )
      scl<-1
    else
      scl<-scale.sdev*x$sdev
    barplot(acomp((x$Loadings*scl)[1:npcs,]),...,
            main=main,total=gsi.getD(x$Loadings))
  }
  else if(type=="relative") {
    tmp <- relativeLoadings(x,scale.sdev=scale.sdev)[,1:npcs]
    tmp <- barplot(t(tmp),...,main=main,beside=TRUE,legend=TRUE)
    abline(h=1)
    invisible(tmp)
  } else  {
  if( type=="screeplot" ) type <- "lines"
  if( type=="variance" ) type <- "barplot"
  screeplot(x,...,npcs=npcs, main=main,type=type)
  }
}

predict.princomp.acomp <- function(object,newdata,...) {
  NextMethod("predict",object,newdata=clr(newdata),...)
}

                                
#panel.princomp.acomp <- function(x,choice,t,...){
#  straight.panel.acomp(x$Center,x$Loadings)
#}


princomp.rcomp <- function(x,...,scores=TRUE,center=attr(covmat,"center"),
                           covmat=var(x,robust=robust,giveCenter=TRUE),robust=getOption("robust")) {
  cl <- match.call()
  D <- gsi.getD(x)
  tmp <- princomp(cpt(x),...,scores=scores,covmat=covmat,center=cpt(center))
  tmp$sdev        <- tmp$sdev[-D]
  tmp$loadings    <- gsi.mystructure(tmp$loadings[,-D],class="loadings")
  tmp$Center      <- cptInv(tmp$center,x)
  tmp$Loadings    <- cptInv(t(tmp$loadings),x)
  tmp$call <- cl
  gsi.addclass(tmp,"princomp.rcomp")
}


print.princomp.rcomp <- function(x,...) {
  NextMethod("print",x,...)
}

plot.princomp.rcomp <- function(x,y=NULL,...,npcs=min(10,length(x$sdev)),
                                        type=c("screeplot","variance",
                                          "biplot","loadings","relative"),
                                main=NULL,scale.sdev=1) {
  if( missing(main) ) main <- deparse(substitute(x))
  type <- match.arg(type)
  if( type=="biplot" )
    erg<-biplot(x,...,main=main)
  else if( type=="loadings" ) {
    if( is.na(scale.sdev) )
      scl<-1
    else
      scl<-scale.sdev*x$sdev
    erg<-barplot((rmult(t(x$loadings))*scl)[1:npcs,],...,
            main=main)
  }
  else if(type=="relative") {
    tmp <- relativeLoadings(x,scale.sdev=scale.sdev)[,1:npcs]
    tmp <- barplot(t(tmp),...,main=main,beside=TRUE,legend=TRUE)
    erg<-invisible(tmp)
  } else  {
  if( type=="screeplot" ) type <- "lines"
  if( type=="variance" ) type <- "barplot"
  erg<-screeplot(x,...,npcs=npcs, main=main,type=type)
  }
  replot(plot=match.call(),add=FALSE)  
  invisible(erg)
}

predict.princomp.rcomp <- function(object,newdata,...) {
  NextMethod("predict",object,newdata=cpt(newdata),...)
}

princomp.aplus <- function(x,...,scores=TRUE,center=attr(covmat,"center"),
                           covmat=var(x,robust=robust,giveCenter=TRUE),robust=getOption("robust")) {
  cl <- match.call()
  D <- gsi.getD(x)
  tmp <- princomp(ilt(x),...,scores=scores,covmat=covmat,center=ilt(center))
  tmp$Center      <- center
  tmp$Loadings  <- iltInv(t(tmp$loadings))
  tmp$DownLoadings<- iltInv(t(-tmp$loadings))
  tmp$call <- cl
  gsi.addclass(tmp,"princomp.aplus")
}

print.princomp.aplus <- function(x,...) {
  NextMethod("print",x,...)
  cat("Mean (compositional):\n")
  print(x$Center)
  cat("+Loadings (compositional):\n")
  print(x$Loadings)
  cat("-Loadings (compositional):\n")
  print(x$DownLoadings)
  invisible(x)
}

plot.princomp.aplus <- function(x,y=NULL,...,npcs=min(10,length(x$sdev)),
                                        type=c("screeplot","variance",
                                          "biplot","loadings","relative"),
                                main=NULL,scale.sdev=1) {
  if( missing(main) ) main <- deparse(substitute(x))
  type <- match.arg(type)
  if( type=="biplot" )
    erg<-biplot(x,...,main=main)
  else if( type=="loadings" ) {
        if( is.na(scale.sdev) )
      scl<-1
    else
      scl<-scale.sdev*x$sdev
    erg<-barplot(aplus((x$Loadings*scl)[1:npcs,]),...,
            main=main)
  }
  else if(type=="relative") {
    tmp <- relativeLoadings(x,scale.sdev=scale.sdev)[,1:npcs]
    tmp <- barplot(t(tmp),...,main=main,beside=TRUE,legend=TRUE)
    abline(h=1)
    erg<-invisible(tmp)
  } else  {
  if( type=="screeplot" ) type <- "lines"
  if( type=="variance" ) type <- "barplot"
  erg<-screeplot(x,...,npcs=npcs, main=main,type=type)
  }
  replot(plot=match.call(),add=FALSE)  
  invisible(erg)
}

predict.princomp.aplus <- function(object,newdata,...) {
  NextMethod("predict",object,newdata=ilt(newdata),...)
}

princomp.rplus <- function(x,...,scores=TRUE,center=attr(covmat,"center"),
                           covmat=var(x,robust=robust,giveCenter=TRUE),robust=getOption("robust")) {
  cl <- match.call()
  robust<-robust
  tmp <- princomp(iit(x),...,scores=scores,covmat=covmat,center=iit(center))
  tmp$Center      <- iitInv(center)
  tmp$call <- cl
  tmp$Loadings <- rmult(t(tmp$loadings))
  gsi.addclass(tmp,"princomp.rplus")
}

print.princomp.rplus <- function(x,...) {
  NextMethod("print",x,...)
  cat("Mean:\n")
  print(x$Center)
  cat("Loadings:\n")
  print(x$Loadings)
  invisible(x)
}

plot.princomp.rplus <- function(x,y=NULL,...,npcs=min(10,length(x$sdev)),
                                        type=c("screeplot","variance",
                                          "biplot","loadings","relative"),
                                main=NULL,scale.sdev=1) {
  if( missing(main) ) main <- deparse(substitute(x))
  type <- match.arg(type)
  if( type=="biplot" )
    erg<-biplot(x,...,main=main)
  else if( type=="loadings" ) {
    if( is.na(scale.sdev) )
      scl<-1
    else
      scl<-scale.sdev*x$sdev
    erg<-barplot((rmult(t(x$loadings))*scl)[1:npcs,],...,
            main=main)
  }
  else if(type=="relative") {
    tmp <- relativeLoadings(x,scale.sdev=scale.sdev)[,1:npcs]
    tmp <- barplot(t(tmp),...,main=main,beside=TRUE,legend=TRUE)
    erg<-invisible(tmp)
  } else  {
  if( type=="screeplot" ) type <- "lines"
  if( type=="variance" ) type <- "barplot"
  erg<-screeplot(x,...,npcs=npcs, main=main,type=type)
  }
  replot(plot=match.call(),add=FALSE)  
  invisible(erg)
}

predict.princomp.rplus <- function(object,newdata,...) {
  NextMethod("predict",object,newdata=iit(newdata),...)
}


princomp.rmult <- function(x,cor=FALSE,scores=TRUE,
                           covmat=var(rmult(x[subset,]),robust=robust,giveCenter=TRUE),center=attr(covmat,"center"),  subset = rep(TRUE, nrow(x)),...,robust=getOption("robust")) {
Nprincomp <-
    function(x, cor = FALSE, scores = TRUE, covmat = NULL,center=center,
             subset = rep(TRUE, nrow(as.matrix(x))), ...)
{
    cl <- match.call()
    cl[[1]] <- as.name("princomp")
    #if(!missing(x) && !missing(covmat))
    #    warning("both 'x' and 'covmat' were supplied: 'x' will be ignored")
    z <- as.matrix(unclass(x))[subset, , drop = FALSE]
    cv <- covmat
    n.obs <- nrow(x) # NA is maybe more appropriate
    cen <- center
    dn <- dim(z)
    if(dn[1] < dn[2])
      stop("'princomp' can only be used with more units than variables")
    if(!is.numeric(cv)) stop("PCA applies only to numerical variables")
    if (cor) {
        sds <- sqrt(diag(cv))
        if(any(sds == 0))
            stop("cannot use cor=TRUE with a constant variable")
        cv <- cv/(sds %o% sds)
    }
    edc <- eigen(cv, symmetric = TRUE)
    ev <- edc$values
    if (any(neg <- ev < 0)) { # S-PLUS sets all := 0
        ## 9 * : on Solaris found case where 5.59 was needed (MM)
        if (any(ev[neg] < - 9 * .Machine$double.eps * ev[1]))
            stop("covariance matrix is not non-negative definite")
        else
            ev[neg] <- 0
    }
    cn <- paste("Comp.", 1:ncol(cv), sep = "")
    names(ev) <- cn
    dimnames(edc$vectors) <- if(missing(x))
        list(dimnames(cv)[[2]], cn) else list(dimnames(x)[[2]], cn)
    sdev <- sqrt(ev)
    sc <- if (cor) sds else rep(1, ncol(cv))
    names(sc) <- colnames(cv)
    scr <- #if (scores && !missing(x) && !is.null(cen))
      (unclass((rmult(z)-rmult(cen))/sc))%*%edc$vectors
    #  scale(z, center = cen, scale = sc) %*% edc$vectors
    if (is.null(cen)) cen <- rep(NA_real_, nrow(cv))
    edc <- list(sdev = sdev,
                loadings = gsi.mystructure(edc$vectors, class="loadings"),
                center = c(unclass(cen)), scale = sc, n.obs = n.obs,
                scores = scr, call = cl)
    class(edc) <- "princomp"
    edc
}
Nprincomp(unclass(x),cor=cor,scores=scores,covmat=covmat,center=unclass(center),subset=subset,...)
}

gsi.pairrelativeMatrix <- function(names) {
  n  <- length(names)
  ii <- rep(1:n,n)
  jj <- rep(1:n,each=n)
  jgi <- jj>ii
  ii <- ii[jgi]
  jj <- jj[jgi]
  N <- length(ii)
  erg <- rep(0,N*n)
  erg[1:N+N*(ii-1)]<-  1
  erg[1:N+N*(jj-1)]<- -1
  erg <- matrix(erg,nrow=N,ncol=n)
  colnames(erg)  <- names
  row.names(erg) <- paste(names[ii],names[jj],sep="/") 
  erg
}

relativeLoadings <- function(x,...) UseMethod("relativeLoadings",x)
relativeLoadings.princomp.acomp <- function(x,...,log=FALSE,scale.sdev=NA,cutoff=0.1) {
  if( is.na(scale.sdev) ) 
    scale <- rep(1,length(x$sdev))
  else 
    scale <- scale.sdev*x$sdev
  bl <- gsi.pairrelativeMatrix(row.names(x$loadings)) %*% (unclass(x$loadings) %*% diag(scale))
  colnames(bl) <- colnames(x$loadings)
  if( !log )
    bl <- exp(bl)
  gsi.mystructure(bl,class="relativeLoadings.princomp.acomp",cutoff=cutoff,scale=scale,log=log)
}

relativeLoadings.princomp.aplus <- function(x,...,log=FALSE,scale.sdev=NA,cutoff=0.1) {
  if( is.na(scale.sdev) ) 
    scale <- rep(1,length(x$sdev))
  else 
    scale <- scale.sdev*x$sdev
  bl <- gsi.pairrelativeMatrix(row.names(x$loadings)) %*% (unclass(x$loadings) %*% diag(scale))
  colnames(bl) <- colnames(x$loadings)
  if( !log )
    bl <- exp(bl)
  gsi.mystructure(bl,class="relativeLoadings.princomp.aplus",cutoff=cutoff,scale=scale,log=log)
}

relativeLoadings.princomp.rcomp <- function(x,...,scale.sdev=NA,cutoff=0.1) {
  if( is.na(scale.sdev) ) 
    scale <- rep(1,length(x$sdev))
  else 
    scale <- scale.sdev*x$sdev
  bl <- gsi.pairrelativeMatrix(row.names(x$loadings)) %*% (unclass(x$loadings) %*% diag(scale))
  colnames(bl) <- colnames(x$loadings)
  gsi.mystructure(bl,class="relativeLoadings.princomp.rcomp",cutoff=cutoff,scale=scale)
}

relativeLoadings.princomp.rplus <- function(x,...,scale.sdev=NA,cutoff=0.1) {
  if( is.na(scale.sdev) ) 
    scale <- rep(1,length(x$sdev))
  else 
    scale <- scale.sdev*x$sdev
  bl <- gsi.pairrelativeMatrix(row.names(x$loadings)) %*% (unclass(x$loadings) %*% diag(scale))
  colnames(bl) <- colnames(x$loadings)
  gsi.mystructure(bl,class="relativeLoadings.princomp.rplus",cutoff=cutoff,scale=scale)
}


print.relativeLoadings.princomp.acomp <- function(x,...,
                                                 cutoff=attr(x,"cutoff"),
                                                 digits=2
                                                 ) {
  bt <- format(x,digits=digits)
  if( !attr(x,"log") ) { 
    if( !is.na(cutoff) )
      bt[abs(log(x))<cutoff] <- ""
  } else {
    if( !is.na(cutoff) )
      bt[abs(x)<cutoff] <- ""
  }
  print(bt,quote=FALSE)
  x
}

print.relativeLoadings.princomp.aplus <- print.relativeLoadings.princomp.acomp

print.relativeLoadings.princomp.rcomp <- function(x,...,
                                                 cutoff=attr(x,"cutoff"),
                                                 digits=2
                                                 ) {
  bt <- format(x,digits=digits)
  bt[abs(x)<cutoff] <- ""
  print(bt,quote=FALSE)
  x
}

print.relativeLoadings.princomp.rplus <- function(x,...,
                                                 cutoff=attr(x,"cutoff"),
                                                 digits=2
                                                 ) {
  bt <- format(x,digits=digits)
  bt[abs(x)<cutoff] <- ""
  print(bt,quote=FALSE)
  x
}


plot.relativeLoadings.princomp.acomp<- function(x,...) {
  barplot(t(x),...,beside=TRUE)
  if( !attr(x,"log") )
    abline(h=1)
  replot(plot=match.call(),add=FALSE)  
  invisible(x)
}
plot.relativeLoadings.princomp.aplus<- function(x,...) {
  barplot(t(x),...,beside=TRUE)
  if( !attr(x,"log") )
    abline(h=1)
  replot(plot=match.call(),add=FALSE)  
  invisible(x)
}

plot.relativeLoadings.princomp.rcomp<- function(x,...) {
  barplot(t(x),...,beside=TRUE)
  replot(plot=match.call(),add=FALSE)  
  invisible(x)
}

plot.relativeLoadings.princomp.rplus<- function(x,...) {
  barplot(t(x),...,beside=TRUE)
  replot(plot=match.call(),add=FALSE)  
  invisible(x)
}



read.geoeas <- function (file){
#read title
print("reading title:...")
title <- read.table(file, nrows=1, quote="", colClasses="character", sep="\t")
print("reading title: OK")

#read number of variables
print("reading number of variables:...")
nvars <- read.table(file, skip=1, nrows=1, sep="\t")
nvars <- as.integer(nvars)
#read labels of the variables
print("reading variables:...")
labels <- scan(file, skip=2, nmax=nvars, nlines= nvars, sep="\t", quote="", what="character")

#read data matrix
print("reading dataset:...")
dades <- read.table(file, skip=2+nvars)
print("reading dataset: OK")
#relate variables with their names
colnames(dades)=as.vector(labels)
#add title as an attribute
attr(dades,"title") <- as.character(title)
return(dades)
}

read.geoEAS <- function(file){ read.geoeas(file) }



#read.standard <- function (file){
##read title
#print("reading title:...")
#title <- read.table(file, nrows=1, quote="", colClasses="character", sep="\t")
#print("reading title: OK")

#read data matrix
#print("reading dataset:...")
#dades <- read.table(file, skip=1, header=T)
#print("reading dataset: OK")#

#add title as an attribute
#attr(dades,"title") <- as.character(title)
#return(dades)
#}

 #  =========================================================================#
# Based on the the tedrahedron plot from MixeR
# http://vlado.fmf.uni-lj.si/pub/MixeR/
# Vladimir Batagelj & Matevz Bren
# plots mix object 'm' into tetrahedron and exports it in kinemage format
#   clu - partition -> color of points
#   vec - vector of values -> size of points
#   col - color of points if clu=NULL
#   scale - relative size of points
#   king - FALSE (for Mage); TRUE (for King)
kingTetrahedron <- function(X,parts=1:4,file="tmptetrahedron.kin",clu=NULL,vec=NULL,king=TRUE,scale=0.2,col=1,title="Compositional Tetrahedron"){
  m <- list()
  m$mat <- data.frame(clo(X,parts=parts))
  m$tit <- title
  kinColors <- c('white', 'red', 'blue', 'yellow',
    'green', 'cyan', 'magenta', 'pink', 'lime',
    'orange', 'peach', 'gold', 'purple', 'sea',
    'gray', 'sky', 'brown', 'lilac', 'hotpink',
    'yellowtint', 'pinktint', 'peachtint',
    'greentint', 'bluetint', 'lilactint',
    'deadwhite', 'deadblack', 'invisible')
  warn <- ""
  if (king) warn <- "\n*** works only with KiNG viewer: https://en.wikipedia.org/wiki/Kinemage"
  head <- paste("@text\n",
    file," / ",date(),
    "\nDataset: ", m$tit,warn,
"\nLayout obtained using composition
based on  MixeR
http://vlado.fmf.uni-lj.si/pub/MixeR/
Vladimir Batagelj & Matevz Bren
Institute of Mathematics, Physics and Mechanics
Ljubljana, Slovenia
@kinemage 1
@caption\n", m$tit,
"\n@fontsizeword 18
@zoom 1.00
@thinline
@zclipoff
@group {Complete} dominant animate movieview = 1
@spherelist 0 radius= 0.20\n",sep="")
  foot <-
"@vectorlist {}  color=  blue
P 9.500, 0.500, 9.500
0.500, 9.500, 9.500
P 9.500, 0.500, 9.500
0.500, 0.500, 0.500
P 9.500, 0.500, 9.500
9.500, 9.500, 0.500
P 0.500, 9.500, 9.500
0.500, 0.500, 0.500
P 0.500, 9.500, 9.500
9.500, 9.500, 0.500
P 0.500, 0.500, 0.500
9.500, 9.500, 0.500\n"
  kin <- file(file,"w")
  n <- nrow(m$mat)
  if (is.null(clu)) {clu <- rep(col,n)}
  clu <- c(clu,0,0,0,0)
  if (is.null(vec)) {vec <- rep(1,n)}
  vec <- c(vec,1,1,1,1)
  size <- scale/max(vec)
  rn <- c(dimnames(m$mat)[[1]],"A","B","C","D")
  a <- 10/9+c(m$mat[,1],1,0,0,0)
  b <- c(m$mat[,2],0,1,0,0)
  c <- c(m$mat[,3],0,0,1,0)
  d <- c(m$mat[,4],0,0,0,1)
  x <- (a - b - c + d)*0.45
  y <- (a - b + c - d)*0.45
  z <- (a + b - c - d)*0.45
  cat(head,file=kin)
  for (i in 1:length(rn)) {
    color <- "white"
    if (clu[i]>0) color <- kinColors[2+(clu[i]-1)%%18]
    cat("{",rn[i],"} ", color," ",file=kin,sep="")
    if (king) cat(" r=", vec[i]*size," ",file=kin,sep=" ")
    cat(10*x[i],10*(1-y[i]),10*z[i],"\n",file=kin,sep=" ")
  }
  cat(foot,file=kin)
  close(kin)
}


gsi.getBalStruct <- function(descr,names,allowMinus=FALSE,allowOne=FALSE) {
    if( !is.call(descr))
      return(gsi.mystructure(list(),all=list(as.character(descr))))
    command <- as.character(descr[[1]])
                                        # next two lines added!
    if( command == "~" )
      return( Recall(descr[[2]]) )
    if( command == "(" )
      return( Recall(descr[[2]]) )
    if( allowOne && command == "1" )
      return( gsi.mystructure(list(),all=list(as.character(descr))) )
    else if( (allowMinus && command == "-") || command == "/" || command =="*" || command =="+" || command==":") {
      a <- Recall(descr[[2]])
      b <- Recall(descr[[3]])
      aall <- unlist(c(attr(a,"all"),attr(b,"all")))
      if( command == "/" || (command == "-" && allowMinus) ) {
        erg <- c( list(list(attr(a,"all"),attr(b,"all"))),
                 c(a),c(b)
                 )
      } else {
        erg <- c( c(a),c(b) )
        
      }
      attr(erg,"all") <- aall
      erg
    } else {
      gsi.mystructure(list(),all=list(as.character(command)))
    }
  }


balanceBase <- function(X,...) UseMethod("balanceBase",X)

balanceBase.acomp <- function(X,expr,...) {
  if( !is.character(X) )
    X <- colnames(oneOrDataset(X))
  bs <- gsi.getBalStruct(expr)
  nam <- sapply(bs,function(k) {
    paste(paste(unlist(k[[1]]),sep="",collapse=""),
          paste(unlist(k[[2]]),sep="",collapse=""),sep="/")
  })
  bas <- sapply(bs,function(k) {
    x <- rep(0,length(X))
    x[match(k[[1]],X)]<-1/length(k[[1]])
    x[match(k[[2]],X)]<- - 1/length(k[[2]])
    x <- x/sqrt(sum(x^2))
    x
  })
  colnames(bas)<-nam
  rownames(bas)<-X
  bas
}

balanceBase.aplus <- function(X,expr,...) {
  if( !is.character(X) )
    X <- colnames(oneOrDataset(X))
  bs <- gsi.getBalStruct(expr,allowOne=TRUE)
  nam <- sapply(bs,function(k) {
    paste(paste(unlist(k[[1]]),sep="",collapse=""),
          paste(unlist(k[[2]]),sep="",collapse=""),sep="/")
  })
  bas <- sapply(bs,function(k) {
    x <- rep(0,length(X))
    if(length(k[[1]])>0) x[match(k[[1]],X)]<-1/length(k[[1]])
    if(length(k[[2]])>0) x[match(k[[2]],X)]<- - 1/length(k[[2]])
    x <- x/sqrt(sum(x^2))
    x
  })
  colnames(bas)<-nam
  rownames(bas)<-X
  bas
}


balanceBase.rcomp <- function(X,expr,...) {
  if( !is.character(X) )
    X <- colnames(oneOrDataset(X))
  bs <- gsi.getBalStruct(expr,allowMinus=TRUE)
  nam <- sapply(bs,function(k) {
    paste(paste(unlist(k[[1]]),sep="",collapse=""),
          paste(unlist(k[[2]]),sep="",collapse=""),sep="-")
  })
  bas <- sapply(bs,function(k) {
    x <- rep(0,length(X))
    x[match(k[[1]],X)]<-1
    x[match(k[[2]],X)]<- -1
    x
  })
  colnames(bas)<-nam
  rownames(bas)<-X
  bas
}

balanceBase.rplus <- function(X,expr,...) {
  if( !is.character(X) )
    X <- colnames(oneOrDataset(X))
  bs <- gsi.getBalStruct(expr,allowMinus=TRUE,allowOne=TRUE)
  nam <- sapply(bs,function(k) {
    paste(paste(unlist(k[[1]]),sep="",collapse=""),
          paste(unlist(k[[2]]),sep="",collapse=""),sep="-")
  })
  bas <- sapply(bs,function(k) {
    x <- rep(0,length(X))
    if(length(k[[1]])>0) x[match(k[[1]],X)]<-1
    if(length(k[[2]])>0) x[match(k[[2]],X)]<- -1
    x
  })
  colnames(bas)<-nam
  rownames(bas)<-X
  bas
}


balance <- function(X,...) UseMethod("balance",X)

balance.acomp <- function(X,expr,...) {
  ilr(X,balanceBase(X,expr))
}

balance.aplus <- function(X,expr,...) {
  clr2ilr(ilt(X),balanceBase(X,expr))
}

balance.rcomp <- function(X,expr,...) {
  clr2ilr(iit(rcomp(X)),balanceBase(X,expr))
}

balance.rplus <- function(X,expr,...) {
  clr2ilr(ilt(X),balanceBase(X,expr))
}

balance01 <- function(X,...) UseMethod("balance01",X)

balance01.acomp <- function(X,expr,...) {
  ilr(X,balanceBase(X,expr))
}


balance01.acomp <- function(X,expr,...) {
bal01 <- function(X) {
  A <- exp(unclass(oneOrDataset(X))*sqrt(2))
  A / (1+A)
}
bal01(balance(X,expr))
}


balance01.rcomp <- function(X,expr,...) {
  bb <- balanceBase(X,expr)
  p <- clr2ilr(iit(rcomp(X)),ifelse(bb>0,1,0))
  t <- clr2ilr(iit(rcomp(X)),ifelse(bb!=0,1,0))
  p/t
}
  
print.acomp <- function(x,...,replace0=TRUE) {
pad <- function(x,n) {
  maxN <- max(n)
  padding <- substring(rep(paste(rep(" ",maxN),collapse="",sep=""),max(length(n),length(x))),1,pmax(n-nchar(x),0))
  paste(padding,x,sep="")
}

subser <- function(erg,x) {
  at <- attributes(x)
  nc <- nchar(erg)
  if( any(nc<4) )
    erg[nc<4]<-pad(erg[nc<4],4)  
  nc <- nchar(erg)
  erg<-gsub(" NaN$"," MAR",erg)
  erg<-gsub("  NA$","MNAR",erg)
  erg<-gsub("-Inf$","  SZ",erg)
  zero <- is.finite(x)&x==0
  if( any(zero) )
    erg[zero]<-pad("BDL",nchar(erg[zero]))
  erg<-gsub("^ *-","<",erg)
  erg<-gsub("Inf$","ERR",erg)
  attributes(erg) <- at
  erg
}

if( is.matrix(x) )
     erg<- apply(x,2,format,...)
  else 
     erg<-format(x,...)
erg <- subser(erg,x)
if( !is.null(attr(x,"Losts"))) {
  L <- oneOrDataset(attr(x,"Losts"))
   attr(erg,"Losts")<-noquote(c("..."=paste("Containing ", sum(L)," lost and replaced values!")))
 }

                             
                                        #  dm <-dim(erg)
                                        #  dim(erg)<-dm
                                        #  dimnames(erg)<-dimnames(x)
quote <- FALSE
ddd = list(...)
if( !is.null(list(...)$quote )){
  ddd$quote <- quote
}
ddd$x <- erg
do.call("print.default", args=ddd)
invisible(x)
}



print.aplus<- print.acomp
print.rcomp<- print.acomp
formals(print.rcomp)$replace0 <- FALSE
print.rplus<- print.rcomp

#"(.acomp" <- function(x,...) { 
#  if(is.matrix(x))
#     return(acomp(x[...]))
#  else
#     return(acomp(oneOrDataset(x)[...]))
#  acomp(oneOrDataset(x)[...])
#}

AitchisonDistributionIntegrals <- function(
         theta=alpha+sigma %*% clr(mu),
         beta=-1/2*gsi.svdinverse(sigma),
         alpha=mean(theta),
         mu=clrInv(c(sigma%*%(theta-alpha))),
         sigma=-1/2*gsi.svdinverse(beta),
         grid=30,
         mode=3) {
if( !xor( missing(theta) , (missing(mu) || missing(alpha)) ) )
  stop("Specify either theta or mu and alpha")
if( !xor( missing(beta) , missing(sigma) ) )
  stop("Specify either beta or sigma")
D <- length(theta)
if( nrow(beta) == D-1 )
  beta <- ilrvar2clr(beta)
if( any(abs(beta-t(beta))>1E-10) ) {
  warning("AitchisonDistributionIntegrals: beta was not symmetric 1")
  print(beta)
}
gsiInt(dim(beta),2)
stopifnot( length(dim(beta))==2,ncol(beta)==D,nrow(beta)==D)
erg <- .C(gsiAitchisonDistributionIntegral,
          D   =gsiInt(D,1),
          grid=gsiInt(grid,1),
          mode=gsiInt(mode,1),
          theta=gsiDouble(theta,D),
          beta =gsiDouble(beta,D*D),
          expKappa =numeric(1),
          loggxMean=numeric(1),
          clrMean  =numeric(D),
          clrVar   =numeric(D*D)
          )
erg$beta <- matrix(erg$beta,nrow=D)
erg$SqIntegral <- matrix(erg$clrVar,nrow=D,ncol=D)
erg$alpha=alpha
erg$mu=mu
erg$sigma=sigma
erg$clrSqExpectation <- matrix(erg$clrVar,nrow=D,ncol=D)
dim(erg$clrVar) <- c(D,D)
  return(erg[c("theta","beta","alpha","mu","sigma",if( mode>=0 ) c("expKappa","loggxMean") else c(),if(mode >= 1) "clrMean" else c(),if(mode==2) "clrSqExpectation" else if(mode>=3) "clrVar" else c())])
}



dAitchison <- function(x,theta=alpha+sigma %*% clr(mu),beta=-1/2*gsi.svdinverse(sigma),alpha=mean(theta),mu=clrInv(c(sigma%*%(theta-alpha))),sigma=-1/2*gsi.svdinverse(beta),grid=30,
realdensity=FALSE,expKappa=AitchisonDistributionIntegrals(theta,beta,grid=grid,mode=1)$expKappa) {
if( !xor( missing(theta) , (missing(mu) || missing(alpha)) ) )
  stop("Specify either theta or mu and alpha")
if( !xor( missing(beta) , missing(sigma) ) )
  stop("Specify either beta or sigma")
D <- length(theta)
if( any(abs(beta-t(beta))>1E-10) ) {
  warning("dAitchison: beta was not symmetric 1")
  print(beta)
}
if( nrow(beta) == D-1 )
  beta <- ilrvar2clr(beta)
if( any(abs(beta-t(beta))>1E-10) ) {
  warning("dAtichison: beta was not symmetric 2")
  print(beta)
}
stopifnot(gsi.getD(x)==D)
clrx <- clr(x)
cf <- if(realdensity) 1 else 0
exp((clrx%*%beta)%*%clrx+ult(x)%*%rmult(theta-cf))/expKappa
}


rAitchison <- function(n,theta=alpha+sigma %*% clr(mu),beta=-1/2*gsi.svdinverse(sigma),alpha=mean(theta),mu=clrInv(c(sigma%*%(theta-alpha))),sigma=-1/2*gsi.svdinverse(beta),withfit=FALSE) {
#withfit=FALSE # in the future, this should allow to simulate more efficiently by playing with the decomposition Ait = Normal x Dirichlet
if( !xor(missing(theta),missing(mu) || missing(alpha)) )
  stop("Specify either theta or mu and alpha")
if( !xor(missing(beta),missing(sigma)) )
  stop("Specify either beta or sigma")
if( !missing(theta) ) nam <- names(theta) else if( !missing(mu) ) nam<- names(mu)
D <- length(theta)
if( nrow(sigma) == D-1 )
  sigma <- ilrvar2clr(sigma)
  else
  sigma <- ilrvar2clr(clrvar2ilr(sigma))
# Prepare Sigma
if( any(abs(sigma-t(sigma))>1E-10) )
  warning("rAtichison: sigma was not symmetric")
SVD <- svd(sigma)
if( any(SVD$d < -1E-8 ) )
  warning("rAitchison currently only works correctly with positive semidefinit sigmas. Results wrong!!!")
sqrtSigma <- with(SVD,u%*% gsi.diagGenerate(sqrt(d)) %*% t(v))
if( withfit ) {
     # find the best decomposition Ait = Normal x Dirichlet; where both have the same mode
	bestfit <- gsiFindSolutionWithDerivative(
                           function(alpha) exp(alpha)+sigma%*%alpha-theta,
                           function(alpha) diag(exp(alpha))+sigma,
                           c(theta),
                           iter=20)
	if( attr(bestfit,"status")!="ok" ) {
	warning("Problems in finding optimal simulation algorith, using fallback")
	}
	# Compute best fitter
	mu <- bestfit - sum(bestfit)
	SimTheta <- exp(bestfit)
	stopifnot(abs(sum(SimTheta)-sum(theta))<1E-6)
} else {
    # use as normal(0,sigma) and as dirichlet(theta)
	SimTheta <- theta
	mu <- theta*0
	# SimTheta <- rep(alpha, length(theta))
	# mu <- mu
}
if( ! all(SimTheta>0) ) {
  if( all(theta>0) ) {
	SimTheta <- theta
	mu <- theta*0
        warning("rAitchison: withfit ignored");
      } else {
        stop("rAitchison: This implementation only works with positive theta")
      }
}
# Compute with rejection sampling
erg <- .C(gsirandomClr1Aitchison,
   D=gsiInt(D,1),
   n=gsiInt(n,1),
   erg=numeric(D*n),
   theta=gsiDouble(SimTheta,D),
   mu=gsiDouble(mu,D),
   sqrtSigma=gsiDouble(sqrtSigma,D*D)
   )
# Format result from CLR
res <- clrInv(matrix(erg$erg,nrow=n))
names(res) <- nam
res
}


gsiFindSolutionWithDerivative <- function(f,Der,start,iter=30) {
  nstart <- start
  try({
    it <- 0
    for( i in 1:iter) {
      y  <- f(c(nstart))
      ny = norm(c(y))
      if( i == 1) firstnorm = ny
      Div  <- Der(c(nstart))
      nstart <- nstart-solve(Div,y)
      it <- i
      if( ny <1E-14 && ny/firstnorm<1E-6 )
        break
    }
    return(gsi.mystructure(nstart,value=y,status=if(ny/firstnorm<1E-6 || ny <1E-15) "ok" else "not converged",iterations=it))
  },silent=FALSE)
  return(gsi.mystructure(start,value=f(c(start)),status="failed",iterations=it))
}

R2 <- function(object,...) UseMethod("R2",object)
R2.lm <- function(object,...,adjust=TRUE,ref=0) {
  if( !is.numeric(ref))
    ref<-Recall(ref,...,adjust=adjust)
  pr <- predict(object)
  re <- resid(object)
  n  <- nrow(re)
    if (is.null(n)) n <- length(re) # consider the case of one-dimensional response
  y  <- pr+re
  erg <- if( adjust ) {
    dfres<-object$df.residual
    1-(mvar(re)*(n-1)/dfres)/mvar(y)
  } else
    1-mvar(re)/mvar(y)
  (erg-ref)/(1-ref)
}
R2.default <- function(object,...,ref=0) {
  if( !is.numeric(ref))
    ref<-Recall(ref,...)
  pr <- predict(object)
  re <- resid(object)
  n  <- nrow(re)
    if (is.null(n)) n <- length(re)  # consider the case of one-dimensional response
  y  <- pr+re
  erg <- 1-mvar(re)/mvar(y)
  (erg-ref)/(1-ref)
}
var.mlm <- function(x,...) {r<-unclass(resid(x));(t(r)%*%r)/x$df.residual} 
var.lm <- function(x,...) {r<-unclass(resid(x));sum(r^2)/x$df.residual} 


vcovAcomp <- function(object,...){
  co <- coef(object)
  aperm(gsi.mystructure(vcov(object,...),
        dim=c(dim(co),dim(co)),
        dimnames=c(dimnames(co),dimnames(co))),
        c(2,4,1,3))
}
qHotellingsTsq <- function(p,n,m){
  qf(p,n,m-n+1)*(n*m)/(m-n+1)
}
pHotellingsTsq <- function(q,n,m){
  pf(q/((n*m)/(m-n+1)),n,m-n+1)
}


ConfRadius <- function(model,prob=1-alpha,alpha) {
  sqrt(qHotellingsTsq(prob,ncol(coef(model)),model$df.residual))
}