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#' @title Spatial Rank
#'
#' @description Used to compute the \code{Spatial Rank} of a p-variate observation with respect to a p-variate data cloud.
#' @param x A numeric p-variate vector whose spatial rank is to be calculated.
#' @param data A matrix or a data.frame with each row as a p-variate observation.
#' @author Somedip Karmakar <somedip@yahoo.co.in>
#' @author Omker Mahalanobish <omker.scorpio@gmail.com>
#' @export
#' @return The spatial rank of \code{x} with respect to \code{data}.
#' @examples
#' u<-matrix(rnorm(90,0,1),ncol=3)
#' u0<-runif(3,0,1)
#' spatial.rank(u0,u)
spatial.rank=function(x,data)
{
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)
}
v
}
#' @title Multivariate Quantile
#'
#' @description Used to compute the \code{p-variate quantile} of a p-variate observation with respect to a p-variate data cloud.
#' @param x A numeric p-variate \code{spatial rank}. Elements must lie within -1 and +1, with a 0-vector denoting the median.
#' @param data A matrix or a data.frame with each row as a p-variate observation.
#' @author Somedip Karmakar <somedip@yahoo.co.in>
#' @author Omker Mahalanobish <omker.scorpio@gmail.com>
#' @import stats
#' @export
#' @return The \code{x}th mutivariate quantile with respect to \code{data}.
#' @seealso \code{\link{spatial.rank}}
#' @examples
#' u<-matrix(rnorm(90,0,1),ncol=3)
#' u0<-runif(3,0,1)
#' multi.quant(spatial.rank(u0,u),u)
multi.quant=function(x,data)
{
fr <- function(y) {
s=0
for(i in 1:nrow(data))
{
s=s+sqrt(sum((data[i,]-y)^2))+t(x)%*%(data[i,]-y)
}
s
}
zq=optim(rep(0,ncol(data)), fr)$par
zq
}
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