R/skewsymmetry.R

In asymmetry: Multidimensional Scaling of Asymmetric Proximities

skewsymmetry <- function(x)
{
  if (nrow(x)!=ncol(x)) stop("the same number of rows and columns are expected")
  S <-.5*(t(x)+x)
  A <-.5*(x - t(x))
  lin <- rowMeans(A)
  nobj <- nrow(x)
  Svectors <- matrix(0.0,nrow(x),nrow(x))
  s <- svd(A)
  for(i in seq(1,(nrow(x)-1),by=2)){
    pred1<- s$u[,i:(i+1)] %*% (s$d[i:(i+1)]*diag(2)) %*% t(s$v[,i:(i+1)]) #good
    pred2 <- (s$u[,i]%*%t(s$u[,(i+1)])-s$u[,(i+1)]%*%t(s$u[,i]))*s$d[i]
    if(sum(abs(pred1-pred2)>1e-10)==0)
    {
      Svectors[,i]<-s$u[,i]
      Svectors[,i+1]<-s$u[,i+1]
    } else {
      Svectors[,i+1]<-s$u[,i]
      Svectors[,i]<-s$u[,i+1]
    }
}
  if(!is.null(rownames(x)))
    rownames(Svectors)<-rownames(x)

  lk <- list(S = S, A = A, linear = lin, sv = Svectors, sval = s$d, nobj = nobj)
  class(lk) <- "skewsymmetry"
  lk
}