Nothing
R/depth.mdata.R
In fda.usc: Functional Data Analysis and Utilities for Statistical Computing
Defines functions
mdepth.Liu1
mdepth.TD1
mdepth.FM1
MhD1
LD1
TD1
Liu1
FM1
mdepth.SD
ntriang
triang
isiindata
mdepth.TD
mdepth.Liu
mdepth.FM
mdepth.MhD
mdepth.RP
mdepth.HS
mdepth.LD
Documented in
mdepth.FM
mdepth.HS
mdepth.LD
mdepth.MhD
mdepth.RP
mdepth.SD
mdepth.TD
#' @name depth.mdata
#'
#' @title Provides the depth measure for multivariate data
#'
#' @description Compute measure of centrality of the multivariate data. Type of depth
#' function: simplicial depth (SD), Mahalanobis depth (MhD), Random Half--Space
#' depth (HS), random projection depth (RP) and Likelihood Depth (LD).
#'
#' @details Type of depth measures:
#' \itemize{
#' \item The \code{\link{mdepth.SD}} calculates the simplicial depth (HD) of the points in \code{x} w.r.t.
#' \code{xx} (for bivariate data).
#' \item The \code{\link{mdepth.HS}} function calculates the random half--space depth (HS)
#' of the points in \code{x} w.r.t. \code{xx} based on random projections \code{proj}.
#' \item The \code{\link{mdepth.MhD}} function calculates the Mahalanobis depth (MhD)
#' of the points in \code{x} w.r.t. \code{xx}.
#' \item The \code{\link{mdepth.RP}} calculates the random' projection depth (RP)
#' of the points in \code{x} w.r.t. \code{xx} based on random projections \code{proj}.
#' \item The \code{\link{mdepth.LD}} calculates the Likelihood depth (LD) of the points
#' in \code{x} w.r.t. \code{xx}.
#' \item The \code{\link{mdepth.TD}} function provides the Tukey depth measure for multivariate data.
# \item The \code{\link{mdepth.MB}} calculates the Modified Band
#depth (MB) of the points in \code{x} w.r.t. \code{xx}. }
#' }
#' @aliases Depth.Multivariate mdepth.FM mdepth.HS mdepth.MhD mdepth.SD mdepth.LD
#' mdepth.TD mdepth.RP mdepth.FSD mdepth.KFSD
#' @param x is a set of points, a d-column matrix.
#' @param xx is a d-dimension multivariate reference sample (a d-column matrix)
#' where \code{x} points are evaluated.
#' @param proj are the directions for random projections, by default 500 random
#' projections generated from a scaled \code{runif(500,-1,1)}.
#' @param scale =TRUE, scale the depth, see \link[base]{scale}.
#' @param metric Metric function, by default \code{\link{metric.dist}}.
#' Distance matrix between \code{x} and \code{xx} is computed.
#' @param xeps Accuracy. The left limit of the empirical distribution function.
#' @param random =TRUE for random projections. =FALSE for deterministic
#' projections.
#' @param h Bandwidth, \code{h>0}. Default argument values are provided as the
#' 15\%--quantile of the distance between \code{x} and \code{xx}.
#' @param trim The alpha of the trimming.
#' @param draw =TRUE, draw the curves, the sample median and trimmed mean.
#' @param dfunc type of univariate depth function used inside depth function:
#' "FM1" refers to the original Fraiman and Muniz univariate depth (default),
#' "TD1" Tukey (Halfspace),"Liu1" for simplical depth, "LD1" for Likelihood
#' depth and "MhD1" for Mahalanobis 1D depth. Also, any user function
#' fulfilling the following pattern \code{FUN.USER(x,xx,...)} and returning a
#' \code{dep} component can be included.
#' @param \dots Further arguments passed to or from other methods.
#' @return
#' \itemize{
#' \item {lmed}{ Index of deepest element \code{median} of \code{xx}.}
#' \item {ltrim}{ Index of set of points \code{x} with trimmed mean
#' \code{mtrim}. }
#' \item {dep}{ Depth of each point \code{x} w.r.t. \code{xx}.}
#' \item {proj}{ The projection value of each point on set of points. }
#' \item {x}{is a set of points to be evaluated.}
#' \item {xx}{ a reference sample}
#' \item {name}{ Name of depth method }
#' }
#' @author \code{\link{mdepth.RP}}, \code{\link{mdepth.MhD}} and
#' \code{\link{mdepth.HS}} are versions created by Manuel Febrero Bande and
#' Manuel Oviedo de la Fuente of the original version created by Jun Li, Juan
#' A. Cuesta Albertos and Regina Y. Liu for polynomial classifier.
#'
#' @seealso Functional depth functions: \code{\link{depth.FM}},
#' \code{\link{depth.mode}}, \code{\link{depth.RP}}, \code{\link{depth.RPD}}
#' and \code{\link{depth.RT}}.
#'
#' @references Liu, R. Y., Parelius, J. M., and Singh, K. (1999). Multivariate
#' analysis by data depth: descriptive statistics, graphics and inference,(with
#' discussion and a rejoinder by Liu and Singh). \emph{The Annals of
#' Statistics}, 27(3), 783-858.
#'
#' @keywords descriptive
#' @examples
#' \dontrun{
#' data(iris)
#' group<-iris[,5]
#' x<-iris[,1:2]
#'
#' MhD<-mdepth.MhD(x)
#' PD<-mdepth.RP(x)
#' HD<-mdepth.HS(x)
#' SD<-mdepth.SD(x)
#'
#' x.setosa<-x[group=="setosa",]
#' x.versicolor<-x[group=="versicolor",]
#' x.virginica<-x[group=="virginica",]
#' d1<-mdepth.SD(x,x.setosa)$dep
#' d2<-mdepth.SD(x,x.versicolor)$dep
#' d3<-mdepth.SD(x,x.virginica)$dep
#' }
#' @rdname depth.mdata
#' @export
mdepth.LD=function(x,xx=x,metric=metric.dist,
h=NULL,scale=FALSE,...){
if (is.vector(x)){
if (all(xx==x)) x<-xx<-matrix(x,ncol=1)#stop("One of x or xx must be a matrix")
else {
m2=ncol(xx)
if (length(x)!=m2) stop("Length of x does not match with dimension of xx")
x=matrix(x,ncol=m2)
}
}
m2=ncol(xx)
n2=nrow(xx)
n<-nrow(x)
m<-ncol(x)
if (is.null(rownames(x))) rownames(x)<-1:nrow(x)
nms<-rownames(x)
x<-na.omit(x)
xx<-na.omit(xx)
nas<-na.action(x)
nullans<-!is.null(nas)
d <- ncol(x)
if (is.null(n) && is.null(m)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.matrix(metric)) {mdist=metric}
else { mdist=metric(xx,xx,...) }
class(mdist)<-"matrix"
if (n==n2 & m==m2) {
equal<-all(x==xx)
if (equal) mdist2<-mdist
else mdist2<-metric(x,xx,...)}
else mdist2<-metric(x,xx,...)
if (is.null(h)) {
h<-0.15
hq2=quantile(mdist,probs=h,na.rm=TRUE)
}
else {
if (is.numeric(h)) hq2<-h
else hq2=quantile(mdist,probs=as.numeric(h),na.rm=TRUE)
}
class(mdist)<-class(mdist2)<-c("matrix")
ans<-Ker.norm(mdist2/hq2) ####
ans<-apply(ans,1,sum,na.rm=TRUE)
mx = scale
if (scale) {
# mn<-min(ans,na.rm=TRUE)
ans2=Ker.norm(mdist/hq2)
ans2=apply(ans2,1,sum,na.rm=TRUE)
mx<-max(ans2,na.rm=TRUE)
ans=as.vector(ans/mx)
}
if (nullans){
ans1<-rep(NA,len=n)
ans1[-nas] <-ans
ans<-ans1
}
names(ans)<-nms
out<-list("dep" = ans,"hq"=hq2,dscale=mx,
x=x,xx=xx,name="LD")
class(out)<-"mdepth"
return(invisible(out))
}
#' @rdname depth.mdata
#' @export
mdepth.HS <-function(x, xx=x,proj=50,scale=FALSE,xeps=1e-15,random=FALSE)
{
#mdepth.HS: calculates the half-space depth (HS) of the points in x w.r.t. xx based on projections
#xx is a d-dimension multivariate sample, a d-column matrix
#x is a set of points, a d-column matrix, x can be missing
#proj are the directions for projections
if (is.vector(x)) {
x<-matrix(x,nrow=1)
# ans<-pmin(sum(x<=xx)/m,sum(x>=xx)/m)
Fn=ecdf(xx)
ans=pmin(Fn(x),(1-Fn(x-xeps)))
if (scale) ans<-ans*2
return(invisible(list(dep = ans, Fn=Fn)))
}
if ( is.null(rownames(x))) rownames(x)<-1:nrow(x)
nms<-rownames(x)
m0<-nrow(x)
xx<-na.omit(xx)
x<-na.omit(x)
nas<-na.action(x)
nullans<-!is.null(nas)
n <- nrow(x)
d <- dim(xx)[2]
lenn<-length(proj)
if (lenn==1) {
mm<-proj[1]
if (d==2 & !random) {
sq<-seq(0,2*pi,len=mm)
# proj<-data.matrix(expand.grid(cos(sq),sin(sq)))
proj2d<-function(angl){matrix(c(cos(angl),sin(angl)),2)}
proj<-t(sapply(sq,proj2d ))
}
else {
if (d==3 & !random) {
mmr=floor(sqrt(mm))+1
phi=seq(0,2*pi,len=mmr)
theta=seq(0,pi,len=mmr)
exgrid=expand.grid(phi=phi,theta=theta)
proj=cbind(sin(exgrid$theta)*cos(exgrid$phi),sin(exgrid$theta)*sin(exgrid$phi),cos(exgrid$theta))
mm<-nrow(proj)
}
else{
warning("Method based on Random Projections")
u <- matrix(runif(d*mm,-1,1),mm,d)
norm <- sqrt(rowSums(u*u))
proj <- (u/norm)
}
}
}
else mm<-nrow(proj)
out <- matrix(0, mm,n)
if (d==3 & !random) {
for(i in 1:mm) {
# z<-t(a[,,i]%*%t(x))# este calculo esta malm debe dar nproj*ndatos
# z2<-t(a[,,i]%*%t(xx))
z <- proj %*% t(x)
z2 <- proj %*% t(xx)
out[i,] <- sapply(z[i,], function(y) min(sum(y<=z2[i,])/n,sum(y>=z2[i,])/n))
}
}
else{
z <- proj %*% t(x)
z2 <- proj %*% t(xx)
for(i in 1:mm) {
out[i,] <- sapply(z[i,], function(y) min(sum(y<=z2[i,])/n,sum(y>=z2[i,])/n))
}
}
ans = as.vector(apply(out,2,min))
if (scale) ans<-ans*2
if (nullans){
ans1<-rep(NA,len=m0)
ans1[-nas] <-ans
ans<-ans1
}
names(ans)<-nms
out <- list(dep = ans, proj = proj, x=x,xx=xx,name="HS")
return(invisible(out))
}
#' @rdname depth.mdata
#' @export
mdepth.RP<-function(x, xx=x,proj=50,scale=FALSE){
#################################################################################################################
# depth.RD: calculates the projection depth (PD) of the points in x w.r.t. xx based on random projections proj
#xx is a d-dimension multivariate sample, a d-column matrix
#x is a set of points, a d-column matrix, x can be missing
#proj are the directions fo random projections
#trim the alpha of the trimming
#draw=TRUE, draw the points in a gray scale of its depth, the sample median (in red) and trimmed mean (in yellow)
#################################################################################################################
if (is.vector(x)){
if (all(xx==x)) x<-xx<-matrix(x,ncol=1)#stop("One of x or xx must be a matrix")
else {
m2=ncol(xx)
if (length(x)!=m2) stop("Length of x does not match with dimension of xx")
x=matrix(x,ncol=m2)
}
}
if ( is.null(rownames(x))) rownames(x)<-1:nrow(x)
nms<-rownames(x)
m0<-nrow(x)
xx<-na.omit(xx)
x<-na.omit(x)
nas<-na.action(x)
nullans<-!is.null(nas)
n <- nrow(x)
d <- ncol(x)
lenn<-length(proj)
if (lenn==1) {
u <- matrix(runif(d*proj,-1,1),proj,d)
norm <- sqrt(rowSums(u*u))
proj <- u/norm
}
z <- proj %*% t(xx)
z1 <- proj %*% t(x)
mm<-nrow(proj)
pdep=matrix(NA,nrow=n,ncol=mm)
for (i in 1:mm){
pdep[,i]=mdepth.TD1(z1[i,],z[i,],scale=scale)$dep
# m1 <- m2 <- rep(0, mm)
# for(i in 1:mm) {
# m1[i]= min(z[i,])
# m2[i]= max(z[i,])
# m1[i] <- median(z[i, ])
# m2[i] <- median(abs(z[i, ] - m1[i]))
}
out1 <- apply(pdep,1,mean)
# for(j in 1:n) { out1[j] <- max(abs(z1[, j] - m1)/m2) }
# for(j in 1:n) { out1[j] <- mean(abs(z1[, j] - m1)/(m2-m1)) }
ans=out1
# ans = 1/(1 + out1)
# if (scale){
# ans<-ans/max(ans) #*2 =/.5
# }
if (nullans){
ans1<-rep(NA,len=m0)
ans1[-nas] <-ans
ans<-ans1
}
names(ans)<-nms
out <- list( dep = ans, proj = proj,x=x,xx=xx,name="RP")
return(invisible(out))
}
#' @rdname depth.mdata
#' @export
mdepth.MhD <- function(x,xx=x,scale=FALSE){
#mdepth.MhD: calculates the Mahalanobis depth (MhD) of the points in x w.r.t. xx
#xx is a d-dimension multivariate sample, a d-column matrix
#x is a set of points, a d-column matrix, x can be missing
#trim the alpha of the trimming
#draw=TRUE, draw the points in a gray scale of its depth, the sample median (in red) and trimmed mean (in yellow)
m0 <- nrow(x)
if (!is.vector(x) & is.null(rownames(x))) rownames(x)<-1:nrow(x)
nms<-rownames(x)
x<-na.omit(x)
xx<-na.omit(xx)
nas<-na.action(x)
nullans<-!is.null(nas)
if (is.vector(x)) {
D<- (1+(x-(mean(xx)))^2/sd(xx)^2)
}
else{
n <- nrow(xx)
m <- nrow(x)
d<-ncol(x)
mu <-colMeans(xx)
sigma <- cov(xx)
D <-rep(0,m)
sigma.inv <- try(solve(sigma),silent=TRUE)#new
if (!is.matrix(sigma.inv)) {
sv<-svd(sigma)
sigma.inv<-sv$v%*%diag(1/sv$d)%*%t(sv$u)
warning("Inverse of sigma computed by SVD")
}
D <- 1+apply(t(x)-mu,2, function(x) t(x)%*%sigma.inv%*%x)
}
ans<-1/D
if (nullans){
ans1<-rep(NA,len=m0)
ans1[-nas] <-1/D
ans<-ans1
}
names(ans)<-nms
# if (scale) { ans <- ans/max(ans) }
out <- list( dep = ans, x=x,xx=xx,name="MhD")
return(invisible(out))
}
#' @rdname depth.mdata
#' @export
mdepth.KFSD=function (x, xx = x, trim = 0.25,
h=NULL,scale = FALSE, draw = FALSE){
if (is.matrix(x) & is.matrix(xx)){
m0=nrow(x)
rownames(x) <- 1:nrow(x)
nms <- rownames(x)
x <- na.omit(x)
xx <- na.omit(xx)
m2 <- ncol(xx)
n2 <- nrow(xx)
n <- nrow(x)
m <- ncol(x)
if (m2!=m) stop ("Error in dimensions of x and xx")
nas <- na.action(x)
nullans <- !is.null(nas)
}
else {
stop("no matrix object")
}
if (is.null(n) && is.null(m))
stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2))
stop("ERROR IN THE DATA DIMENSIONS")
mdist=matrix(NA,ncol=n2,nrow=n2)
for (i in 1:(n2-1)){for (j in (i+1):n2){
mdist[i,j]<-mdist[j,i]<-sqrt(sum((xx[i,]-xx[j,])^2))
}}
if (is.null(h)) {
h<-0.15
hq2=quantile(mdist,probs=h,na.rm=TRUE)
#print("es nulo h")
}
else {
#cat("no es nulo h ",h,"\n")
if (is.numeric(h)) hq2<-h
else hq2=quantile(mdist,probs=as.numeric(h),na.rm=TRUE)
}
kern=function(x,y,h=hq2){exp(-sum((x-y)^2)/h^2)}
K02=rep(1,nrow(x))
K01=rep(1,nrow(xx))
M1=matrix(NA,nrow=n2,ncol=n2)
M2=matrix(NA,nrow=n,ncol=n2)
M=array(NA,dim=c(n,n2,n2))
for (i in 1:n2){for (j in i:n2){
if (i==j) M1[i,i]=K01[i] else M1[i,j]<-M1[j,i]<-kern(xx[i,],xx[j,],h=hq2)
}}
same.dim <- FALSE
if (n==n2 & m==m2){ same.dim <- TRUE}
if (same.dim)
if (all(x==xx)) {
M2=M1
} else {same.dim <- FALSE}
if (!same.dim){
for (i in 1:n){for (j in 1:n2){
if (all(x[i,] == xx[j,])) M2[i,j]=K02[i] else M2[i,j]=kern(x[i,],xx[j,],h=hq2)
}}}
for (i in 1:n){for (j in 1:n2){for (k in 1:n2){
M[i,j,k]<-(K02[i]+M1[j,k]-M2[i,j]-M2[i,k])/(sqrt(K02[i]+K01[j]-2*M2[i,j])*sqrt(K02[i]+K01[k]-2*M2[i,k]))
}}}
l=which(!is.finite(M))
M[l]=NA
dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n
if (scale) {
MO=array(NA,dim=c(n2,n2,n2))
for (i in 1:n2){for (j in 1:n2){for (k in 1:n2){
MO[i,j,k]<-(K02[i]+M1[j,k]-M1[i,j]-M1[i,k])/(sqrt(K02[i]+K01[j]-2*M1[i,j])*sqrt(K02[i]+K01[k]-2*M1[i,k]))
}}}
l=which(!is.finite(MO))
MO[l]=NA
dep2=1-sqrt(apply(MO,1,sum,na.rm=TRUE))/n2
mn <- min(dep2, na.rm = TRUE)
mx <- max(dep2, na.rm = TRUE)
dep = as.vector(dep/mx)
}
if (nullans) {
ans1 <- rep(NA, len = m0)
ans1[-nas] <- dep
dep <- ans1
}
names(dep)=nms
k = which.max(dep)
med = matrix(x[k,],nrow=1)
nl = length(trim)
lista=vector("list",nl)
tr <- paste("KFSD.tr", round(trim * 100,2), "%", sep = "")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim = matrix(NA, nrow = nl, ncol = m)
for (j in 1:length(trim)) {
lista[[j]] = which(dep >= quantile(dep, probs = trim[j], na.rm = TRUE))
if (length(lista[[j]])==1) {
mtrim[j,]<-x[lista[[j]],]
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim[j,]=apply(x[lista[[j]],],2,mean)
}
rownames(med) <- "KFSD.med"
rownames(mtrim) <- tr
out <- list(median = med, lmed = k, mtrim = mtrim, ltrim = if (nl==1) unlist(lista) else lista,
dep = dep, h = h, hq=hq2,name="KFSD")
if (scale)
out$dscale = mx
class(out) <- "mdepth"
if (draw) {
plot.mdepth(x,xx,out)
}
return(invisible(out))
}
#' @rdname depth.mdata
#' @export
mdepth.FSD=function (x, xx = x,
trim = 0.25, scale = FALSE, draw = FALSE){
if (is.matrix(x) & is.matrix(xx)) {
if (is.null(rownames(x)))
rownames(x) <- 1:nrow(x)
nms <- rownames(x)
m0 <- nrow(x)
x <- na.omit(x)
xx <- na.omit(xx)
nas <- na.action(x)
nullans <- !is.null(nas)
n <- nrow(x)
m <- ncol(x)
m2 <- ncol(xx)
n2 <- nrow(xx)
if (m2!=m) stop("Error in data dimensions")
}
else {
stop("no matrix object")
}
if (is.null(n) && is.null(m))
stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2))
stop("ERROR IN THE DATA DIMENSIONS")
kern=function(x,y){sum(x*y)}
K02=diag(x%*%t(x))
K01=diag(xx%*%t(xx))
M1=matrix(NA,nrow=n2,ncol=n2)
M2=matrix(NA,nrow=n,ncol=n2)
M=array(NA,dim=c(n,n2,n2))
if (scale) MO=array(NA,dim=c(n2,n2,n2))
for (i in 1:n2){for (j in i:n2){
if (i==j) M1[i,i]=K01[i] else M1[i,j]<-M1[j,i]<-kern(xx[i,],xx[j,])
}}
same.dim <- FALSE
if (n==n2 & m==m2){ same.dim <- TRUE}
if (same.dim)
if (all(x==xx)) {
M2=M1
} else {same.dim <- FALSE}
if (!same.dim){
for (i in 1:n){for (j in 1:n2){
if (all(x[i,] == xx[j,])) M2[i,j]=K02[i] else M2[i,j]=kern(x[i,],xx[j,])
}}
}
for (i in 1:n){for (j in 1:n2){for (k in 1:n2){
if (all(x[i,] == xx[j,]) | all(x[i,] == xx[k,])) M[i,j,k]=NA else M[i,j,k]<-(K02[i]+M1[j,k]-M2[i,j]-M2[i,k])/(sqrt(K02[i]+K01[j]-2*M2[i,j])*sqrt(K02[i]+K01[k]-2*M2[i,k]))
}}}
l=which(!is.finite(M))
M[l]=NA
dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n
if (scale) {
for (i in 1:n2){for (j in 1:n2){for (k in 1:n2){
if (all(xx[i,] == xx[j,]) | all(xx[i,] == xx[k,])) MO[i,j,k]=NA else MO[i,j,k]<-(K01[i]+M1[j,k]-M1[i,j]-M1[i,k])/(sqrt(K01[i]+K01[j]-2*M1[i,j])*sqrt(K01[i]+K01[k]-2*M1[i,k]))
}}}
l=which(!is.finite(MO))
MO[l]=NA
dep2=1-sqrt(apply(MO,1,sum,na.rm=TRUE))/n2
mn <- min(dep2, na.rm = TRUE)
mx <- max(dep2, na.rm = TRUE)
dep = as.vector(dep/mx)
}
if (nullans) {
ans1 <- rep(NA, len = m0)
ans1[-nas] <- dep
dep <- ans1
}
names(dep)=nms
k = which.max(dep)
med = matrix(x[k,],nrow=1)
nl = length(trim)
lista=vector("list",nl)
tr <- paste("FSD.tr", round(trim * 100,2), "%", sep = "")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim = matrix(NA, nrow = nl, ncol = m)
for (j in 1:length(trim)) {
lista[[j]] = which(dep >= quantile(dep, probs = trim[j], na.rm = TRUE))
if (length(lista[[j]])==1) {
mtrim[j,]<-x[lista[[j]],]
if (draw) {draw=FALSE;warning("Too data in mtrim. The plot is not drawn")}
}
else mtrim[j,]=apply(x[lista[[j]],],2,mean)
}
rownames(med) <- "FSD.med"
rownames(mtrim) <- tr
out <- list(median = med, lmed = k, mtrim = mtrim, ltrim = if (nl==1) unlist(lista) else lista,
dep = dep,name="FSD")
if (scale)
out$dscale <- mx
class(out) <- "mdepth"
if (draw) {
plot.mdepth(out)
}
return(invisible(out))
}
mdepth.MB <-function (x, xx = NULL,trim=0.25, scale=FALSE, draw =FALSE,
grayscale = FALSE, band = FALSE, band.limits = NULL, lty = 1, lwd = 2,
col = NULL, cold = NULL, colRef = NULL, ylim = NULL, cex = 1, ...)
{
x <- data.matrix(x)
n <- nrow(x)
d <- ncol(x)
depth.ori<-NULL
fdataori<-xx
fdataobj<-x
tt<-1:d
# dtt<-c(0,dtt,0)/sum(dtt)*d
if (length(xx) == 0) {
if (ncol(x) == 1) {
x <- t(x)
}
depth <- matrix(0, 1,n)
ordered.matrix <- x
if (n > 1) {
for (columns in 1:d) {
ordered.matrix[, columns] <- sort(x[, columns])
for (element in 1:n) {
index.1 <- length(which(ordered.matrix[, columns] <
(x[element, columns])))
index.2 <- length(which(ordered.matrix[, columns] <=
(x[element, columns])))
multiplicity <- index.2 - index.1
depth[element] <- depth[element]+ index.1 *
(n - (index.2)) + multiplicity * (n - index.2 +
index.1) + choose(multiplicity, 2)
}
}
depth <- depth/(d * choose(n, 2))
}
if (n == 1) {
deepest <- x
depth <- 0
}
ordering <- order(depth, decreasing = TRUE)
#########################################
if (draw) {
par(mar = c(4, 5, 3, 3), xpd = FALSE)
fobj <- t(x[ordering[n:2], ,drop=FALSE ])
lwdd <- lwd[1]
if (is.null(cold)) {
cold <- 2
}
if (is.null(ylim)) {
ylim <- range(x)
}
if (band) {
lty <- lty[1]
if (is.null(band.limits)) {
band.limits <- c(0.5, 1)
}
else {
band.limits <- unique(sort(band.limits))
}
if (floor(n * (band.limits[1])) < 2) {
stop("Check the limits. The band must contain at least 2 curves...")
}
no.poly <- length(band.limits)
if (is.null(col)) {
if (grayscale) {
color <- rev(gray((1:no.poly)/(no.poly +
1)))
}
else {
color <- 3:(2 + no.poly)
}
}
else {
if (length(col) < no.poly) {
color <- rep(col, length.out = no.poly)[1:no.poly]
}
else {
color <- col[1:no.poly]
}
}
par(mar = c(4, 5, 5, 3), xpd = FALSE)
# matplot(Gene.Expression, ylim = ylim, type = "l",lty = 0, ...)
matplot(fobj, ylim = ylim, type = "l",lty = 0, ...)
for (poly in no.poly:1) {
limit <- band.limits[poly]
no.points <- floor(limit * n)
xx2 <- t(x[ordering[no.points:1],])
upper <- apply(xx2, 1, max)
lower <- apply(xx2, 1, min)
polygon(c(tt, rev(tt)), c(upper, rev(lower)),
col = color[poly])
}
}
else {
if (is.null(col)) {
if (grayscale) {
color <- rev(gray((1:n)/(n + 1)))
}
else {
color <- rep(8, n)
}
}
else {
if (length(col) < n) {
color <- rep(col, length.out = n)[n:1]
}
else {
color <- col[n:1]
}
}
matplot(fobj, type = "l", ylim = ylim,lty = lty, lwd = lwd, col = color[n:2], ...)
}
lines(x[ordering[1], ], lty = lty, lwd = lwdd, col = cold)
par(xpd = TRUE)
legend("top", legend = "deepest sample", col = cold,
lty = lty, lwd = lwdd, cex = cex)
if (band) {
legend("top", inset = -0.1 * cex, horiz = TRUE,
legend = band.limits, col = color, pch = 15,
title = "Proportion of central samples", cex = cex,
bty = "n")
}
}
#########################################
}
else {
xRef<-xx
xRef <- data.matrix(xRef)
if (ncol(xRef) != d) {
stop("Dimensions of x and xRef do not match")
}
n0 <- nrow(xRef)
if (ncol(x) == 1) {
x <- t(x)
}
depth <- matrix(0, 1,n)
depth.ori <- matrix(0, 1,n0)
ordered.matrix <- xRef
if (n0 > 1) {
for (columns in 1:d) {
ordered.matrix[, columns] <- sort(xRef[, columns])
for (element in 1:n) {
index.1 <- length(which(ordered.matrix[, columns] <
x[element, columns]))
index.2 <- length(which(ordered.matrix[, columns] <=
x[element, columns]))
multiplicity <- index.2 - index.1
depth[element] <- depth[element]+(index.1 +
multiplicity) * (n0 - index.1 - multiplicity) +
multiplicity * (index.1 + (multiplicity -
1)/2)
}
for (element in 1:n0) {
index.1 <- length(which(ordered.matrix[, columns] <
xRef[element, columns]))
index.2 <- length(which(ordered.matrix[, columns] <=
xRef[element, columns]))
multiplicity <- index.2 - index.1
depth.ori[element] <- depth.ori[element]+(index.1 +
multiplicity) * (n0 - index.1 - multiplicity) +
multiplicity * (index.1 + (multiplicity -
1)/2)
}
}
depth <- depth/(d * choose(n0, 2))
depth.ori <- depth.ori/(d * choose(n0, 2))
}
if (n == 1) {
deepest <- x
depth <- 0
}
ordering <- order(depth, decreasing = TRUE)
if (draw) {
par(mar = c(4, 5, 3, 3), xpd = FALSE)
fdobj<- t(xRef)
if (is.null(colRef)) {
colRef <- 4
}
else {
colRef <- colRef[1]
}
if (is.null(cold)) {
cold <- 2
}
if (is.null(ylim)) {
ylim <- range(x, xRef)
}
lwdd <- lwd[1]
if (band) {
lty <- lty[1]
if (is.null(band.limits)) {
band.limits <- c(0.5, 1)
}
band.limits <- unique(sort(band.limits))
if (floor(n * (band.limits[1])) < 2) {
stop("Check the limits. The band must contain at least 2 curves...")
}
no.poly <- length(band.limits)
par(mar = c(4, 5, 5, 3), xpd = FALSE)
matplot(fdobj, type = "l", ylim = ylim,
lty = lty, lwd = lwd/2, col = colRef, ...)
if (is.null(col)) {
if (grayscale) {
color <- rev(gray((1:no.poly)/(no.poly +
1)))
}
else {
color <- 5:(no.poly + 4)
}
}
else {
if (length(col) < no.poly) {
color <- rep(col, length.out = no.poly)[1:no.poly]
}
else {
color <- col[1:no.poly]
}
}
for (poly in no.poly:1) {
limit <- band.limits[poly]
no.points <- floor(limit * n)
xx2<- t(x[ordering[no.points:1],])
upper <- apply(xx2, 1, max)
lower <- apply(xx2, 1, min)
polygon(c(tt, rev(tt)), c(upper, rev(lower)),
col = color[poly])
}
lines(x[ordering[1], ], lty = lty, lwd = lwdd,
col = cold)
}
else {
matplot(fdobj, type = "l", ylim = ylim,
lty = lty, lwd = lwd/2, col = colRef, ...)
if (is.null(col)) {
if (grayscale) {
color <- rev(gray(1/(n + 1):(n/(n + 1))))
}
else {
color <- rep(8, n)
}
}
else {
if (length(col) < n) {
color <- rep(col, length.out = n)[n:1]
}
else {
color <- col[n:1]
}
}
matlines(t(x[ordering[n:2], ]), lwd = lwd, col = color[n:2],
lty = lty)
lines(x[ordering == 1, ], lwd = lwdd, lty = lty[1],
col = cold)
}
par(xpd = TRUE)
legend("top", legend = c("deepest sample", "reference set"),
col = c(cold, colRef), lty = lty, lwd = c(lwdd,
lwd/2), cex = cex)
if (band) {
legend("top", inset = -0.1 * cex, horiz = TRUE,
legend = band.limits, col = color, pch = 15,
title = "Proportion of central samples", cex = cex,
bty = "n")
}
}
if (scale) depth.ori<-depth.ori/max(depth.ori)
}
med<-fdataobj[ordering[1]]
lista = which(depth >= quantile(depth[1,], probs = trim, na.rm = TRUE))
mtrim= apply(x[lista, ], 2, mean)
# tr<-paste("band.tr",trim*100,"\u0025",sep="")
# names2<-fdataobj[["names"]]
# med$names$main<-"depth.mode median"
# names2$main<-paste("depth.mbandtrim ",trim*100,"\u0025",sep="")
# mtrim<-fdata(mtrim,tt,rtt,names2)
# rownames(med)<-"mode.med"
# rownames(mtrim)<-tr
if (scale) depth[1,]<-depth[1,]/max(depth[1,])
return(invisible(list("median"=med,"lmed"=ordering[1],ordering=ordering,
"mtrim"=mtrim,"ltrim"=lista,"dep"=depth[1,],"dep.ori"=depth.ori)))
}
# multivariate version
#' @rdname depth.mdata
#' @export
mdepth.FM=function(x,xx=x,scale=FALSE,dfunc="TD1"){
n<-nrow(x)
m<-ncol(xx)
d<-matrix(NA,nrow=n,ncol=m)
Fn<-list()
print(m)
par.dfunc<-list()
for (i in 1:m) {
if (dfunc %in% c("TD1","Liu1","FM1")){
Fn[[i]]=ecdf(xx[,i])
par.dfunc$x=x[,i]
par.dfunc$Fn=Fn[[i]]
d[,i]=do.call(dfunc,par.dfunc)
}
else {
par.dfunc$x=x[,i]
par.dfunc$xx=xx[,i]
d[,i]=do.call(dfunc,par.dfunc)
}
}
d<-apply(d,1,mean,na.rm=TRUE)[1:n]
return(list("dep"=d,"Fn"=Fn)) #
}
mdepth.Liu=function(x,xx=x,xeps=1e-15,scale=FALSE){
n<-nrow(x)
m<-ncol(x)
d<-matrix(NA,nrow=n,ncol=m)
Fn<-list()
for (i in 1:m){
Fn[[i]]=ecdf(xx[,i])
d[,i]=Fn[[i]](x[,i])*(1-Fn[[i]](x[,i]-xeps))
}
if (scale){ d<-d*4 }
d<-apply(d,1,mean,na.rm=TRUE)[1:n]
return(list("dep"=d,"Fn"=Fn))
}
# multivariate version
#' @rdname depth.mdata
#' @export
mdepth.TD=function(x,xx=x,xeps=1e-15,scale=FALSE){
#print("entra TD")
n<-nrow(x)
m<-ncol(x)
d<-matrix(NA,nrow=n,ncol=m)
Fn<-list()
for (i in 1:m){
Fn[[i]]=ecdf(xx[,i])
d[,i]=pmin(Fn[[i]](x[,i]),(1-Fn[[i]](x[,i]-xeps)))
}
if (scale){ d<-d*2 }
d<-apply(d,1,mean,na.rm=TRUE)[1:n]
return(list("dep"=d,"Fn"=Fn)) #"dep.ori"=d2,
}
isiindata<-function(i,x){
n<-nrow(x)
ind<-rep(NA,len=n)
for (j in 1:n){
ind[j]<-all(i==x[j,])
}
ind
}
triang=function(Q,P1,P2,P3){
q1=Q-P1;a1=atan2(q1[2],q1[1])
q2=Q-P2;a2=atan2(q2[2],q2[1])
q3=Q-P3;a3=atan2(q3[2],q3[1])
a=sort(c(a1,a2,a3))
return(((a[2]-a[1])<=pi) && ((a[3]-a[2])<=pi) && ((a[3]-a[1])>=pi))
}
ntriang<-function(q,puntos,plot=FALSE){
#print("entra ntriang")
# if (dim(x)[2]!=2) stop("The dimension of the data points is not a 2-column matrix")
# if (dim(x)[1]<3) stop("The dimension of the data points must be at least 3 rows.")
# if (length(q)!=2) stop("El punto q debe tener dos componentes")
n=dim(puntos)[1]
#nq=q-puntos
nq<-sweep(puntos,2,q,"-")
alfa=atan2(nq[,2],nq[,1])
a=sort(alfa)
di<-ci<-numeric(n);di=numeric(n)
#ci=di=numeric(n)
ind.a<-a>0
k<-ifelse(sum(ind.a)>0,min(which(ind.a)),n)
#k=min(min(which(a>0)),n)
#if (is.infinite(k)) k=n
lista=1:(k-1)
for (i in 1:n){
ci[i]=max(which((a-a[i])<=pi))
di[i]=min(c(which((a-a[i])>=pi)),n+1)
}
e1=ci[k]*(ci[k]+1-2*k)+k*(3-k)-2
d1=n*(n-k+1)+0.5*k*(k-1)-0.5*n*(n+1)
e=(lista+n-1)*ci[lista]
f=(ci[lista]+1)*ci[lista]+(di[lista]-1)*(di[lista]-2*lista-2)
sume=sum(e)+0.5*n*e1
sumf=sum(f/2)+n*d1
ttriang=n*(n-1)*(n-2)/6 #n sobre 3
return(list("triang"=sume-sumf,"ttriang"=ttriang))
}
#' @rdname depth.mdata
#' @export
mdepth.SD=function(x,xx=NULL,scale=FALSE){
if (dim(x)[2]!=2) stop("The dimension of the data points is not a 2-column matrix")
if (dim(x)[1]<3) stop("The dimension of the data points must be at least 3 rows.")
if (is.data.frame(x)) {
x <- data.matrix(x)
}
if (is.null(xx)) {
xx<-x
al<-TRUE
}
else {
al<-FALSE
xx <- data.matrix(xx)
}
nam<-colnames(xx)
if ( is.null(rownames(x))) rownames(x)<-1:nrow(x)
nms<-rownames(x)
m0<-nrow(x)
xx<-na.omit(xx)
x<-na.omit(x)
nas<-na.action(x)
nullans<-!is.null(nas)
n=nrow(x)
nn=nrow(xx)
rownames(xx)<-NULL#1:nn
d=ncol(xx)
dep=numeric(n)
if (al){
# print("entra al l")
ttriang=nn*(nn-1)*(nn-2)/6
# print(al); print("all(x==xx)")
fac<-(nn-1)*(nn-2)/2
for (i in 1:n){
# dep[i]=(ntriang(x[i,],x[-i,],TRUE)$triang+(n-1)*(n-2)/2)/ttriang
dep[i]<-ntriang(x[i,],xx[-i,])$triang
# cat("i ",i); print(dep[i])
}
dep<-(dep+fac)/ttriang
}
else{
ttriang=(nn+1)*(nn)*(nn-1)/6
fac<-(nn)*(nn-1)/2
for (i in 1:n){
dep[i]=ntriang(x[i,],xx)$triang
}
dep<-(dep+fac)/ttriang
}
if (scale){
dep<-dep/max(dep)
}
if (nullans){
ans1<-rep(NA,len=m0)
ans1[-nas] <-dep
dep<-ans1
}
names(dep)<-nms
return(invisible(list(dep = dep,x=x,xx=xx)))
}
FM1<-function(x,Fn,scale=FALSE) {
d=1-abs(0.5-Fn(x))
if (scale){ d<-(d-.5)*2 }
d
}
Liu1<-function(x,Fn,xeps=1e-15,scale=FALSE) {
d=Fn(x)*(1-Fn(x-xeps))
if (scale){ d<-d*4 }
d
}
TD1<-function(x,Fn,xeps=1e-15,scale=FALSE) {
d=pmin(Fn(x),(1-Fn(x-xeps))) #HS1D
if (scale){ d<-d*2 }
d
}
LD1<-function(x,xx=x,scale=TRUE) {
mdepth.LD(matrix(x,ncol=1),matrix(xx,ncol=1),scale=scale)$dep
}
MhD1 <- function(x,xx=x,scale=FALSE){
if (is.vector(x)) {
D<- (1+(x-(mean(xx)))^2/sd(xx)^2)
}
else{stop("x is no a vector") }
ans <- 1/D
ans
}
# Univariate version
mdepth.FM1=function(x,xx=x,scale=FALSE){
isx<-is.vector(x)
isxx<-is.vector(xx)
if (!isx) stop("x object is not a vector")
if (!isxx) stop("xx object is not a vector")
n<-length(x)
m<-length(xx)
if (n!=m) stop("The length of x is not the same of xx")
Fn<-list()
Fn=ecdf(xx)
d=1-abs(0.5-Fn(x))
if (scale){ d<-(d-.5)*2 }
return(list("dep"=d,"Fn"=Fn)) #
}
# univariate version
mdepth.TD1=function(x,xx=x,xeps=1e-15,scale=FALSE){
#print("entra TD")
isx<-is.vector(x)
isxx<-is.vector(xx)
if (!isx) stop("x object is not a vector")
if (!isxx) stop("xx object is not a vector")
n<-length(x)
m<-length(xx)
if (n!=m) stop("The length of x is not the same of xx")
Fn=ecdf(xx)
d=pmin(Fn(x),(1-Fn(x-xeps)))
if (scale){ d<-d*2 }
return(list("dep"=d,"Fn"=Fn)) #
}
# univariate version
mdepth.Liu1=function(x,xx=x,xeps=1e-15,scale=FALSE){
isx<-is.vector(x)
isxx<-is.vector(xx)
if (!isx) stop("x object is not a vector")
if (!isxx) stop("xx object is not a vector")
n<-length(x)
m<-length(xx)
if (n!=m) stop("The length of x is not the same of xx")
Fn=ecdf(xx)
d=Fn(x)*(1-Fn(x-xeps))
if (scale){ d<-d*4 }
return(list("dep"=d,"Fn"=Fn))
}
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Defines functions mdepth.Liu1 mdepth.TD1 mdepth.FM1 MhD1 LD1 TD1 Liu1 FM1 mdepth.SD ntriang triang isiindata mdepth.TD mdepth.Liu mdepth.FM mdepth.MhD mdepth.RP mdepth.HS mdepth.LD
Documented in mdepth.FM mdepth.HS mdepth.LD mdepth.MhD mdepth.RP mdepth.SD mdepth.TD
#' @name depth.mdata
#'
#' @title Provides the depth measure for multivariate data
#'
#' @description Compute measure of centrality of the multivariate data. Type of depth
#' function: simplicial depth (SD), Mahalanobis depth (MhD), Random Half--Space
#' depth (HS), random projection depth (RP) and Likelihood Depth (LD).
#'
#' @details Type of depth measures:
#' \itemize{
#' \item The \code{\link{mdepth.SD}} calculates the simplicial depth (HD) of the points in \code{x} w.r.t.
#' \code{xx} (for bivariate data).
#' \item The \code{\link{mdepth.HS}} function calculates the random half--space depth (HS)
#' of the points in \code{x} w.r.t. \code{xx} based on random projections \code{proj}.
#' \item The \code{\link{mdepth.MhD}} function calculates the Mahalanobis depth (MhD)
#' of the points in \code{x} w.r.t. \code{xx}.
#' \item The \code{\link{mdepth.RP}} calculates the random' projection depth (RP)
#' of the points in \code{x} w.r.t. \code{xx} based on random projections \code{proj}.
#' \item The \code{\link{mdepth.LD}} calculates the Likelihood depth (LD) of the points
#' in \code{x} w.r.t. \code{xx}.
#' \item The \code{\link{mdepth.TD}} function provides the Tukey depth measure for multivariate data.
# \item The \code{\link{mdepth.MB}} calculates the Modified Band
#depth (MB) of the points in \code{x} w.r.t. \code{xx}. }
#' }
#' @aliases Depth.Multivariate mdepth.FM mdepth.HS mdepth.MhD mdepth.SD mdepth.LD
#' mdepth.TD mdepth.RP mdepth.FSD mdepth.KFSD
#' @param x is a set of points, a d-column matrix.
#' @param xx is a d-dimension multivariate reference sample (a d-column matrix)
#' where \code{x} points are evaluated.
#' @param proj are the directions for random projections, by default 500 random
#' projections generated from a scaled \code{runif(500,-1,1)}.
#' @param scale =TRUE, scale the depth, see \link[base]{scale}.
#' @param metric Metric function, by default \code{\link{metric.dist}}.
#' Distance matrix between \code{x} and \code{xx} is computed.
#' @param xeps Accuracy. The left limit of the empirical distribution function.
#' @param random =TRUE for random projections. =FALSE for deterministic
#' projections.
#' @param h Bandwidth, \code{h>0}. Default argument values are provided as the
#' 15\%--quantile of the distance between \code{x} and \code{xx}.
#' @param trim The alpha of the trimming.
#' @param draw =TRUE, draw the curves, the sample median and trimmed mean.
#' @param dfunc type of univariate depth function used inside depth function:
#' "FM1" refers to the original Fraiman and Muniz univariate depth (default),
#' "TD1" Tukey (Halfspace),"Liu1" for simplical depth, "LD1" for Likelihood
#' depth and "MhD1" for Mahalanobis 1D depth. Also, any user function
#' fulfilling the following pattern \code{FUN.USER(x,xx,...)} and returning a
#' \code{dep} component can be included.
#' @param \dots Further arguments passed to or from other methods.
#' @return
#' \itemize{
#' \item {lmed}{ Index of deepest element \code{median} of \code{xx}.}
#' \item {ltrim}{ Index of set of points \code{x} with trimmed mean
#' \code{mtrim}. }
#' \item {dep}{ Depth of each point \code{x} w.r.t. \code{xx}.}
#' \item {proj}{ The projection value of each point on set of points. }
#' \item {x}{is a set of points to be evaluated.}
#' \item {xx}{ a reference sample}
#' \item {name}{ Name of depth method }
#' }
#' @author \code{\link{mdepth.RP}}, \code{\link{mdepth.MhD}} and
#' \code{\link{mdepth.HS}} are versions created by Manuel Febrero Bande and
#' Manuel Oviedo de la Fuente of the original version created by Jun Li, Juan
#' A. Cuesta Albertos and Regina Y. Liu for polynomial classifier.
#'
#' @seealso Functional depth functions: \code{\link{depth.FM}},
#' \code{\link{depth.mode}}, \code{\link{depth.RP}}, \code{\link{depth.RPD}}
#' and \code{\link{depth.RT}}.
#'
#' @references Liu, R. Y., Parelius, J. M., and Singh, K. (1999). Multivariate
#' analysis by data depth: descriptive statistics, graphics and inference,(with
#' discussion and a rejoinder by Liu and Singh). \emph{The Annals of
#' Statistics}, 27(3), 783-858.
#'
#' @keywords descriptive
#' @examples
#' \dontrun{
#' data(iris)
#' group<-iris[,5]
#' x<-iris[,1:2]
#'
#' MhD<-mdepth.MhD(x)
#' PD<-mdepth.RP(x)
#' HD<-mdepth.HS(x)
#' SD<-mdepth.SD(x)
#'
#' x.setosa<-x[group=="setosa",]
#' x.versicolor<-x[group=="versicolor",]
#' x.virginica<-x[group=="virginica",]
#' d1<-mdepth.SD(x,x.setosa)$dep
#' d2<-mdepth.SD(x,x.versicolor)$dep
#' d3<-mdepth.SD(x,x.virginica)$dep
#' }
#' @rdname depth.mdata
#' @export
mdepth.LD=function(x,xx=x,metric=metric.dist,
h=NULL,scale=FALSE,...){
if (is.vector(x)){
if (all(xx==x)) x<-xx<-matrix(x,ncol=1)#stop("One of x or xx must be a matrix")
else {
m2=ncol(xx)
if (length(x)!=m2) stop("Length of x does not match with dimension of xx")
x=matrix(x,ncol=m2)
}
}
m2=ncol(xx)
n2=nrow(xx)
n<-nrow(x)
m<-ncol(x)
if (is.null(rownames(x))) rownames(x)<-1:nrow(x)
nms<-rownames(x)
x<-na.omit(x)
xx<-na.omit(xx)
nas<-na.action(x)
nullans<-!is.null(nas)
d <- ncol(x)
if (is.null(n) && is.null(m)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.matrix(metric)) {mdist=metric}
else { mdist=metric(xx,xx,...) }
class(mdist)<-"matrix"
if (n==n2 & m==m2) {
equal<-all(x==xx)
if (equal) mdist2<-mdist
else mdist2<-metric(x,xx,...)}
else mdist2<-metric(x,xx,...)
if (is.null(h)) {
h<-0.15
hq2=quantile(mdist,probs=h,na.rm=TRUE)
}
else {
if (is.numeric(h)) hq2<-h
else hq2=quantile(mdist,probs=as.numeric(h),na.rm=TRUE)
}
class(mdist)<-class(mdist2)<-c("matrix")
ans<-Ker.norm(mdist2/hq2) ####
ans<-apply(ans,1,sum,na.rm=TRUE)
mx = scale
if (scale) {
# mn<-min(ans,na.rm=TRUE)
ans2=Ker.norm(mdist/hq2)
ans2=apply(ans2,1,sum,na.rm=TRUE)
mx<-max(ans2,na.rm=TRUE)
ans=as.vector(ans/mx)
}
if (nullans){
ans1<-rep(NA,len=n)
ans1[-nas] <-ans
ans<-ans1
}
names(ans)<-nms
out<-list("dep" = ans,"hq"=hq2,dscale=mx,
x=x,xx=xx,name="LD")
class(out)<-"mdepth"
return(invisible(out))
}
#' @rdname depth.mdata
#' @export
mdepth.HS <-function(x, xx=x,proj=50,scale=FALSE,xeps=1e-15,random=FALSE)
{
#mdepth.HS: calculates the half-space depth (HS) of the points in x w.r.t. xx based on projections
#xx is a d-dimension multivariate sample, a d-column matrix
#x is a set of points, a d-column matrix, x can be missing
#proj are the directions for projections
if (is.vector(x)) {
x<-matrix(x,nrow=1)
# ans<-pmin(sum(x<=xx)/m,sum(x>=xx)/m)
Fn=ecdf(xx)
ans=pmin(Fn(x),(1-Fn(x-xeps)))
if (scale) ans<-ans*2
return(invisible(list(dep = ans, Fn=Fn)))
}
if ( is.null(rownames(x))) rownames(x)<-1:nrow(x)
nms<-rownames(x)
m0<-nrow(x)
xx<-na.omit(xx)
x<-na.omit(x)
nas<-na.action(x)
nullans<-!is.null(nas)
n <- nrow(x)
d <- dim(xx)[2]
lenn<-length(proj)
if (lenn==1) {
mm<-proj[1]
if (d==2 & !random) {
sq<-seq(0,2*pi,len=mm)
# proj<-data.matrix(expand.grid(cos(sq),sin(sq)))
proj2d<-function(angl){matrix(c(cos(angl),sin(angl)),2)}
proj<-t(sapply(sq,proj2d ))
}
else {
if (d==3 & !random) {
mmr=floor(sqrt(mm))+1
phi=seq(0,2*pi,len=mmr)
theta=seq(0,pi,len=mmr)
exgrid=expand.grid(phi=phi,theta=theta)
proj=cbind(sin(exgrid$theta)*cos(exgrid$phi),sin(exgrid$theta)*sin(exgrid$phi),cos(exgrid$theta))
mm<-nrow(proj)
}
else{
warning("Method based on Random Projections")
u <- matrix(runif(d*mm,-1,1),mm,d)
norm <- sqrt(rowSums(u*u))
proj <- (u/norm)
}
}
}
else mm<-nrow(proj)
out <- matrix(0, mm,n)
if (d==3 & !random) {
for(i in 1:mm) {
# z<-t(a[,,i]%*%t(x))# este calculo esta malm debe dar nproj*ndatos
# z2<-t(a[,,i]%*%t(xx))
z <- proj %*% t(x)
z2 <- proj %*% t(xx)
out[i,] <- sapply(z[i,], function(y) min(sum(y<=z2[i,])/n,sum(y>=z2[i,])/n))
}
}
else{
z <- proj %*% t(x)
z2 <- proj %*% t(xx)
for(i in 1:mm) {
out[i,] <- sapply(z[i,], function(y) min(sum(y<=z2[i,])/n,sum(y>=z2[i,])/n))
}
}
ans = as.vector(apply(out,2,min))
if (scale) ans<-ans*2
if (nullans){
ans1<-rep(NA,len=m0)
ans1[-nas] <-ans
ans<-ans1
}
names(ans)<-nms
out <- list(dep = ans, proj = proj, x=x,xx=xx,name="HS")
return(invisible(out))
}
#' @rdname depth.mdata
#' @export
mdepth.RP<-function(x, xx=x,proj=50,scale=FALSE){
#################################################################################################################
# depth.RD: calculates the projection depth (PD) of the points in x w.r.t. xx based on random projections proj
#xx is a d-dimension multivariate sample, a d-column matrix
#x is a set of points, a d-column matrix, x can be missing
#proj are the directions fo random projections
#trim the alpha of the trimming
#draw=TRUE, draw the points in a gray scale of its depth, the sample median (in red) and trimmed mean (in yellow)
#################################################################################################################
if (is.vector(x)){
if (all(xx==x)) x<-xx<-matrix(x,ncol=1)#stop("One of x or xx must be a matrix")
else {
m2=ncol(xx)
if (length(x)!=m2) stop("Length of x does not match with dimension of xx")
x=matrix(x,ncol=m2)
}
}
if ( is.null(rownames(x))) rownames(x)<-1:nrow(x)
nms<-rownames(x)
m0<-nrow(x)
xx<-na.omit(xx)
x<-na.omit(x)
nas<-na.action(x)
nullans<-!is.null(nas)
n <- nrow(x)
d <- ncol(x)
lenn<-length(proj)
if (lenn==1) {
u <- matrix(runif(d*proj,-1,1),proj,d)
norm <- sqrt(rowSums(u*u))
proj <- u/norm
}
z <- proj %*% t(xx)
z1 <- proj %*% t(x)
mm<-nrow(proj)
pdep=matrix(NA,nrow=n,ncol=mm)
for (i in 1:mm){
pdep[,i]=mdepth.TD1(z1[i,],z[i,],scale=scale)$dep
# m1 <- m2 <- rep(0, mm)
# for(i in 1:mm) {
# m1[i]= min(z[i,])
# m2[i]= max(z[i,])
# m1[i] <- median(z[i, ])
# m2[i] <- median(abs(z[i, ] - m1[i]))
}
out1 <- apply(pdep,1,mean)
# for(j in 1:n) { out1[j] <- max(abs(z1[, j] - m1)/m2) }
# for(j in 1:n) { out1[j] <- mean(abs(z1[, j] - m1)/(m2-m1)) }
ans=out1
# ans = 1/(1 + out1)
# if (scale){
# ans<-ans/max(ans) #*2 =/.5
# }
if (nullans){
ans1<-rep(NA,len=m0)
ans1[-nas] <-ans
ans<-ans1
}
names(ans)<-nms
out <- list( dep = ans, proj = proj,x=x,xx=xx,name="RP")
return(invisible(out))
}
#' @rdname depth.mdata
#' @export
mdepth.MhD <- function(x,xx=x,scale=FALSE){
#mdepth.MhD: calculates the Mahalanobis depth (MhD) of the points in x w.r.t. xx
#xx is a d-dimension multivariate sample, a d-column matrix
#x is a set of points, a d-column matrix, x can be missing
#trim the alpha of the trimming
#draw=TRUE, draw the points in a gray scale of its depth, the sample median (in red) and trimmed mean (in yellow)
m0 <- nrow(x)
if (!is.vector(x) & is.null(rownames(x))) rownames(x)<-1:nrow(x)
nms<-rownames(x)
x<-na.omit(x)
xx<-na.omit(xx)
nas<-na.action(x)
nullans<-!is.null(nas)
if (is.vector(x)) {
D<- (1+(x-(mean(xx)))^2/sd(xx)^2)
}
else{
n <- nrow(xx)
m <- nrow(x)
d<-ncol(x)
mu <-colMeans(xx)
sigma <- cov(xx)
D <-rep(0,m)
sigma.inv <- try(solve(sigma),silent=TRUE)#new
if (!is.matrix(sigma.inv)) {
sv<-svd(sigma)
sigma.inv<-sv$v%*%diag(1/sv$d)%*%t(sv$u)
warning("Inverse of sigma computed by SVD")
}
D <- 1+apply(t(x)-mu,2, function(x) t(x)%*%sigma.inv%*%x)
}
ans<-1/D
if (nullans){
ans1<-rep(NA,len=m0)
ans1[-nas] <-1/D
ans<-ans1
}
names(ans)<-nms
# if (scale) { ans <- ans/max(ans) }
out <- list( dep = ans, x=x,xx=xx,name="MhD")
return(invisible(out))
}
#' @rdname depth.mdata
#' @export
mdepth.KFSD=function (x, xx = x, trim = 0.25,
h=NULL,scale = FALSE, draw = FALSE){
if (is.matrix(x) & is.matrix(xx)){
m0=nrow(x)
rownames(x) <- 1:nrow(x)
nms <- rownames(x)
x <- na.omit(x)
xx <- na.omit(xx)
m2 <- ncol(xx)
n2 <- nrow(xx)
n <- nrow(x)
m <- ncol(x)
if (m2!=m) stop ("Error in dimensions of x and xx")
nas <- na.action(x)
nullans <- !is.null(nas)
}
else {
stop("no matrix object")
}
if (is.null(n) && is.null(m))
stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2))
stop("ERROR IN THE DATA DIMENSIONS")
mdist=matrix(NA,ncol=n2,nrow=n2)
for (i in 1:(n2-1)){for (j in (i+1):n2){
mdist[i,j]<-mdist[j,i]<-sqrt(sum((xx[i,]-xx[j,])^2))
}}
if (is.null(h)) {
h<-0.15
hq2=quantile(mdist,probs=h,na.rm=TRUE)
#print("es nulo h")
}
else {
#cat("no es nulo h ",h,"\n")
if (is.numeric(h)) hq2<-h
else hq2=quantile(mdist,probs=as.numeric(h),na.rm=TRUE)
}
kern=function(x,y,h=hq2){exp(-sum((x-y)^2)/h^2)}
K02=rep(1,nrow(x))
K01=rep(1,nrow(xx))
M1=matrix(NA,nrow=n2,ncol=n2)
M2=matrix(NA,nrow=n,ncol=n2)
M=array(NA,dim=c(n,n2,n2))
for (i in 1:n2){for (j in i:n2){
if (i==j) M1[i,i]=K01[i] else M1[i,j]<-M1[j,i]<-kern(xx[i,],xx[j,],h=hq2)
}}
same.dim <- FALSE
if (n==n2 & m==m2){ same.dim <- TRUE}
if (same.dim)
if (all(x==xx)) {
M2=M1
} else {same.dim <- FALSE}
if (!same.dim){
for (i in 1:n){for (j in 1:n2){
if (all(x[i,] == xx[j,])) M2[i,j]=K02[i] else M2[i,j]=kern(x[i,],xx[j,],h=hq2)
}}}
for (i in 1:n){for (j in 1:n2){for (k in 1:n2){
M[i,j,k]<-(K02[i]+M1[j,k]-M2[i,j]-M2[i,k])/(sqrt(K02[i]+K01[j]-2*M2[i,j])*sqrt(K02[i]+K01[k]-2*M2[i,k]))
}}}
l=which(!is.finite(M))
M[l]=NA
dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n
if (scale) {
MO=array(NA,dim=c(n2,n2,n2))
for (i in 1:n2){for (j in 1:n2){for (k in 1:n2){
MO[i,j,k]<-(K02[i]+M1[j,k]-M1[i,j]-M1[i,k])/(sqrt(K02[i]+K01[j]-2*M1[i,j])*sqrt(K02[i]+K01[k]-2*M1[i,k]))
}}}
l=which(!is.finite(MO))
MO[l]=NA
dep2=1-sqrt(apply(MO,1,sum,na.rm=TRUE))/n2
mn <- min(dep2, na.rm = TRUE)
mx <- max(dep2, na.rm = TRUE)
dep = as.vector(dep/mx)
}
if (nullans) {
ans1 <- rep(NA, len = m0)
ans1[-nas] <- dep
dep <- ans1
}
names(dep)=nms
k = which.max(dep)
med = matrix(x[k,],nrow=1)
nl = length(trim)
lista=vector("list",nl)
tr <- paste("KFSD.tr", round(trim * 100,2), "%", sep = "")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim = matrix(NA, nrow = nl, ncol = m)
for (j in 1:length(trim)) {
lista[[j]] = which(dep >= quantile(dep, probs = trim[j], na.rm = TRUE))
if (length(lista[[j]])==1) {
mtrim[j,]<-x[lista[[j]],]
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim[j,]=apply(x[lista[[j]],],2,mean)
}
rownames(med) <- "KFSD.med"
rownames(mtrim) <- tr
out <- list(median = med, lmed = k, mtrim = mtrim, ltrim = if (nl==1) unlist(lista) else lista,
dep = dep, h = h, hq=hq2,name="KFSD")
if (scale)
out$dscale = mx
class(out) <- "mdepth"
if (draw) {
plot.mdepth(x,xx,out)
}
return(invisible(out))
}
#' @rdname depth.mdata
#' @export
mdepth.FSD=function (x, xx = x,
trim = 0.25, scale = FALSE, draw = FALSE){
if (is.matrix(x) & is.matrix(xx)) {
if (is.null(rownames(x)))
rownames(x) <- 1:nrow(x)
nms <- rownames(x)
m0 <- nrow(x)
x <- na.omit(x)
xx <- na.omit(xx)
nas <- na.action(x)
nullans <- !is.null(nas)
n <- nrow(x)
m <- ncol(x)
m2 <- ncol(xx)
n2 <- nrow(xx)
if (m2!=m) stop("Error in data dimensions")
}
else {
stop("no matrix object")
}
if (is.null(n) && is.null(m))
stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2))
stop("ERROR IN THE DATA DIMENSIONS")
kern=function(x,y){sum(x*y)}
K02=diag(x%*%t(x))
K01=diag(xx%*%t(xx))
M1=matrix(NA,nrow=n2,ncol=n2)
M2=matrix(NA,nrow=n,ncol=n2)
M=array(NA,dim=c(n,n2,n2))
if (scale) MO=array(NA,dim=c(n2,n2,n2))
for (i in 1:n2){for (j in i:n2){
if (i==j) M1[i,i]=K01[i] else M1[i,j]<-M1[j,i]<-kern(xx[i,],xx[j,])
}}
same.dim <- FALSE
if (n==n2 & m==m2){ same.dim <- TRUE}
if (same.dim)
if (all(x==xx)) {
M2=M1
} else {same.dim <- FALSE}
if (!same.dim){
for (i in 1:n){for (j in 1:n2){
if (all(x[i,] == xx[j,])) M2[i,j]=K02[i] else M2[i,j]=kern(x[i,],xx[j,])
}}
}
for (i in 1:n){for (j in 1:n2){for (k in 1:n2){
if (all(x[i,] == xx[j,]) | all(x[i,] == xx[k,])) M[i,j,k]=NA else M[i,j,k]<-(K02[i]+M1[j,k]-M2[i,j]-M2[i,k])/(sqrt(K02[i]+K01[j]-2*M2[i,j])*sqrt(K02[i]+K01[k]-2*M2[i,k]))
}}}
l=which(!is.finite(M))
M[l]=NA
dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n
if (scale) {
for (i in 1:n2){for (j in 1:n2){for (k in 1:n2){
if (all(xx[i,] == xx[j,]) | all(xx[i,] == xx[k,])) MO[i,j,k]=NA else MO[i,j,k]<-(K01[i]+M1[j,k]-M1[i,j]-M1[i,k])/(sqrt(K01[i]+K01[j]-2*M1[i,j])*sqrt(K01[i]+K01[k]-2*M1[i,k]))
}}}
l=which(!is.finite(MO))
MO[l]=NA
dep2=1-sqrt(apply(MO,1,sum,na.rm=TRUE))/n2
mn <- min(dep2, na.rm = TRUE)
mx <- max(dep2, na.rm = TRUE)
dep = as.vector(dep/mx)
}
if (nullans) {
ans1 <- rep(NA, len = m0)
ans1[-nas] <- dep
dep <- ans1
}
names(dep)=nms
k = which.max(dep)
med = matrix(x[k,],nrow=1)
nl = length(trim)
lista=vector("list",nl)
tr <- paste("FSD.tr", round(trim * 100,2), "%", sep = "")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim = matrix(NA, nrow = nl, ncol = m)
for (j in 1:length(trim)) {
lista[[j]] = which(dep >= quantile(dep, probs = trim[j], na.rm = TRUE))
if (length(lista[[j]])==1) {
mtrim[j,]<-x[lista[[j]],]
if (draw) {draw=FALSE;warning("Too data in mtrim. The plot is not drawn")}
}
else mtrim[j,]=apply(x[lista[[j]],],2,mean)
}
rownames(med) <- "FSD.med"
rownames(mtrim) <- tr
out <- list(median = med, lmed = k, mtrim = mtrim, ltrim = if (nl==1) unlist(lista) else lista,
dep = dep,name="FSD")
if (scale)
out$dscale <- mx
class(out) <- "mdepth"
if (draw) {
plot.mdepth(out)
}
return(invisible(out))
}
mdepth.MB <-function (x, xx = NULL,trim=0.25, scale=FALSE, draw =FALSE,
grayscale = FALSE, band = FALSE, band.limits = NULL, lty = 1, lwd = 2,
col = NULL, cold = NULL, colRef = NULL, ylim = NULL, cex = 1, ...)
{
x <- data.matrix(x)
n <- nrow(x)
d <- ncol(x)
depth.ori<-NULL
fdataori<-xx
fdataobj<-x
tt<-1:d
# dtt<-c(0,dtt,0)/sum(dtt)*d
if (length(xx) == 0) {
if (ncol(x) == 1) {
x <- t(x)
}
depth <- matrix(0, 1,n)
ordered.matrix <- x
if (n > 1) {
for (columns in 1:d) {
ordered.matrix[, columns] <- sort(x[, columns])
for (element in 1:n) {
index.1 <- length(which(ordered.matrix[, columns] <
(x[element, columns])))
index.2 <- length(which(ordered.matrix[, columns] <=
(x[element, columns])))
multiplicity <- index.2 - index.1
depth[element] <- depth[element]+ index.1 *
(n - (index.2)) + multiplicity * (n - index.2 +
index.1) + choose(multiplicity, 2)
}
}
depth <- depth/(d * choose(n, 2))
}
if (n == 1) {
deepest <- x
depth <- 0
}
ordering <- order(depth, decreasing = TRUE)
#########################################
if (draw) {
par(mar = c(4, 5, 3, 3), xpd = FALSE)
fobj <- t(x[ordering[n:2], ,drop=FALSE ])
lwdd <- lwd[1]
if (is.null(cold)) {
cold <- 2
}
if (is.null(ylim)) {
ylim <- range(x)
}
if (band) {
lty <- lty[1]
if (is.null(band.limits)) {
band.limits <- c(0.5, 1)
}
else {
band.limits <- unique(sort(band.limits))
}
if (floor(n * (band.limits[1])) < 2) {
stop("Check the limits. The band must contain at least 2 curves...")
}
no.poly <- length(band.limits)
if (is.null(col)) {
if (grayscale) {
color <- rev(gray((1:no.poly)/(no.poly +
1)))
}
else {
color <- 3:(2 + no.poly)
}
}
else {
if (length(col) < no.poly) {
color <- rep(col, length.out = no.poly)[1:no.poly]
}
else {
color <- col[1:no.poly]
}
}
par(mar = c(4, 5, 5, 3), xpd = FALSE)
# matplot(Gene.Expression, ylim = ylim, type = "l",lty = 0, ...)
matplot(fobj, ylim = ylim, type = "l",lty = 0, ...)
for (poly in no.poly:1) {
limit <- band.limits[poly]
no.points <- floor(limit * n)
xx2 <- t(x[ordering[no.points:1],])
upper <- apply(xx2, 1, max)
lower <- apply(xx2, 1, min)
polygon(c(tt, rev(tt)), c(upper, rev(lower)),
col = color[poly])
}
}
else {
if (is.null(col)) {
if (grayscale) {
color <- rev(gray((1:n)/(n + 1)))
}
else {
color <- rep(8, n)
}
}
else {
if (length(col) < n) {
color <- rep(col, length.out = n)[n:1]
}
else {
color <- col[n:1]
}
}
matplot(fobj, type = "l", ylim = ylim,lty = lty, lwd = lwd, col = color[n:2], ...)
}
lines(x[ordering[1], ], lty = lty, lwd = lwdd, col = cold)
par(xpd = TRUE)
legend("top", legend = "deepest sample", col = cold,
lty = lty, lwd = lwdd, cex = cex)
if (band) {
legend("top", inset = -0.1 * cex, horiz = TRUE,
legend = band.limits, col = color, pch = 15,
title = "Proportion of central samples", cex = cex,
bty = "n")
}
}
#########################################
}
else {
xRef<-xx
xRef <- data.matrix(xRef)
if (ncol(xRef) != d) {
stop("Dimensions of x and xRef do not match")
}
n0 <- nrow(xRef)
if (ncol(x) == 1) {
x <- t(x)
}
depth <- matrix(0, 1,n)
depth.ori <- matrix(0, 1,n0)
ordered.matrix <- xRef
if (n0 > 1) {
for (columns in 1:d) {
ordered.matrix[, columns] <- sort(xRef[, columns])
for (element in 1:n) {
index.1 <- length(which(ordered.matrix[, columns] <
x[element, columns]))
index.2 <- length(which(ordered.matrix[, columns] <=
x[element, columns]))
multiplicity <- index.2 - index.1
depth[element] <- depth[element]+(index.1 +
multiplicity) * (n0 - index.1 - multiplicity) +
multiplicity * (index.1 + (multiplicity -
1)/2)
}
for (element in 1:n0) {
index.1 <- length(which(ordered.matrix[, columns] <
xRef[element, columns]))
index.2 <- length(which(ordered.matrix[, columns] <=
xRef[element, columns]))
multiplicity <- index.2 - index.1
depth.ori[element] <- depth.ori[element]+(index.1 +
multiplicity) * (n0 - index.1 - multiplicity) +
multiplicity * (index.1 + (multiplicity -
1)/2)
}
}
depth <- depth/(d * choose(n0, 2))
depth.ori <- depth.ori/(d * choose(n0, 2))
}
if (n == 1) {
deepest <- x
depth <- 0
}
ordering <- order(depth, decreasing = TRUE)
if (draw) {
par(mar = c(4, 5, 3, 3), xpd = FALSE)
fdobj<- t(xRef)
if (is.null(colRef)) {
colRef <- 4
}
else {
colRef <- colRef[1]
}
if (is.null(cold)) {
cold <- 2
}
if (is.null(ylim)) {
ylim <- range(x, xRef)
}
lwdd <- lwd[1]
if (band) {
lty <- lty[1]
if (is.null(band.limits)) {
band.limits <- c(0.5, 1)
}
band.limits <- unique(sort(band.limits))
if (floor(n * (band.limits[1])) < 2) {
stop("Check the limits. The band must contain at least 2 curves...")
}
no.poly <- length(band.limits)
par(mar = c(4, 5, 5, 3), xpd = FALSE)
matplot(fdobj, type = "l", ylim = ylim,
lty = lty, lwd = lwd/2, col = colRef, ...)
if (is.null(col)) {
if (grayscale) {
color <- rev(gray((1:no.poly)/(no.poly +
1)))
}
else {
color <- 5:(no.poly + 4)
}
}
else {
if (length(col) < no.poly) {
color <- rep(col, length.out = no.poly)[1:no.poly]
}
else {
color <- col[1:no.poly]
}
}
for (poly in no.poly:1) {
limit <- band.limits[poly]
no.points <- floor(limit * n)
xx2<- t(x[ordering[no.points:1],])
upper <- apply(xx2, 1, max)
lower <- apply(xx2, 1, min)
polygon(c(tt, rev(tt)), c(upper, rev(lower)),
col = color[poly])
}
lines(x[ordering[1], ], lty = lty, lwd = lwdd,
col = cold)
}
else {
matplot(fdobj, type = "l", ylim = ylim,
lty = lty, lwd = lwd/2, col = colRef, ...)
if (is.null(col)) {
if (grayscale) {
color <- rev(gray(1/(n + 1):(n/(n + 1))))
}
else {
color <- rep(8, n)
}
}
else {
if (length(col) < n) {
color <- rep(col, length.out = n)[n:1]
}
else {
color <- col[n:1]
}
}
matlines(t(x[ordering[n:2], ]), lwd = lwd, col = color[n:2],
lty = lty)
lines(x[ordering == 1, ], lwd = lwdd, lty = lty[1],
col = cold)
}
par(xpd = TRUE)
legend("top", legend = c("deepest sample", "reference set"),
col = c(cold, colRef), lty = lty, lwd = c(lwdd,
lwd/2), cex = cex)
if (band) {
legend("top", inset = -0.1 * cex, horiz = TRUE,
legend = band.limits, col = color, pch = 15,
title = "Proportion of central samples", cex = cex,
bty = "n")
}
}
if (scale) depth.ori<-depth.ori/max(depth.ori)
}
med<-fdataobj[ordering[1]]
lista = which(depth >= quantile(depth[1,], probs = trim, na.rm = TRUE))
mtrim= apply(x[lista, ], 2, mean)
# tr<-paste("band.tr",trim*100,"\u0025",sep="")
# names2<-fdataobj[["names"]]
# med$names$main<-"depth.mode median"
# names2$main<-paste("depth.mbandtrim ",trim*100,"\u0025",sep="")
# mtrim<-fdata(mtrim,tt,rtt,names2)
# rownames(med)<-"mode.med"
# rownames(mtrim)<-tr
if (scale) depth[1,]<-depth[1,]/max(depth[1,])
return(invisible(list("median"=med,"lmed"=ordering[1],ordering=ordering,
"mtrim"=mtrim,"ltrim"=lista,"dep"=depth[1,],"dep.ori"=depth.ori)))
}
# multivariate version
#' @rdname depth.mdata
#' @export
mdepth.FM=function(x,xx=x,scale=FALSE,dfunc="TD1"){
n<-nrow(x)
m<-ncol(xx)
d<-matrix(NA,nrow=n,ncol=m)
Fn<-list()
print(m)
par.dfunc<-list()
for (i in 1:m) {
if (dfunc %in% c("TD1","Liu1","FM1")){
Fn[[i]]=ecdf(xx[,i])
par.dfunc$x=x[,i]
par.dfunc$Fn=Fn[[i]]
d[,i]=do.call(dfunc,par.dfunc)
}
else {
par.dfunc$x=x[,i]
par.dfunc$xx=xx[,i]
d[,i]=do.call(dfunc,par.dfunc)
}
}
d<-apply(d,1,mean,na.rm=TRUE)[1:n]
return(list("dep"=d,"Fn"=Fn)) #
}
mdepth.Liu=function(x,xx=x,xeps=1e-15,scale=FALSE){
n<-nrow(x)
m<-ncol(x)
d<-matrix(NA,nrow=n,ncol=m)
Fn<-list()
for (i in 1:m){
Fn[[i]]=ecdf(xx[,i])
d[,i]=Fn[[i]](x[,i])*(1-Fn[[i]](x[,i]-xeps))
}
if (scale){ d<-d*4 }
d<-apply(d,1,mean,na.rm=TRUE)[1:n]
return(list("dep"=d,"Fn"=Fn))
}
# multivariate version
#' @rdname depth.mdata
#' @export
mdepth.TD=function(x,xx=x,xeps=1e-15,scale=FALSE){
#print("entra TD")
n<-nrow(x)
m<-ncol(x)
d<-matrix(NA,nrow=n,ncol=m)
Fn<-list()
for (i in 1:m){
Fn[[i]]=ecdf(xx[,i])
d[,i]=pmin(Fn[[i]](x[,i]),(1-Fn[[i]](x[,i]-xeps)))
}
if (scale){ d<-d*2 }
d<-apply(d,1,mean,na.rm=TRUE)[1:n]
return(list("dep"=d,"Fn"=Fn)) #"dep.ori"=d2,
}
isiindata<-function(i,x){
n<-nrow(x)
ind<-rep(NA,len=n)
for (j in 1:n){
ind[j]<-all(i==x[j,])
}
ind
}
triang=function(Q,P1,P2,P3){
q1=Q-P1;a1=atan2(q1[2],q1[1])
q2=Q-P2;a2=atan2(q2[2],q2[1])
q3=Q-P3;a3=atan2(q3[2],q3[1])
a=sort(c(a1,a2,a3))
return(((a[2]-a[1])<=pi) && ((a[3]-a[2])<=pi) && ((a[3]-a[1])>=pi))
}
ntriang<-function(q,puntos,plot=FALSE){
#print("entra ntriang")
# if (dim(x)[2]!=2) stop("The dimension of the data points is not a 2-column matrix")
# if (dim(x)[1]<3) stop("The dimension of the data points must be at least 3 rows.")
# if (length(q)!=2) stop("El punto q debe tener dos componentes")
n=dim(puntos)[1]
#nq=q-puntos
nq<-sweep(puntos,2,q,"-")
alfa=atan2(nq[,2],nq[,1])
a=sort(alfa)
di<-ci<-numeric(n);di=numeric(n)
#ci=di=numeric(n)
ind.a<-a>0
k<-ifelse(sum(ind.a)>0,min(which(ind.a)),n)
#k=min(min(which(a>0)),n)
#if (is.infinite(k)) k=n
lista=1:(k-1)
for (i in 1:n){
ci[i]=max(which((a-a[i])<=pi))
di[i]=min(c(which((a-a[i])>=pi)),n+1)
}
e1=ci[k]*(ci[k]+1-2*k)+k*(3-k)-2
d1=n*(n-k+1)+0.5*k*(k-1)-0.5*n*(n+1)
e=(lista+n-1)*ci[lista]
f=(ci[lista]+1)*ci[lista]+(di[lista]-1)*(di[lista]-2*lista-2)
sume=sum(e)+0.5*n*e1
sumf=sum(f/2)+n*d1
ttriang=n*(n-1)*(n-2)/6 #n sobre 3
return(list("triang"=sume-sumf,"ttriang"=ttriang))
}
#' @rdname depth.mdata
#' @export
mdepth.SD=function(x,xx=NULL,scale=FALSE){
if (dim(x)[2]!=2) stop("The dimension of the data points is not a 2-column matrix")
if (dim(x)[1]<3) stop("The dimension of the data points must be at least 3 rows.")
if (is.data.frame(x)) {
x <- data.matrix(x)
}
if (is.null(xx)) {
xx<-x
al<-TRUE
}
else {
al<-FALSE
xx <- data.matrix(xx)
}
nam<-colnames(xx)
if ( is.null(rownames(x))) rownames(x)<-1:nrow(x)
nms<-rownames(x)
m0<-nrow(x)
xx<-na.omit(xx)
x<-na.omit(x)
nas<-na.action(x)
nullans<-!is.null(nas)
n=nrow(x)
nn=nrow(xx)
rownames(xx)<-NULL#1:nn
d=ncol(xx)
dep=numeric(n)
if (al){
# print("entra al l")
ttriang=nn*(nn-1)*(nn-2)/6
# print(al); print("all(x==xx)")
fac<-(nn-1)*(nn-2)/2
for (i in 1:n){
# dep[i]=(ntriang(x[i,],x[-i,],TRUE)$triang+(n-1)*(n-2)/2)/ttriang
dep[i]<-ntriang(x[i,],xx[-i,])$triang
# cat("i ",i); print(dep[i])
}
dep<-(dep+fac)/ttriang
}
else{
ttriang=(nn+1)*(nn)*(nn-1)/6
fac<-(nn)*(nn-1)/2
for (i in 1:n){
dep[i]=ntriang(x[i,],xx)$triang
}
dep<-(dep+fac)/ttriang
}
if (scale){
dep<-dep/max(dep)
}
if (nullans){
ans1<-rep(NA,len=m0)
ans1[-nas] <-dep
dep<-ans1
}
names(dep)<-nms
return(invisible(list(dep = dep,x=x,xx=xx)))
}
FM1<-function(x,Fn,scale=FALSE) {
d=1-abs(0.5-Fn(x))
if (scale){ d<-(d-.5)*2 }
d
}
Liu1<-function(x,Fn,xeps=1e-15,scale=FALSE) {
d=Fn(x)*(1-Fn(x-xeps))
if (scale){ d<-d*4 }
d
}
TD1<-function(x,Fn,xeps=1e-15,scale=FALSE) {
d=pmin(Fn(x),(1-Fn(x-xeps))) #HS1D
if (scale){ d<-d*2 }
d
}
LD1<-function(x,xx=x,scale=TRUE) {
mdepth.LD(matrix(x,ncol=1),matrix(xx,ncol=1),scale=scale)$dep
}
MhD1 <- function(x,xx=x,scale=FALSE){
if (is.vector(x)) {
D<- (1+(x-(mean(xx)))^2/sd(xx)^2)
}
else{stop("x is no a vector") }
ans <- 1/D
ans
}
# Univariate version
mdepth.FM1=function(x,xx=x,scale=FALSE){
isx<-is.vector(x)
isxx<-is.vector(xx)
if (!isx) stop("x object is not a vector")
if (!isxx) stop("xx object is not a vector")
n<-length(x)
m<-length(xx)
if (n!=m) stop("The length of x is not the same of xx")
Fn<-list()
Fn=ecdf(xx)
d=1-abs(0.5-Fn(x))
if (scale){ d<-(d-.5)*2 }
return(list("dep"=d,"Fn"=Fn)) #
}
# univariate version
mdepth.TD1=function(x,xx=x,xeps=1e-15,scale=FALSE){
#print("entra TD")
isx<-is.vector(x)
isxx<-is.vector(xx)
if (!isx) stop("x object is not a vector")
if (!isxx) stop("xx object is not a vector")
n<-length(x)
m<-length(xx)
if (n!=m) stop("The length of x is not the same of xx")
Fn=ecdf(xx)
d=pmin(Fn(x),(1-Fn(x-xeps)))
if (scale){ d<-d*2 }
return(list("dep"=d,"Fn"=Fn)) #
}
# univariate version
mdepth.Liu1=function(x,xx=x,xeps=1e-15,scale=FALSE){
isx<-is.vector(x)
isxx<-is.vector(xx)
if (!isx) stop("x object is not a vector")
if (!isxx) stop("xx object is not a vector")
n<-length(x)
m<-length(xx)
if (n!=m) stop("The length of x is not the same of xx")
Fn=ecdf(xx)
d=Fn(x)*(1-Fn(x-xeps))
if (scale){ d<-d*4 }
return(list("dep"=d,"Fn"=Fn))
}
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