## The partial regression-on-predecessors scatterplot matrix defined in section 4.3.4 

"partial.r"<-function(x=matrix(rnorm(120),20,6),...){
  # For testing purposes only (set to F if you don't need "2 vs. 1" labels):
  showlabels <- F

  # Make sure x is in matrix form
  x <- as.matrix(x)
  n <- ncol(x)

  # Make sure we clean up our mess (revert back to original "par" parameters)
  # when we're done
  oldpar <- par("pty", "oma", "mar", "cex", "tck",
    "mgp", "mex", "mfrow")
  on.exit({par(oldpar)})

  # Set layout, size and margin parameters
  # make plots square
  par(pty="s")
  # determine new optimal plotting character size
  CEX <- par("cex") * max(7.7/(2*(n-1)+3), 0.6)*0.5
  # specify grid of (n-1) by (n-1) plots
  par(mfcol = c(n-1,n-1))
  # magically cause plots to pack together nicely
  par(oma = rep(3,4))
  par(mar = rep(0.3,4))
  dif <- diff(par("fin"))/2
  if(dif > 0)
    par(omi = c(dif*(n-1), 0, dif*(n-1), 0) + par("omi"))
  else
    par(omi = c(0, (-dif)*(n-1), 0, (-dif)*(n-1)) + par("omi"))
  # re-specify plotting character size (since par(mfrow) screwed it up)
  par(cex = CEX)
  # specify the points type
  par(pch=16)

  
  dat <- x
  m <- n-1  
  mat.x <- NULL
  mat.y <- NULL

  for (k in (1:m)){
   fres <- sapply(1:(m+1-k), function(i) if(k==1 && i==1) dat[,i] else residuals(lm(dat[,i] ~ dat[,c(1:(i+k-1))][,-c(i)])))
   bres <- sapply(1:(m+1-k), function(i) if(k==1 && i==1) dat[,i+k] else residuals(lm(dat[,i+k] ~ dat[,c(1:(i+k-1))][,-c(i)])))
   mat.x <- cbind(mat.x,fres)
   mat.y <- cbind(mat.y,bres)
  }

  locmat <- matrix(rep(0,m^2),nrow=m)
  count <- 0
  for (i in (1:m)){
    for (j in (1:(m+1-i))){
      count <- count+1
      locmat[i,j] <- count
    }
  }
  
  # Make plots (i from top to bottom, j from left to right)
  for (i in (2:n)){
    for(j in (1:(n-1))){
      if (j < i-1){
        # prepare an empty plot with correct limits and no axes
	plot(range(x[!is.na(x[,j]),j]), range(x[!is.na(x[,i]),i]),
	   type = "n", axes = F, ...)
	# create empty plot and put border around it
        box()
	# show points for j'th vs. i'th columns of x
	points(as.vector(x[,j]),as.vector(x[,i]), ...)
	# show which variables are being plotted
	if (showlabels)
	  text(mean(range(x[!is.na(x[,j]),j])),
	mean(range(x[!is.na(x[,i]),i])),
        paste(j,"vs.",i),cex=1.5*CEX)
      }
      else{
        # Get the information of which variables to be plotted against each other on this grid
        loc <- locmat[j-i+2,i-1] 
        # prepare an empty plot with correct limits and no axes
        plot(range(mat.x[!is.na(mat.x[,loc]),loc]), range(mat.y[!is.na(mat.y[,loc]),loc]),     
	   type = "n", axes = F, ...)
        # create empty plot and put border around it
        box()
        # show points for j'th vs. i'th columns of x
        points(as.vector(mat.x[,loc]),as.vector(mat.y[,loc]), ...)
      }
    }
  } 
}