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#' @title Depth-Depth Plots
#'
#' @description \code{dd.plot} is a multivariate genralization of a normal \code{QQ-plot}.
#' It produces a DD-plot of two datasets.
#' @param data1 A matrix or a data.frame with each row as a p-variate observation.
#' @param data2 A matrix or a data.frame (defaults to a standard independent p-variate normal).
#' @param main Plot labels. The title of the plot.
#' @param xlab Plot labels. The \code{x-axis} label of the plot.
#' @param ylab Plot labels. The \code{y-axis} label of the plot.
#' @param col The color of the points
#' @param pch character string or vector of 1-characters or integers for plotting characters.
#' @import mvtnorm
#' @import graphics
#' @author Somedip Karmakar <somedip@yahoo.co.in>
#' @author Omker Mahalanobish <omker.scorpio@gmail.com>
#' @export
#' @seealso \code{\link{spatial.depth}}
#' @return A \code{DD-plot} of the input data
#' @examples
#' u<-matrix(rnorm(300,1,4),ncol=3)
#' dd.plot(u)
#'
dd.plot<-function(data1,data2=rmvnorm(nrow(data1),array(0,ncol(data1)),diag(1,ncol(data1),ncol(data1))),
main="Normal DD-plot",xlab="Sample Depths",ylab="Normal Depths",col="black",pch=20){
spatial.depth=function(data,x){
spd<-function(data,x)
{
v=array(0,ncol(data))
for(j in 1:ncol(data))
{
for(i in 1:nrow(data))
{
if(sqrt(sum((x-data[i,])^2))!=0)
v[j]=v[j]+((x[j]-data[i,j])/sqrt(sum((x-data[i,])^2)))
}
v[j]=v[j]/nrow(data)
}
sd=1-sqrt(sum(v^2))
}
sd<-apply(x,1,function(y){spd(data,y)})
sd
}
something1<-c(spatial.depth(data1,data1),spatial.depth(data1,data2))
something2<-c(spatial.depth(data2,data1),spatial.depth(data2,data2))
x<-cbind(something1,something2)
matplot(x[,1],x[,2],main=main,xlab=xlab,ylab=ylab,col=col,pch=pch)
}
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