Nothing
R/depth.fdata.r
In fda.usc: Functional Data Analysis and Utilities for Statistical Computing
Defines functions
depth.FM
depth.RP
depth.mode
Documented in
depth.FM
depth.mode
depth.RP
#' @name depth.fdata
#'
#' @title Computation of depth measures for functional data
#'
#' @description Several depth measures can be computed for functional data for descriptive
#' or classification purposes.
#'
#' @details Type of depth functions: Fraiman and Muniz (FM)
#' depth, modal depth, random Tukey (RT), random projection (RP) depth and
#' double random projection depth (RPD).
#' \itemize{
#' \item \code{\link{depth.FM}} computes the integration of an univariate depth
#' along the axis x (see Fraiman and Muniz 2001). It is also known as
#' Integrated Depth.
#'
#' \item \code{\link{depth.mode}} implements the modal depth (see Cuevas et al
#' 2007).
#'
#' \item \code{\link{depth.RT}} implements the Random Tukey depth (see
#' Cuesta--Albertos and Nieto--Reyes 2008).
#'
#' \item \code{\link{depth.RP}} computes the Random Projection depth (see
#' Cuevas et al. 2007).
#'
#' \item \code{\link{depth.RPD}} implements a depth measure based on random
#' projections possibly using several derivatives (see Cuevas et al. 2007).
#'
#' \item \code{\link{depth.FSD}} computes the Functional Spatial Depth (see
#' Sguera et al. 2014).
#'
#' \item \code{\link{depth.KFSD}} implements the Kernelized Functional Spatial
#' Depth (see Sguera et al. 2014).
#' }
#' \itemize{
#' \item The \code{\link{depth.mode}} function calculates the depth of a datum
#' accounting the number of curves in its neighbourhood. By default, the
#' distance is calculated using \code{\link{metric.lp}} function although any
#' other distance could be employed through argument \code{metric} (with the
#' general pattern \code{USER.DIST(fdataobj,fdataori)}).
#' \item The \code{\link{depth.RP}} function summarizes the random projections
#' through averages whereas the \code{\link{depth.RT}} function uses the
#' minimum of all projections.
#' \item The \code{\link{depth.RPD}} function involves the original
#' trajectories and the derivatives of each curve in two steps. It builds
#' random projections for the function and their derivatives (indicated in the
#' parameter \code{deriv}) and then applies a depth function (by default
#' \code{\link{depth.mode}}) to this set of random projections (by default the
#' Tukey one).
#' \item The \code{\link{depth.FSD}} and \code{\link{depth.KFSD}} are the
#' implementations of the default versions of the functional spatial depths
#' proposed in Sguera et al 2014. At this moment, it is not possible to change
#' the kernel in the second one.#'
#' }
#'
#' @aliases Depth depth.FM depth.mode depth.RP depth.RPD depth.RT depth.FSD
#' depth.KFSD
#' @param fdataobj The set of new curves to evaluate the depth.
#' \code{\link{fdata}} class object.
#' @param fdataori The set of reference curves respect to which the depth is
#' computed. \code{\link{fdata}} class object.
#' @param trim The alpha of the trimming.
#' @param nproj The number of projections. Ignored if a \code{fdata} class
#' object is provided in \code{proj}
#' @param proj if a \code{fdata} class, projections provided by the user.
#' Otherwise, it is the \code{sigma} parameter of \code{\link{rproc2fdata}}
#' function.
#' @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.f
#' @param par.dfunc List of parameters for \emph{dfunc}.
#' @param dfunc2 Multivariate depth function (second step depth function) in
#' RPD depth, by default \code{\link{mdepth.LD}}. Any user function with the
#' pattern \code{FUN.USER(x,xx,...)} can be employed.
#' @param deriv Number of derivatives described in integer vector \code{deriv}.
#' \code{=0} means no derivative.
#' @param method Type of derivative method. See \code{\link{fdata.deriv}} for
#' more details.
#' @param h Bandwidth parameter.
#' \itemize{
#' \item If \code{h} is a numerical value, the procedure considers the argument
#' value as the bandwidth.
#' \item If is \code{NULL} (by default) the bandwidth is provided as the
#' 15\%--quantile of the distance among curves of
#' \code{fdataori}.
#' \item If \code{h} is a character string (like \code{"0.15"}), the procedure
#' reads the numeric value and consider it as the quantile of the distance in
#' \code{fdataori} (as in the second case).
#' }
#' @param metric Metric function, by default \code{\link{metric.lp}}. Distance
#' matrix between \code{fdataobj} and \code{fdataori}.
#' @param scale =TRUE, the depth is scaled respect to depths in
#' \code{fdataori}.
#' @param xeps Accuracy. The left limit of the empirical distribution function.
#' @param draw =TRUE, draw the curves, the sample median and trimmed mean.
#' @param \dots Further arguments passed to or from other methods. For
#' \code{depth.mode} parameters for \code{metric}. For random projection
#' depths, parameters to be included in \code{rproc2fdata} not included before.
#' @return Return a list with:
#' \itemize{
#' \item {median}{ Deepest curve.}
#' \item {lmed}{ Index deepest element \code{median}.}
#' \item {mtrim}{ \code{fdata} class object with the average from the \code{(1-trim)\%} deepest curves. }
#' \item {ltrim}{ Indexes of curves that conform the trimmed mean \code{mtrim}. }
#' \item {dep}{ Depth of each curve of fdataobj w.r.t. fdataori.}
#' \item {dep.ori}{ Depth of each curve of fdataori w.r.t. fdataori.}
#' \item {proj}{ The projection value of each point on the curves. }
#' \item {dist}{ Distance matrix between curves or functional data.}
#' }
#' @author Manuel Febrero-Bande, Manuel Oviedo de la Fuente
#' \email{manuel.oviedo@@udc.es}
#' @seealso See Also as \code{\link{Descriptive}}.
#' @references Cuevas, A., Febrero-Bande, M., Fraiman, R. (2007). Robust
#' estimation and classification for functional data via projection-based depth
#' notions. \emph{Computational Statistics} 22, 3, 481-496.
#'
#' Fraiman R, Muniz G. (2001). Trimmed means for functional data. \emph{Test}
#' 10: 419-440.
#'
#' Cuesta--Albertos, JA, Nieto--Reyes, A. (2008) The Random Tukey Depth.
#' \emph{Computational Statistics and Data Analysis} Vol. 52, Issue 11,
#' 4979-4988.
#'
#' Febrero-Bande, M, Oviedo de la Fuente, M. (2012). Statistical Computing in
#' Functional Data Analysis: The R Package fda.usc. \emph{Journal of
#' Statistical Software}, 51(4), 1-28. \url{https://www.jstatsoft.org/v51/i04/}
#'
#' Sguera C, Galeano P, Lillo R (2014). Spatial depth based classification for
#' functional data. \emph{TEST} 23(4):725--750.
#' @keywords descriptive
#' @examples
#' \dontrun{
#' #Ex: CanadianWeather data
#' tt=1:365
#' fdataobj<-fdata(t(CanadianWeather$dailyAv[,,1]),tt)
#' # Fraiman-Muniz Depth
#' out.FM=depth.FM(fdataobj,trim=0.1,draw=TRUE)
#' #Modal Depth
#' out.mode=depth.mode(fdataobj,trim=0.1,draw=TRUE)
#' out.RP=depth.RP(fdataobj,trim=0.1,draw=TRUE)
#' out.RT=depth.RT(fdataobj,trim=0.1,draw=TRUE)
#' out.FSD=depth.FSD(fdataobj,trim=0.1,draw=TRUE)
#' out.KFSD=depth.KFSD(fdataobj,trim=0.1,draw=TRUE)
#' ## Double Random Projections
#' out.RPD=depth.RPD(fdataobj,deriv=c(0,1),dfunc2=mdepth.LD,
#' trim=0.1,draw=TRUE)
#' out<-c(out.FM$mtrim,out.mode$mtrim,out.RP$mtrim,out.RPD$mtrim)
#' plot(fdataobj,col="grey")
#' lines(out)
#' cdep<-cbind(out.FM$dep,out.mode$dep,out.RP$dep,out.RT$dep,out.FSD$dep,out.KFSD$dep)
#' colnames(cdep)<-c("FM","mode","RP","RT","FSD","KFSD")
#' pairs(cdep)
#' round(cor(cdep),2)
#' }
#'
#' @rdname depth.fdata
#' @export depth.mode
depth.mode=function(fdataobj,fdataori=fdataobj,trim=0.25,
metric=metric.lp,h=NULL,scale=FALSE,
draw=FALSE,...){
#if (is.fdata(fdataobj)) {
# fdat<-TRUE
# nas<-is.na.fdata(fdataobj)
#if (any(nas)) {
# fdataobj$data<-fdataobj$data[!nas,]
# cat("Warning: ",sum(nas)," curves with NA are not used in the calculations \n")
# }
if (is.null(rownames(fdataobj$data))) rownames(fdataobj$data)<-1:nrow(fdataobj$data)
nms<-rownames(fdataobj$data)
m0<-nrow(fdataobj)
fdataobj2=fdataobj
fdataobj<-na.omit.fdata(fdataobj)
fdataori<-na.omit.fdata(fdataori)
nas<-na.action(fdataobj)
nullans<-!is.null(nas)
# data<-fdataobj[["data"]]
# data2<-fdataori[["data"]]
names1<-names2<-fdataobj[["names"]]
names1$main<-"depth.mode median"
names2$main<-paste("depth.mode trim ",trim*100,"\u0025",sep="")
tt=fdataobj[["argvals"]]
rtt<-fdataobj[["rangeval"]]
#print("is fdata")
#}
#else { stop("no fdata class object")
# data<-fdataobj
# data2<-fdataori
# fdat<-FALSE
# }
n<-nrow(fdataobj)
m<-ncol(fdataobj)
m2<-ncol(fdataori)
n2<-nrow(fdataori)
if (is.null(n) && is.null(m)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.matrix(metric)) mdist=metric
else mdist=metric(fdataori,fdataori,...)
class(mdist) <- "matrix"
if (n==n2 & m==m2) {
equal<-all(fdataobj$data==fdataori$data)
if (equal) mdist2<-mdist
else mdist2<-metric(fdataobj,fdataori,...)}
else mdist2<-metric(fdataobj,fdataori,...)
if (is.null(h)) {
h<-0.15
hq2=quantile(mdist,probs=h,na.rm=TRUE)
}
else {
if (is.numeric(h)) hq2<-h
else hq2=quantile(mdist,probs=as.numeric(h),na.rm=TRUE)
}
class(mdist) <- class(mdist2) <- c("matrix","fdist")
dep<-Ker.norm(mdist2/hq2) ####
dep<-apply(dep,1,sum,na.rm=TRUE)
if (scale) {
dep2=Ker.norm(mdist/hq2)
dep2=apply(dep2,1,sum,na.rm=TRUE)
mn<-min(dep2,na.rm=TRUE)
mx<-max(dep2,na.rm=TRUE)
dep=as.vector(dep/mx)
}
if (nullans) {
ans1<-rep(NA,len=m0)
ans1[-nas] <-dep
dep<-ans1
}
names(dep)<-nms
k=which.max(dep)
med=fdataobj[k]
nl=length(trim)
lista=vector("list",nl)
tr<-paste("mode.tr",round(trim*100,2),"\u0025",sep="")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim=fdata(matrix(NA,ncol=length(tt),nrow=length(trim)),tt,rtt,names2)
for (j in 1:nl){
lista[[j]]=which(dep>=quantile(dep,probs=trim[j],na.rm=TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj2[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=apply(fdataobj2$data[lista[[j]],,drop=FALSE],2,mean,na.rm=TRUE)
}
rownames(med$data)<-"mode.med"
rownames(mtrim$data)<-tr
out<-list("median"=med,"lmed"=k,"mtrim"=mtrim,"ltrim"=if (nl==1) unlist(lista) else lista,
"dep"=dep,"hq"=hq2,name="Mode")
if (scale) out$dscale=mx
out$trim <- trim
out$name <- "mode"
out$fdataobj <- fdataobj
out$fdataori <- fdataori
class(out) <- "depth"
if (draw){
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export depth.RP
depth.RP<-function(fdataobj,fdataori=fdataobj,trim=0.25,nproj=50,proj="vexponential",
dfunc="TD1",par.dfunc=list(),scale=FALSE,draw=FALSE,...){
if (!is.fdata(fdataobj)) fdataobj=fdata(fdataobj)
if (!is.fdata(fdataori)) fdataori=fdata(fdataori)
# nas<-is.na.fdata(fdataobj)
# if (any(nas)) {
# fdataobj$data<-fdataobj$data[!nas,]
# cat("Warning: ",sum(nas)," curves with NA are not used in the calculations \n")
# }
if (is.null(rownames(fdataobj$data))) rownames(fdataobj$data)<-1:nrow(fdataobj$data)
nms<-rownames(fdataobj$data)
m0<-nrow(fdataobj)
fdataobj2<-fdataobj
fdataobj<-na.omit.fdata(fdataobj)
fdataori<-na.omit.fdata(fdataori)
nas<-na.action(fdataobj)
nullans<-!is.null(nas)
#data<-fdataobj[["data"]]
#data2<-fdataori[["data"]]
n<-nrow(fdataobj)
m<-ncol(fdataobj)
m2<-ncol(fdataori)
n2<-nrow(fdataori)
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")
tt=fdataobj[["argvals"]]
rtt<-fdataobj[["rangeval"]]
names1<-names2<-fdataobj[["names"]]
names1$main<-"depth.RP median"
names2$main<-paste("RP trim",trim*100,"\u0025",sep="")
#### new
if (is.fdata(proj)) {
nproj<-nrow(proj)
if (fdataobj$argvals!=proj$argvals || ncol(fdataobj)!=ncol(proj)) stop("Error in proj dimension")
z<-proj
}
else {
z<-rproc2fdata(nproj,tt,sigma=proj,norm=TRUE,...)
}
##
dep=matrix(0.0,ncol=nproj,nrow=n)
dep2=matrix(0.0,ncol=nproj,nrow=n2)
if (dfunc %in% c("Liu1","TD1","FM1")) {
Fn<-list()
for (j in 1:nproj){
valor=inprod.fdata(fdataobj,z[j])
valor2=inprod.fdata(fdataori,z[j])
Fn[[j]]=ecdf(valor2)
par.dfunc$x<-valor
par.dfunc$Fn<-Fn[[j]]
dep[,j]<-do.call(dfunc,par.dfunc)
if (scale) {par.dfunc$x=valor2;dep2[,j]<-do.call(dfunc,par.dfunc)}
}
dep=apply(dep,1,mean) #dep/nproj
}
else if (dfunc %in% c("MhD1","LD1")) {
for (j in 1:nproj){
valor=inprod.fdata(fdataobj,z[j])
valor2=inprod.fdata(fdataori,z[j])
par.dfunc$x<-drop(valor)
par.dfunc$xx<-drop(valor2)
dep[,j]<-do.call(dfunc,par.dfunc)
if (scale) {par.dfunc$x=valor2;dep2[,j]<-do.call(dfunc,par.dfunc)}
# dep<-dep+dp
}
dep=apply(dep,1,mean) #dep/nproj
}
if (scale){ dep2=apply(dep2,1,mean);dep<-dep/max(dep2) }
names(dep)<-nms
k=which.max(dep)
med=fdataobj[k]
if (nullans) {
ans1<-rep(NA,len=m0)
ans1[-nas] <-dep
dep<-ans1
}
nl=length(trim)
lista=vector("list",nl)
tr<-paste("RP.tr",round(trim*100,2),"\u0025",sep="")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim=fdata(matrix(NA,ncol=length(tt),nrow=length(trim)),tt,rtt,names1)
for (j in 1:nl){
lista[[j]]=which(dep>=quantile(dep,probs=trim[j],na.rm=TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj2[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=apply(fdataobj2$data[lista[[j]],,drop=FALSE],2,mean,na.rm=TRUE)
}
rownames(med$data)<-"RP.med"
rownames(mtrim$data)<-tr
out=list("median"=med,"lmed"=k,"mtrim"=mtrim,"ltrim"=if (nl==1) unlist(lista) else lista, "dep"=dep,"proj"=z,dfunc=dfunc,par.dfunc=par.dfunc)
out$trim <- trim
out$name <- "RP"
out$fdataobj <- fdataobj
out$fdataori <- fdataori
class(out) <- "depth"
if (draw){
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export depth.RPD
depth.RPD<-function (fdataobj,fdataori=fdataobj, nproj = 20, proj=1,deriv = c(0, 1), trim = 0.25,
dfunc2 = mdepth.LD, method = "fmm", draw = FALSE, ...)
{
if (!is.fdata(fdataobj)) fdataobj = fdata(fdataobj)
if (!is.fdata(fdataori)) fdataobj=fdata(fdataori)
if (is.null(rownames(fdataobj$data))) rownames(fdataobj$data)<-1:nrow(fdataobj$data)
nms<-rownames(fdataobj$data)
m0<-nrow(fdataobj)
fdataobj2<- fdataobj
fdataobj<-na.omit.fdata(fdataobj)
fdataori<-na.omit.fdata(fdataori)
nas<-na.action(fdataobj)
nullans<-!is.null(nas)
names1 <- names2 <- fdataobj[["names"]]
names1$main <- "depth.RPD median"
names2$main <- paste("RPD trim ", trim * 100, "%", sep = "")
n <- nrow(fdataobj)
m <- ncol(fdataobj)
m2<-ncol(fdataori)
n2<-nrow(fdataori)
if (is.null(m) && is.null(m2)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(n) || is.null(m)) stop("Input must be a matrix")
tt = fdataobj[["argvals"]]
rtt <- fdataobj[["rangeval"]]
newfunc=vector("list",length(deriv))
newfunc2=vector("list",length(deriv))
for (ider in 1:length(deriv)) {
if (deriv[ider] == 0) {
newfunc[[ider]]=fdataobj
newfunc2[[ider]]=fdataori
}
else {
newfunc[[ider]] = fdata.deriv(fdataobj, nderiv = deriv[ider], method = method, ...)
newfunc2[[ider]] = fdata.deriv(fdataori, nderiv = deriv[ider], method = method, ...)
}
}
dep = rep(0, n)
dep2 = rep(0, n2)
vproject = matrix(0, nrow = n, ncol = length(deriv))
vproject2 = matrix(0, nrow = n2, ncol = length(deriv))
if (is.fdata(proj)) {
if (fdataobj$argvals!=proj$argvals || m!=ncol(proj)) stop("Error in proj dimension")
z<-proj
nproj<-nrow(z)
}
else { z<-rproc2fdata(nproj,tt,sigma=proj,norm=TRUE,...) }
pb = txtProgressBar(min = 0, max = nproj, style = 3)
for (j in 1:nproj) {
setTxtProgressBar(pb, j - 0.5)
for (ider in 1:length(deriv)) {
vproject[, ider] = inprod.fdata(newfunc[[ider]],z[j])
vproject2[, ider] = inprod.fdata(newfunc2[[ider]],z[j])
}
par.dfunc = list()
par.dfunc$x <- vproject
par.dfunc$xx <- vproject2
# par.dfunc$trim <- trim
par.dfunc$scale<-TRUE
resul = do.call(dfunc2, par.dfunc)
dep = dep + resul$dep
setTxtProgressBar(pb, j)
}
close(pb)
names(dep)<-nms
dep = dep/nproj
if (nullans) {
ans1<-rep(NA,len=m0)
ans1[-nas] <-dep
dep<-ans1
}
k = which.max(dep)
med = fdataobj[k]
nl=length(trim)
lista=vector("list",nl)
tr<-paste("RPD.tr",round(trim*100,2),"\u0025",sep="")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim=fdata(matrix(NA,ncol=length(tt),nrow=length(trim)),tt,rtt,names2)
for (j in 1:nl){
lista[[j]]=which(dep>=quantile(dep,probs=trim[j],na.rm=TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj2[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=apply(fdataobj2$data[lista[[j]],,drop=FALSE],2,mean,na.rm=TRUE)
}
#else mtrim=data[lista,,drop=FALSE]
# med<-fdata(med,tt,rtt,names1)
# mtrim<-fdata(mtrim,tt,rtt,names2)
rownames(med$data)<-"RPD.med"
rownames(mtrim$data)<-tr
out=list(median = med, lmed = k, mtrim = mtrim,
ltrim = if (nl==1) unlist(lista) else lista, dep = dep,deriv=deriv,proj = z,name="RPD")
out$trim <- trim
out$name <- "RPD"
out$fdataobj <- fdataobj
out$fdataori <- fdataori
class(out)="depth"
if (draw) {
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export
depth.RT <-function (fdataobj,fdataori=fdataobj, trim = 0.25, nproj = 10, proj = 1, xeps = 1e-07,
draw = FALSE, ...)
{
if (!is.fdata(fdataobj)) fdataobj = fdata(fdataobj)
if (!is.fdata(fdataori)) fdataobj=fdata(fdataori)
if (is.null(rownames(fdataobj$data))) rownames(fdataobj$data)<-1:nrow(fdataobj$data)
nms<-rownames(fdataobj$data)
m0<-nrow(fdataobj)
fdataobj2<-fdataobj
fdataobj<-na.omit.fdata(fdataobj)
nas<-na.action(fdataobj)
nullans<-!is.null(nas)
fdataori=na.omit.fdata(fdataori)
data <- fdataobj[["data"]]
data2 <- fdataori[["data"]]
n <- nrow(fdataobj)
m <- ncol(fdataobj)
m2<-ncol(fdataori)
n2<-nrow(fdataori)
if (is.null(n) && is.null(m)) stop("ERROR IN THE DATA DIMENSIONS OF fdataobj")
if (is.null(n2) && is.null(m2)) stop("ERROR IN THE DATA DIMENSIONS fdataori")
tt = fdataobj[["argvals"]]
rtt <- fdataobj[["rangeval"]]
names1 <- names2 <- names <- fdataobj[["names"]]
names1$main <- "depth.RT median"
names2$main <- paste("RT trim", trim * 100, "%", sep = "")
if (is.fdata(proj)) {
nproj <- nrow(proj)
if (fdataobj$argvals != proj$argvals || ncol(fdataobj) !=
ncol(proj))
stop("Error en proj dimension")
z <- proj
}
else {
z <- rproc2fdata(nproj, tt, sigma = proj, norm = TRUE,...)
}
Fn <- list()
Prod=inprod.fdata(fdataobj,z)
Prod2=inprod.fdata(fdataori,z)
dep = array(NA, dim = c(nproj, n))
for (j in 1:nproj) {
Fn[[j]] = ecdf(Prod2[,j])
dep[j, ] = pmin(Fn[[j]](Prod[,j]-xeps) ,(1 - Fn[[j]](Prod[,j]-xeps)))
}
# print(dep)
dep = apply(dep, 2, min)
if (nullans) {
ans1<-rep(NA,len=m0)
ans1[-nas] <-dep
dep<-ans1
}
names(dep)<-nms
k = which.max(dep)
med = fdataobj2[k]
nl = length(trim)
lista=vector("list",nl)
tr <- paste("RT.tr", round(trim * 100,2), "%", sep = "")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim = fdata(matrix(NA, nrow = nl, ncol = m),tt,rtt,names)
for (j in 1:length(trim)) {
lista[[j]] = which(dep >= quantile(dep, probs = trim[j], na.rm = TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj2[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=func.mean(fdataobj2[lista[[j]]])$data
}
rownames(med$data) <- "RT.med"
rownames(mtrim$data) <- tr
out=list(median = med, lmed = k, mtrim = mtrim,
ltrim = if (nl==1) unlist(lista) else lista, dep = dep, proj = z, Fn = Fn,name="RT")
out$trim <- trim
out$name <- "RT"
out$fdataobj <- fdataobj
out$fdataori <- fdataori
class(out)="depth"
if (draw) {
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export
depth.KFSD=function (fdataobj, fdataori = fdataobj, trim = 0.25,
h=NULL, scale = FALSE, draw = FALSE){
if (is.fdata(fdataobj) & is.fdata(fdataori)) {
if (is.null(rownames(fdataobj$data)))
rownames(fdataobj$data) <- 1:nrow(fdataobj$data)
nms <- rownames(fdataobj$data)
m0 <- nrow(fdataobj)
fdataobj <- na.omit.fdata(fdataobj)
fdataori <- na.omit.fdata(fdataori)
nas <- na.action(fdataobj)
nullans <- !is.null(nas)
names1 <- names2 <- names <- fdataobj[["names"]]
names1$main <- "depth.KFSD median"
names2$main <- paste("depth.KFSD trim ", trim * 100,
"%", sep = "")
tt=fdataobj$argvals
rtt=fdataobj$rangval
n <- nrow(fdataobj)
m <- ncol(fdataobj)
m2 <- ncol(fdataori)
n2 <- nrow(fdataori)
}
else {
stop("no fdata class object on input")
}
if (is.null(n) && is.null(m))
stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2))
stop("ERROR IN THE DATA DIMENSIONS")
mdist=matrix(NA,ncol=n2,nrow=n2)
for (i in 1:(n2-1)){for (j in (i+1):n2){
mdist[i,j]<-mdist[j,i]<-norm.fdata(fdataori[i]-fdataori[j])
}}
if (is.null(h)) {
h<-0.15
hq2=quantile(mdist,probs=h,na.rm=TRUE)
#print("es nulo h")
}
else {
#cat("no es nulo h ",h,"\n")
if (is.numeric(h)) hq2<-h
else hq2=quantile(mdist,probs=as.numeric(h),na.rm=TRUE)
}
kern=function(x,y,h=hq2){exp(-norm.fdata(x-y)^2/h^2)}
K02=rep(1,nrow(fdataobj))
K01=rep(1,nrow(fdataori))
M1=matrix(NA,nrow=n2,ncol=n2)
M2=matrix(NA,nrow=n,ncol=n2)
M=array(NA,dim=c(n,n2,n2))
for (i in 1:n2){for (j in i:n2){
if (i==j) M1[i,i]=K01[i] else M1[i,j]<-M1[j,i]<-kern(fdataori[i],fdataori[j],h=hq2)
}}
same.dim <- FALSE
if (n==n2 & m==m2){ same.dim <- TRUE}
if (same.dim)
if (all(fdataobj$data==fdataori$data)) {
M2=M1
} else {same.dim <- FALSE}
if (!same.dim){
for (i in 1:n){for (j in 1:n2){
if (all(fdataobj[i]$data == fdataori[j]$data)) M2[i,j]=K02[i] else M2[i,j]=kern(fdataobj[i],fdataori[j],h=hq2)
}}
}
for (i in 1:n){for (j in 1:n2){for (k in 1:n2){
M[i,j,k]<-(K02[i]+M1[j,k]-M2[i,j]-M2[i,k])/(sqrt(K02[i]+K01[j]-2*M2[i,j])*sqrt(K02[i]+K01[k]-2*M2[i,k]))
}}}
l=which(!is.finite(M))
M[l]=NA
# Bug 2019/08/30 (change n by n2)
# dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n
dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n2
if (scale) {
MO=array(NA,dim=c(n2,n2,n2))
for (i in 1:n2){for (j in 1:n2){for (k in 1:n2){
MO[i,j,k]<-(K01[i]+M1[j,k]-M1[i,j]-M1[i,k])/(sqrt(K01[i]+K01[j]-2*M1[i,j])*sqrt(K01[i]+K01[k]-2*M1[i,k]))
}}}
l=which(!is.finite(MO))
MO[l]=NA
dep2=1-sqrt(apply(MO,1,sum,na.rm=TRUE))/n2
#mn <- min(dep2, na.rm = TRUE)
#
#print(range(dep)); print(range(dep2))
mx <- max(dep, na.rm = TRUE)
dep = as.vector(dep/mx)
}
if (nullans) {
ans1 <- rep(NA, len = m0)
ans1[-nas] <- dep
dep <- ans1
}
names(dep)=nms
k = which.max(dep)
med = fdataobj[k]
nl = length(trim)
lista = vector("list",nl)
tr <- paste("KFSD.tr", round(trim * 100,2), "%", sep = "")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim = fdata(matrix(NA, nrow = nl, ncol = m),tt,rtt,names)
for (j in 1:length(trim)) {
lista[[j]] = which(dep >= quantile(dep, probs = trim[j], na.rm = TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=func.mean(fdataobj[lista[[j]]])$data
}
rownames(med$data) <- "KFSD.med"
rownames(mtrim$data) <- tr
out <- list(median = med, lmed = k, mtrim = mtrim, ltrim = if (nl==1) unlist(lista) else lista,
dep = dep, h = h, hq=hq2,name="KFSD")
if (scale) out$dscale = mx
class(out)="depth"
out$trim <- trim
out$name <- "KFSD"
out$fdataobj=fdataobj
out$fdataori=fdataori
if (draw) {
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export
depth.FSD=function (fdataobj, fdataori = fdataobj,
trim = 0.25, scale = FALSE, draw = FALSE){
if (is.fdata(fdataobj)) {
if (is.null(rownames(fdataobj$data)))
rownames(fdataobj$data) <- 1:nrow(fdataobj$data)
m0=nrow(fdataobj)
nms <- rownames(fdataobj$data)
fdataobj <- na.omit.fdata(fdataobj)
fdataori <- na.omit.fdata(fdataori)
nas <- na.action(fdataobj)
n <- nrow(fdataobj)
m <- ncol(fdataobj)
m2 <- ncol(fdataori)
n2 <- nrow(fdataori)
nullans <- !is.null(nas)
names1 <- names2 <- names <- fdataobj[["names"]]
names1$main <- "depth.FSD median"
names2$main <- paste("depth.FSD trim ", trim * 100,
"%", sep = "")
tt = fdataobj[["argvals"]]
rtt <- fdataobj[["rangeval"]]
} else {
stop("no fdata class 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){inprod.fdata(x,y)}
K02=norm.fdata(fdataobj)^2
K01=norm.fdata(fdataori)^2
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(fdataori[i],fdataori[j])
}
}
same.dim <- FALSE
if (n==n2 & m==m2){ same.dim <- TRUE}
if (same.dim)
if (all(fdataobj$data==fdataori$data)) {
M2=M1
} else {same.dim <- FALSE}
if (!same.dim){
# print("entra")
for (i in 1:n){
for (j in 1:n2){
if (all(fdataobj[i]$data == fdataori[j]$data))
M2[i,j]=K02[i] else {
M2[i,j]=kern(fdataobj[i],fdataori[j])
}
}
}
}
#print(M2)
for (i in 1:n){
for (j in 1:n2){
for (k in 1:n2){
if (all(fdataobj[i]$data == fdataori[j]$data) |
all(fdataobj[i]$data == fdataori[k]$data))
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
# Bug 2019/08/30 (change n by n2)
# dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n
dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n2
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){
if (all(fdataori[i]$data == fdataori[j]$data) | all(fdataori[i]$data == fdataori[k]$data)) 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)
}
# print("M M2 M")
# print(range(M,na.rm=T))
# print(range(M2,na.rm=T))
# print(range(M0,na.rm=T)
if (nullans) {
ans1 <- rep(NA, len = m0)
ans1[-nas] <- dep
dep <- ans1
}
names(dep)=nms
k = which.max(dep)
med = fdataobj[k]
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 = fdata(matrix(NA, nrow = nl, ncol = m),tt,rtt,names2)
for (j in 1:length(trim)) {
lista[[j]] = which(dep >= quantile(dep, probs = trim[j], na.rm = TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=func.mean(fdataobj[lista[[j]]])$data
}
rownames(med$data) <- "FSD.med"
rownames(mtrim$data) <- tr
out <- list(median = med, lmed = k, mtrim = mtrim, ltrim = if (nl==1) unlist(lista) else lista,
dep = dep,name="FSD")
if (scale)
out$dscale = mx
class(out)="depth"
out$trim <- trim
out$name <- "FSD"
out$fdataobj=fdataobj
out$fdataori=fdataori
if (draw) {
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export
depth.FM=function(fdataobj,fdataori=fdataobj,trim=0.25,scale=FALSE,dfunc="FM1",par.dfunc=list(scale=TRUE),draw=FALSE){
if (!is.fdata(fdataobj)) fdataobj=fdata(fdataobj)
if (!is.fdata(fdataori)) fdataori=fdata(fdataori)
if (is.null(fdataobj)) rownames(fdataobj$data)<-1:nrow(fdataobj$data)
nms<-rownames(fdataobj$data)
#nas<-apply(fd-ataobj$data,1,count.na)
#if (any(nas)) {
# fdataobj$data<-fdataobj$data[!nas,]
# cat("Warning: ",sum(nas)," curves with NA are not used in the calculations \n")
# }
data<-fdataobj[["data"]]
data2<-fdataori[["data"]]
n<-nrow(data)
m<-ncol(data)
m2<-ncol(data2)
n2<-nrow(data2)
d<-matrix(NA,nrow=n,ncol=m)
if (is.null(n) && is.null(m)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.list(dfunc)) dfunc<-dfunc$dfunc
t=fdataobj[["argvals"]]
rtt<-fdataobj[["rangeval"]]
names1<-names2<-names<-fdataobj[["names"]]
names1$main<-"depth.FM median"
Fn<-list()
tr<-paste("FM.tr",trim*100,"\u0025",sep="")
names2$main<- tr
dtt <- diff(t)
eps <- as.double(.Machine[[1]] * 100)
inf <- dtt - eps
sup <- dtt + eps
if (all(dtt > inf) & all(dtt < sup)) { equi = TRUE }
else equi = FALSE
for (i in 1:m) {
if (dfunc %in% c("TD1","Liu1","FM1")){
Fn[[i]]=ecdf(data2[,i])
par.dfunc$x=data[,i]
par.dfunc$Fn=Fn[[i]]
d[,i]=do.call(dfunc,par.dfunc)
}
else {
par.dfunc$x=data[,i]
par.dfunc$xx=data2[,i]
d[,i]=do.call(dfunc,par.dfunc)
}
}
#d<-int.simpson(fdata(d,t,rtt),equi=equi)
d<-apply(d,1,mean)[1:n]
ans<-d
if (scale) { ans=d/max(d)}
names(ans)<-nms
k=which.max(ans)
med=data[k,]
lista=which(ans>=quantile(ans,probs=trim,na.rm=TRUE))
if (n>1) mtrim=apply(data[lista,,drop=FALSE],2,mean,na.rm=TRUE)
else mtrim<-data
med<-fdata(med,t,rtt,names1)
mtrim<-fdata(mtrim,t,rtt,names2)
rownames(med$data)<-"FM.med"
rownames(mtrim$data)<-tr
out=list("median"=med,"lmed"=k,"mtrim"=mtrim,"ltrim"=lista,
"dep"=ans,"Fn"=Fn)
class(out)="depth"
out$trim= out$trim
out$fdataobj=fdataobj
out$fdataori=fdataori
if (draw){
plot.depth(out)
}
return(invisible(out))
}
depth.MB<-function (fdataobj, fdataori = 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, ...)
{
################################################################################
# Wrapper version of modified band depth (original code from depthTools::MBD)
# adapted from mulitvariate to functioinal case by Manuel Oviedo de la Fuente
################################################################################
if (!is.fdata(fdataobj)) {fdataobj=fdata(fdataobj)}
x<-fdataobj$data
n <- nrow(x)
d <- ncol(x)
x <- as.matrix(x)
tt<-fdataobj$argvals
rtt<-diff(fdataobj$rangeval)
dtt<-diff(tt/rtt)
depth.ori<-NULL
# dtt<-c(0,dtt,0)/sum(dtt)*d
if (length(fdataori) == 0) {
if (ncol(x) == 1) {
x <- t(x)
}
depth <- matrix(0, n,d)
ordered.matrix <- x
if (n > 1) {
for (columns in 1:d) {
if (columns>1 & columns<d)
wei <- .5*dtt[columns]+.5*dtt[columns-1]
else {
if (columns==1) { wei <-.5*dtt[columns]}
else {if (columns==d) wei <- .5*dtt[columns-1]}
}
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,columns] <- index.1 *
(n - (index.2)) + multiplicity * (n - index.2 +
index.1) + choose(multiplicity, 2)
}
depth[, columns] <- depth[, columns]* wei *d
}
depth <- rowSums(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 <- fdataobj[ordering[n:2], ]
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)
plot(fobj, ylim = ylim, type = "l",lty = 0, ...)
for (poly in no.poly:1) {
limit <- band.limits[poly]
no.points <- floor(limit * n)
xx <- t(x[ordering[no.points:1],])
upper <- apply(xx, 1, max)
lower <- apply(xx, 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]
}
}
plot(fobj, type = "l", ylim = ylim,lty = lty, lwd = lwd, col = color[n:2], ...)
}
lines(fdataobj[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 {
if (!is.fdata(fdataori)) fdataori=fdata(fdataori)
xRef<-fdataori$data
xRef <- as.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, n,d)
depth.ori <- matrix(0, n0,d)
ordered.matrix <- xRef
if (n0 > 1) {
for (columns in 1:d) {
if (columns>1 & columns<d)
wei <- .5*dtt[columns]+.5*dtt[columns-1]
else {
if (columns==1) { wei <-.5*dtt[columns]}
else {if (columns==d) wei <- .5*dtt[columns-1]}
}
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,columns] <- (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,columns] <- (index.1 +
multiplicity) * (n0 - index.1 - multiplicity) +
multiplicity * (index.1 + (multiplicity -
1)/2)
}
depth[, columns] <- depth[, columns]* wei *d
depth.ori[, columns] <- depth.ori[, columns]* wei *d
}
depth <- rowSums(depth/(d * choose(n0, 2)))
depth.ori <- rowSums(depth.ori/(d * choose(n0, 2)))
# depth <- depth/(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)
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)
plot(fdataori, 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)
xx<- t(x[ordering[no.points:1],])
upper <- apply(xx, 1, max)
lower <- apply(xx, 1, min)
polygon(c(tt, rev(tt)), c(upper, rev(lower)),
col = color[poly])
}
lines(fdataobj[ordering[1], ], lty = lty, lwd = lwdd,
col = cold)
}
else {
plot(fdataori, 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]
}
}
lines(fdataobj[ordering[n:2], ], lwd = lwd, col = color[n:2],
lty = lty)
lines(fdataobj[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, 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$main<-paste("depth.mbandtrim ",trim*100,"\u0025",sep="")
mtrim<-fdata(mtrim,tt,rtt,names2)
rownames(med$data)<-"mode.med"
rownames(mtrim$data)<-tr
if (scale) depth<-depth/max(depth)
return(invisible(list("median"=med,"lmed"=ordering[1],ordering=ordering,
"mtrim"=mtrim,"ltrim"=lista,"dep"=depth,"dep.ori"=depth.ori)))
}
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Defines functions depth.FM depth.RP depth.mode
Documented in depth.FM depth.mode depth.RP
#' @name depth.fdata
#'
#' @title Computation of depth measures for functional data
#'
#' @description Several depth measures can be computed for functional data for descriptive
#' or classification purposes.
#'
#' @details Type of depth functions: Fraiman and Muniz (FM)
#' depth, modal depth, random Tukey (RT), random projection (RP) depth and
#' double random projection depth (RPD).
#' \itemize{
#' \item \code{\link{depth.FM}} computes the integration of an univariate depth
#' along the axis x (see Fraiman and Muniz 2001). It is also known as
#' Integrated Depth.
#'
#' \item \code{\link{depth.mode}} implements the modal depth (see Cuevas et al
#' 2007).
#'
#' \item \code{\link{depth.RT}} implements the Random Tukey depth (see
#' Cuesta--Albertos and Nieto--Reyes 2008).
#'
#' \item \code{\link{depth.RP}} computes the Random Projection depth (see
#' Cuevas et al. 2007).
#'
#' \item \code{\link{depth.RPD}} implements a depth measure based on random
#' projections possibly using several derivatives (see Cuevas et al. 2007).
#'
#' \item \code{\link{depth.FSD}} computes the Functional Spatial Depth (see
#' Sguera et al. 2014).
#'
#' \item \code{\link{depth.KFSD}} implements the Kernelized Functional Spatial
#' Depth (see Sguera et al. 2014).
#' }
#' \itemize{
#' \item The \code{\link{depth.mode}} function calculates the depth of a datum
#' accounting the number of curves in its neighbourhood. By default, the
#' distance is calculated using \code{\link{metric.lp}} function although any
#' other distance could be employed through argument \code{metric} (with the
#' general pattern \code{USER.DIST(fdataobj,fdataori)}).
#' \item The \code{\link{depth.RP}} function summarizes the random projections
#' through averages whereas the \code{\link{depth.RT}} function uses the
#' minimum of all projections.
#' \item The \code{\link{depth.RPD}} function involves the original
#' trajectories and the derivatives of each curve in two steps. It builds
#' random projections for the function and their derivatives (indicated in the
#' parameter \code{deriv}) and then applies a depth function (by default
#' \code{\link{depth.mode}}) to this set of random projections (by default the
#' Tukey one).
#' \item The \code{\link{depth.FSD}} and \code{\link{depth.KFSD}} are the
#' implementations of the default versions of the functional spatial depths
#' proposed in Sguera et al 2014. At this moment, it is not possible to change
#' the kernel in the second one.#'
#' }
#'
#' @aliases Depth depth.FM depth.mode depth.RP depth.RPD depth.RT depth.FSD
#' depth.KFSD
#' @param fdataobj The set of new curves to evaluate the depth.
#' \code{\link{fdata}} class object.
#' @param fdataori The set of reference curves respect to which the depth is
#' computed. \code{\link{fdata}} class object.
#' @param trim The alpha of the trimming.
#' @param nproj The number of projections. Ignored if a \code{fdata} class
#' object is provided in \code{proj}
#' @param proj if a \code{fdata} class, projections provided by the user.
#' Otherwise, it is the \code{sigma} parameter of \code{\link{rproc2fdata}}
#' function.
#' @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.f
#' @param par.dfunc List of parameters for \emph{dfunc}.
#' @param dfunc2 Multivariate depth function (second step depth function) in
#' RPD depth, by default \code{\link{mdepth.LD}}. Any user function with the
#' pattern \code{FUN.USER(x,xx,...)} can be employed.
#' @param deriv Number of derivatives described in integer vector \code{deriv}.
#' \code{=0} means no derivative.
#' @param method Type of derivative method. See \code{\link{fdata.deriv}} for
#' more details.
#' @param h Bandwidth parameter.
#' \itemize{
#' \item If \code{h} is a numerical value, the procedure considers the argument
#' value as the bandwidth.
#' \item If is \code{NULL} (by default) the bandwidth is provided as the
#' 15\%--quantile of the distance among curves of
#' \code{fdataori}.
#' \item If \code{h} is a character string (like \code{"0.15"}), the procedure
#' reads the numeric value and consider it as the quantile of the distance in
#' \code{fdataori} (as in the second case).
#' }
#' @param metric Metric function, by default \code{\link{metric.lp}}. Distance
#' matrix between \code{fdataobj} and \code{fdataori}.
#' @param scale =TRUE, the depth is scaled respect to depths in
#' \code{fdataori}.
#' @param xeps Accuracy. The left limit of the empirical distribution function.
#' @param draw =TRUE, draw the curves, the sample median and trimmed mean.
#' @param \dots Further arguments passed to or from other methods. For
#' \code{depth.mode} parameters for \code{metric}. For random projection
#' depths, parameters to be included in \code{rproc2fdata} not included before.
#' @return Return a list with:
#' \itemize{
#' \item {median}{ Deepest curve.}
#' \item {lmed}{ Index deepest element \code{median}.}
#' \item {mtrim}{ \code{fdata} class object with the average from the \code{(1-trim)\%} deepest curves. }
#' \item {ltrim}{ Indexes of curves that conform the trimmed mean \code{mtrim}. }
#' \item {dep}{ Depth of each curve of fdataobj w.r.t. fdataori.}
#' \item {dep.ori}{ Depth of each curve of fdataori w.r.t. fdataori.}
#' \item {proj}{ The projection value of each point on the curves. }
#' \item {dist}{ Distance matrix between curves or functional data.}
#' }
#' @author Manuel Febrero-Bande, Manuel Oviedo de la Fuente
#' \email{manuel.oviedo@@udc.es}
#' @seealso See Also as \code{\link{Descriptive}}.
#' @references Cuevas, A., Febrero-Bande, M., Fraiman, R. (2007). Robust
#' estimation and classification for functional data via projection-based depth
#' notions. \emph{Computational Statistics} 22, 3, 481-496.
#'
#' Fraiman R, Muniz G. (2001). Trimmed means for functional data. \emph{Test}
#' 10: 419-440.
#'
#' Cuesta--Albertos, JA, Nieto--Reyes, A. (2008) The Random Tukey Depth.
#' \emph{Computational Statistics and Data Analysis} Vol. 52, Issue 11,
#' 4979-4988.
#'
#' Febrero-Bande, M, Oviedo de la Fuente, M. (2012). Statistical Computing in
#' Functional Data Analysis: The R Package fda.usc. \emph{Journal of
#' Statistical Software}, 51(4), 1-28. \url{https://www.jstatsoft.org/v51/i04/}
#'
#' Sguera C, Galeano P, Lillo R (2014). Spatial depth based classification for
#' functional data. \emph{TEST} 23(4):725--750.
#' @keywords descriptive
#' @examples
#' \dontrun{
#' #Ex: CanadianWeather data
#' tt=1:365
#' fdataobj<-fdata(t(CanadianWeather$dailyAv[,,1]),tt)
#' # Fraiman-Muniz Depth
#' out.FM=depth.FM(fdataobj,trim=0.1,draw=TRUE)
#' #Modal Depth
#' out.mode=depth.mode(fdataobj,trim=0.1,draw=TRUE)
#' out.RP=depth.RP(fdataobj,trim=0.1,draw=TRUE)
#' out.RT=depth.RT(fdataobj,trim=0.1,draw=TRUE)
#' out.FSD=depth.FSD(fdataobj,trim=0.1,draw=TRUE)
#' out.KFSD=depth.KFSD(fdataobj,trim=0.1,draw=TRUE)
#' ## Double Random Projections
#' out.RPD=depth.RPD(fdataobj,deriv=c(0,1),dfunc2=mdepth.LD,
#' trim=0.1,draw=TRUE)
#' out<-c(out.FM$mtrim,out.mode$mtrim,out.RP$mtrim,out.RPD$mtrim)
#' plot(fdataobj,col="grey")
#' lines(out)
#' cdep<-cbind(out.FM$dep,out.mode$dep,out.RP$dep,out.RT$dep,out.FSD$dep,out.KFSD$dep)
#' colnames(cdep)<-c("FM","mode","RP","RT","FSD","KFSD")
#' pairs(cdep)
#' round(cor(cdep),2)
#' }
#'
#' @rdname depth.fdata
#' @export depth.mode
depth.mode=function(fdataobj,fdataori=fdataobj,trim=0.25,
metric=metric.lp,h=NULL,scale=FALSE,
draw=FALSE,...){
#if (is.fdata(fdataobj)) {
# fdat<-TRUE
# nas<-is.na.fdata(fdataobj)
#if (any(nas)) {
# fdataobj$data<-fdataobj$data[!nas,]
# cat("Warning: ",sum(nas)," curves with NA are not used in the calculations \n")
# }
if (is.null(rownames(fdataobj$data))) rownames(fdataobj$data)<-1:nrow(fdataobj$data)
nms<-rownames(fdataobj$data)
m0<-nrow(fdataobj)
fdataobj2=fdataobj
fdataobj<-na.omit.fdata(fdataobj)
fdataori<-na.omit.fdata(fdataori)
nas<-na.action(fdataobj)
nullans<-!is.null(nas)
# data<-fdataobj[["data"]]
# data2<-fdataori[["data"]]
names1<-names2<-fdataobj[["names"]]
names1$main<-"depth.mode median"
names2$main<-paste("depth.mode trim ",trim*100,"\u0025",sep="")
tt=fdataobj[["argvals"]]
rtt<-fdataobj[["rangeval"]]
#print("is fdata")
#}
#else { stop("no fdata class object")
# data<-fdataobj
# data2<-fdataori
# fdat<-FALSE
# }
n<-nrow(fdataobj)
m<-ncol(fdataobj)
m2<-ncol(fdataori)
n2<-nrow(fdataori)
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(fdataori,fdataori,...)
class(mdist) <- "matrix"
if (n==n2 & m==m2) {
equal<-all(fdataobj$data==fdataori$data)
if (equal) mdist2<-mdist
else mdist2<-metric(fdataobj,fdataori,...)}
else mdist2<-metric(fdataobj,fdataori,...)
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","fdist")
dep<-Ker.norm(mdist2/hq2) ####
dep<-apply(dep,1,sum,na.rm=TRUE)
if (scale) {
dep2=Ker.norm(mdist/hq2)
dep2=apply(dep2,1,sum,na.rm=TRUE)
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=fdataobj[k]
nl=length(trim)
lista=vector("list",nl)
tr<-paste("mode.tr",round(trim*100,2),"\u0025",sep="")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim=fdata(matrix(NA,ncol=length(tt),nrow=length(trim)),tt,rtt,names2)
for (j in 1:nl){
lista[[j]]=which(dep>=quantile(dep,probs=trim[j],na.rm=TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj2[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=apply(fdataobj2$data[lista[[j]],,drop=FALSE],2,mean,na.rm=TRUE)
}
rownames(med$data)<-"mode.med"
rownames(mtrim$data)<-tr
out<-list("median"=med,"lmed"=k,"mtrim"=mtrim,"ltrim"=if (nl==1) unlist(lista) else lista,
"dep"=dep,"hq"=hq2,name="Mode")
if (scale) out$dscale=mx
out$trim <- trim
out$name <- "mode"
out$fdataobj <- fdataobj
out$fdataori <- fdataori
class(out) <- "depth"
if (draw){
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export depth.RP
depth.RP<-function(fdataobj,fdataori=fdataobj,trim=0.25,nproj=50,proj="vexponential",
dfunc="TD1",par.dfunc=list(),scale=FALSE,draw=FALSE,...){
if (!is.fdata(fdataobj)) fdataobj=fdata(fdataobj)
if (!is.fdata(fdataori)) fdataori=fdata(fdataori)
# nas<-is.na.fdata(fdataobj)
# if (any(nas)) {
# fdataobj$data<-fdataobj$data[!nas,]
# cat("Warning: ",sum(nas)," curves with NA are not used in the calculations \n")
# }
if (is.null(rownames(fdataobj$data))) rownames(fdataobj$data)<-1:nrow(fdataobj$data)
nms<-rownames(fdataobj$data)
m0<-nrow(fdataobj)
fdataobj2<-fdataobj
fdataobj<-na.omit.fdata(fdataobj)
fdataori<-na.omit.fdata(fdataori)
nas<-na.action(fdataobj)
nullans<-!is.null(nas)
#data<-fdataobj[["data"]]
#data2<-fdataori[["data"]]
n<-nrow(fdataobj)
m<-ncol(fdataobj)
m2<-ncol(fdataori)
n2<-nrow(fdataori)
if (is.null(n) && is.null(m)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2)) stop("ERROR IN THE DATA DIMENSIONS")
tt=fdataobj[["argvals"]]
rtt<-fdataobj[["rangeval"]]
names1<-names2<-fdataobj[["names"]]
names1$main<-"depth.RP median"
names2$main<-paste("RP trim",trim*100,"\u0025",sep="")
#### new
if (is.fdata(proj)) {
nproj<-nrow(proj)
if (fdataobj$argvals!=proj$argvals || ncol(fdataobj)!=ncol(proj)) stop("Error in proj dimension")
z<-proj
}
else {
z<-rproc2fdata(nproj,tt,sigma=proj,norm=TRUE,...)
}
##
dep=matrix(0.0,ncol=nproj,nrow=n)
dep2=matrix(0.0,ncol=nproj,nrow=n2)
if (dfunc %in% c("Liu1","TD1","FM1")) {
Fn<-list()
for (j in 1:nproj){
valor=inprod.fdata(fdataobj,z[j])
valor2=inprod.fdata(fdataori,z[j])
Fn[[j]]=ecdf(valor2)
par.dfunc$x<-valor
par.dfunc$Fn<-Fn[[j]]
dep[,j]<-do.call(dfunc,par.dfunc)
if (scale) {par.dfunc$x=valor2;dep2[,j]<-do.call(dfunc,par.dfunc)}
}
dep=apply(dep,1,mean) #dep/nproj
}
else if (dfunc %in% c("MhD1","LD1")) {
for (j in 1:nproj){
valor=inprod.fdata(fdataobj,z[j])
valor2=inprod.fdata(fdataori,z[j])
par.dfunc$x<-drop(valor)
par.dfunc$xx<-drop(valor2)
dep[,j]<-do.call(dfunc,par.dfunc)
if (scale) {par.dfunc$x=valor2;dep2[,j]<-do.call(dfunc,par.dfunc)}
# dep<-dep+dp
}
dep=apply(dep,1,mean) #dep/nproj
}
if (scale){ dep2=apply(dep2,1,mean);dep<-dep/max(dep2) }
names(dep)<-nms
k=which.max(dep)
med=fdataobj[k]
if (nullans) {
ans1<-rep(NA,len=m0)
ans1[-nas] <-dep
dep<-ans1
}
nl=length(trim)
lista=vector("list",nl)
tr<-paste("RP.tr",round(trim*100,2),"\u0025",sep="")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim=fdata(matrix(NA,ncol=length(tt),nrow=length(trim)),tt,rtt,names1)
for (j in 1:nl){
lista[[j]]=which(dep>=quantile(dep,probs=trim[j],na.rm=TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj2[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=apply(fdataobj2$data[lista[[j]],,drop=FALSE],2,mean,na.rm=TRUE)
}
rownames(med$data)<-"RP.med"
rownames(mtrim$data)<-tr
out=list("median"=med,"lmed"=k,"mtrim"=mtrim,"ltrim"=if (nl==1) unlist(lista) else lista, "dep"=dep,"proj"=z,dfunc=dfunc,par.dfunc=par.dfunc)
out$trim <- trim
out$name <- "RP"
out$fdataobj <- fdataobj
out$fdataori <- fdataori
class(out) <- "depth"
if (draw){
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export depth.RPD
depth.RPD<-function (fdataobj,fdataori=fdataobj, nproj = 20, proj=1,deriv = c(0, 1), trim = 0.25,
dfunc2 = mdepth.LD, method = "fmm", draw = FALSE, ...)
{
if (!is.fdata(fdataobj)) fdataobj = fdata(fdataobj)
if (!is.fdata(fdataori)) fdataobj=fdata(fdataori)
if (is.null(rownames(fdataobj$data))) rownames(fdataobj$data)<-1:nrow(fdataobj$data)
nms<-rownames(fdataobj$data)
m0<-nrow(fdataobj)
fdataobj2<- fdataobj
fdataobj<-na.omit.fdata(fdataobj)
fdataori<-na.omit.fdata(fdataori)
nas<-na.action(fdataobj)
nullans<-!is.null(nas)
names1 <- names2 <- fdataobj[["names"]]
names1$main <- "depth.RPD median"
names2$main <- paste("RPD trim ", trim * 100, "%", sep = "")
n <- nrow(fdataobj)
m <- ncol(fdataobj)
m2<-ncol(fdataori)
n2<-nrow(fdataori)
if (is.null(m) && is.null(m2)) stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(n) || is.null(m)) stop("Input must be a matrix")
tt = fdataobj[["argvals"]]
rtt <- fdataobj[["rangeval"]]
newfunc=vector("list",length(deriv))
newfunc2=vector("list",length(deriv))
for (ider in 1:length(deriv)) {
if (deriv[ider] == 0) {
newfunc[[ider]]=fdataobj
newfunc2[[ider]]=fdataori
}
else {
newfunc[[ider]] = fdata.deriv(fdataobj, nderiv = deriv[ider], method = method, ...)
newfunc2[[ider]] = fdata.deriv(fdataori, nderiv = deriv[ider], method = method, ...)
}
}
dep = rep(0, n)
dep2 = rep(0, n2)
vproject = matrix(0, nrow = n, ncol = length(deriv))
vproject2 = matrix(0, nrow = n2, ncol = length(deriv))
if (is.fdata(proj)) {
if (fdataobj$argvals!=proj$argvals || m!=ncol(proj)) stop("Error in proj dimension")
z<-proj
nproj<-nrow(z)
}
else { z<-rproc2fdata(nproj,tt,sigma=proj,norm=TRUE,...) }
pb = txtProgressBar(min = 0, max = nproj, style = 3)
for (j in 1:nproj) {
setTxtProgressBar(pb, j - 0.5)
for (ider in 1:length(deriv)) {
vproject[, ider] = inprod.fdata(newfunc[[ider]],z[j])
vproject2[, ider] = inprod.fdata(newfunc2[[ider]],z[j])
}
par.dfunc = list()
par.dfunc$x <- vproject
par.dfunc$xx <- vproject2
# par.dfunc$trim <- trim
par.dfunc$scale<-TRUE
resul = do.call(dfunc2, par.dfunc)
dep = dep + resul$dep
setTxtProgressBar(pb, j)
}
close(pb)
names(dep)<-nms
dep = dep/nproj
if (nullans) {
ans1<-rep(NA,len=m0)
ans1[-nas] <-dep
dep<-ans1
}
k = which.max(dep)
med = fdataobj[k]
nl=length(trim)
lista=vector("list",nl)
tr<-paste("RPD.tr",round(trim*100,2),"\u0025",sep="")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim=fdata(matrix(NA,ncol=length(tt),nrow=length(trim)),tt,rtt,names2)
for (j in 1:nl){
lista[[j]]=which(dep>=quantile(dep,probs=trim[j],na.rm=TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj2[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=apply(fdataobj2$data[lista[[j]],,drop=FALSE],2,mean,na.rm=TRUE)
}
#else mtrim=data[lista,,drop=FALSE]
# med<-fdata(med,tt,rtt,names1)
# mtrim<-fdata(mtrim,tt,rtt,names2)
rownames(med$data)<-"RPD.med"
rownames(mtrim$data)<-tr
out=list(median = med, lmed = k, mtrim = mtrim,
ltrim = if (nl==1) unlist(lista) else lista, dep = dep,deriv=deriv,proj = z,name="RPD")
out$trim <- trim
out$name <- "RPD"
out$fdataobj <- fdataobj
out$fdataori <- fdataori
class(out)="depth"
if (draw) {
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export
depth.RT <-function (fdataobj,fdataori=fdataobj, trim = 0.25, nproj = 10, proj = 1, xeps = 1e-07,
draw = FALSE, ...)
{
if (!is.fdata(fdataobj)) fdataobj = fdata(fdataobj)
if (!is.fdata(fdataori)) fdataobj=fdata(fdataori)
if (is.null(rownames(fdataobj$data))) rownames(fdataobj$data)<-1:nrow(fdataobj$data)
nms<-rownames(fdataobj$data)
m0<-nrow(fdataobj)
fdataobj2<-fdataobj
fdataobj<-na.omit.fdata(fdataobj)
nas<-na.action(fdataobj)
nullans<-!is.null(nas)
fdataori=na.omit.fdata(fdataori)
data <- fdataobj[["data"]]
data2 <- fdataori[["data"]]
n <- nrow(fdataobj)
m <- ncol(fdataobj)
m2<-ncol(fdataori)
n2<-nrow(fdataori)
if (is.null(n) && is.null(m)) stop("ERROR IN THE DATA DIMENSIONS OF fdataobj")
if (is.null(n2) && is.null(m2)) stop("ERROR IN THE DATA DIMENSIONS fdataori")
tt = fdataobj[["argvals"]]
rtt <- fdataobj[["rangeval"]]
names1 <- names2 <- names <- fdataobj[["names"]]
names1$main <- "depth.RT median"
names2$main <- paste("RT trim", trim * 100, "%", sep = "")
if (is.fdata(proj)) {
nproj <- nrow(proj)
if (fdataobj$argvals != proj$argvals || ncol(fdataobj) !=
ncol(proj))
stop("Error en proj dimension")
z <- proj
}
else {
z <- rproc2fdata(nproj, tt, sigma = proj, norm = TRUE,...)
}
Fn <- list()
Prod=inprod.fdata(fdataobj,z)
Prod2=inprod.fdata(fdataori,z)
dep = array(NA, dim = c(nproj, n))
for (j in 1:nproj) {
Fn[[j]] = ecdf(Prod2[,j])
dep[j, ] = pmin(Fn[[j]](Prod[,j]-xeps) ,(1 - Fn[[j]](Prod[,j]-xeps)))
}
# print(dep)
dep = apply(dep, 2, min)
if (nullans) {
ans1<-rep(NA,len=m0)
ans1[-nas] <-dep
dep<-ans1
}
names(dep)<-nms
k = which.max(dep)
med = fdataobj2[k]
nl = length(trim)
lista=vector("list",nl)
tr <- paste("RT.tr", round(trim * 100,2), "%", sep = "")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim = fdata(matrix(NA, nrow = nl, ncol = m),tt,rtt,names)
for (j in 1:length(trim)) {
lista[[j]] = which(dep >= quantile(dep, probs = trim[j], na.rm = TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj2[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=func.mean(fdataobj2[lista[[j]]])$data
}
rownames(med$data) <- "RT.med"
rownames(mtrim$data) <- tr
out=list(median = med, lmed = k, mtrim = mtrim,
ltrim = if (nl==1) unlist(lista) else lista, dep = dep, proj = z, Fn = Fn,name="RT")
out$trim <- trim
out$name <- "RT"
out$fdataobj <- fdataobj
out$fdataori <- fdataori
class(out)="depth"
if (draw) {
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export
depth.KFSD=function (fdataobj, fdataori = fdataobj, trim = 0.25,
h=NULL, scale = FALSE, draw = FALSE){
if (is.fdata(fdataobj) & is.fdata(fdataori)) {
if (is.null(rownames(fdataobj$data)))
rownames(fdataobj$data) <- 1:nrow(fdataobj$data)
nms <- rownames(fdataobj$data)
m0 <- nrow(fdataobj)
fdataobj <- na.omit.fdata(fdataobj)
fdataori <- na.omit.fdata(fdataori)
nas <- na.action(fdataobj)
nullans <- !is.null(nas)
names1 <- names2 <- names <- fdataobj[["names"]]
names1$main <- "depth.KFSD median"
names2$main <- paste("depth.KFSD trim ", trim * 100,
"%", sep = "")
tt=fdataobj$argvals
rtt=fdataobj$rangval
n <- nrow(fdataobj)
m <- ncol(fdataobj)
m2 <- ncol(fdataori)
n2 <- nrow(fdataori)
}
else {
stop("no fdata class object on input")
}
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]<-norm.fdata(fdataori[i]-fdataori[j])
}}
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(-norm.fdata(x-y)^2/h^2)}
K02=rep(1,nrow(fdataobj))
K01=rep(1,nrow(fdataori))
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(fdataori[i],fdataori[j],h=hq2)
}}
same.dim <- FALSE
if (n==n2 & m==m2){ same.dim <- TRUE}
if (same.dim)
if (all(fdataobj$data==fdataori$data)) {
M2=M1
} else {same.dim <- FALSE}
if (!same.dim){
for (i in 1:n){for (j in 1:n2){
if (all(fdataobj[i]$data == fdataori[j]$data)) M2[i,j]=K02[i] else M2[i,j]=kern(fdataobj[i],fdataori[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
# Bug 2019/08/30 (change n by n2)
# dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n
dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n2
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]<-(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)
#
#print(range(dep)); print(range(dep2))
mx <- max(dep, 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 = fdataobj[k]
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 = fdata(matrix(NA, nrow = nl, ncol = m),tt,rtt,names)
for (j in 1:length(trim)) {
lista[[j]] = which(dep >= quantile(dep, probs = trim[j], na.rm = TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=func.mean(fdataobj[lista[[j]]])$data
}
rownames(med$data) <- "KFSD.med"
rownames(mtrim$data) <- 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$dscale = mx
class(out)="depth"
out$trim <- trim
out$name <- "KFSD"
out$fdataobj=fdataobj
out$fdataori=fdataori
if (draw) {
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export
depth.FSD=function (fdataobj, fdataori = fdataobj,
trim = 0.25, scale = FALSE, draw = FALSE){
if (is.fdata(fdataobj)) {
if (is.null(rownames(fdataobj$data)))
rownames(fdataobj$data) <- 1:nrow(fdataobj$data)
m0=nrow(fdataobj)
nms <- rownames(fdataobj$data)
fdataobj <- na.omit.fdata(fdataobj)
fdataori <- na.omit.fdata(fdataori)
nas <- na.action(fdataobj)
n <- nrow(fdataobj)
m <- ncol(fdataobj)
m2 <- ncol(fdataori)
n2 <- nrow(fdataori)
nullans <- !is.null(nas)
names1 <- names2 <- names <- fdataobj[["names"]]
names1$main <- "depth.FSD median"
names2$main <- paste("depth.FSD trim ", trim * 100,
"%", sep = "")
tt = fdataobj[["argvals"]]
rtt <- fdataobj[["rangeval"]]
} else {
stop("no fdata class object")
}
if (is.null(n) && is.null(m))
stop("ERROR IN THE DATA DIMENSIONS")
if (is.null(m) && is.null(m2))
stop("ERROR IN THE DATA DIMENSIONS")
kern=function(x,y){inprod.fdata(x,y)}
K02=norm.fdata(fdataobj)^2
K01=norm.fdata(fdataori)^2
M1=matrix(NA,nrow=n2,ncol=n2)
M2=matrix(NA,nrow=n,ncol=n2)
M=array(NA,dim=c(n,n2,n2))
# if (scale) MO=array(NA,dim=c(n2,n2,n2))
for (i in 1:n2){
for (j in i:n2){
if (i==j)
M1[i,i]=K01[i] else M1[i,j]<-M1[j,i]<-kern(fdataori[i],fdataori[j])
}
}
same.dim <- FALSE
if (n==n2 & m==m2){ same.dim <- TRUE}
if (same.dim)
if (all(fdataobj$data==fdataori$data)) {
M2=M1
} else {same.dim <- FALSE}
if (!same.dim){
# print("entra")
for (i in 1:n){
for (j in 1:n2){
if (all(fdataobj[i]$data == fdataori[j]$data))
M2[i,j]=K02[i] else {
M2[i,j]=kern(fdataobj[i],fdataori[j])
}
}
}
}
#print(M2)
for (i in 1:n){
for (j in 1:n2){
for (k in 1:n2){
if (all(fdataobj[i]$data == fdataori[j]$data) |
all(fdataobj[i]$data == fdataori[k]$data))
M[i,j,k]=NA else M[i,j,k]<-(K02[i]+M1[j,k]-M2[i,j]-M2[i,k])/(sqrt(K02[i]+K01[j]-2*M2[i,j])*sqrt(K02[i]+K01[k]-2*M2[i,k]))
}}}
l=which(!is.finite(M))
M[l]=NA
# Bug 2019/08/30 (change n by n2)
# dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n
dep=1-sqrt(apply(M,1,sum,na.rm=TRUE))/n2
if (scale) {
MO=array(NA,dim=c(n2,n2,n2))
for (i in 1:n2){for (j in 1:n2){for (k in 1:n2){
if (all(fdataori[i]$data == fdataori[j]$data) | all(fdataori[i]$data == fdataori[k]$data)) MO[i,j,k]=NA else MO[i,j,k]<-(K01[i]+M1[j,k]-M1[i,j]-M1[i,k])/(sqrt(K01[i]+K01[j]-2*M1[i,j])*sqrt(K01[i]+K01[k]-2*M1[i,k]))
}}}
l=which(!is.finite(MO))
MO[l]=NA
dep2=1-sqrt(apply(MO,1,sum,na.rm=TRUE))/n2
# mn <- min(dep2, na.rm = TRUE)
mx <- max(dep2, na.rm = TRUE)
dep = as.vector(dep/mx)
}
# print("M M2 M")
# print(range(M,na.rm=T))
# print(range(M2,na.rm=T))
# print(range(M0,na.rm=T)
if (nullans) {
ans1 <- rep(NA, len = m0)
ans1[-nas] <- dep
dep <- ans1
}
names(dep)=nms
k = which.max(dep)
med = fdataobj[k]
nl = length(trim)
lista=vector("list",nl)
tr <- paste("FSD.tr", round(trim * 100,2), "%", sep = "")
if (nl>1) names(lista)=paste0("tr",round(trim*100,2))
mtrim = fdata(matrix(NA, nrow = nl, ncol = m),tt,rtt,names2)
for (j in 1:length(trim)) {
lista[[j]] = which(dep >= quantile(dep, probs = trim[j], na.rm = TRUE))
if (length(lista[[j]])==1) {
mtrim$data[j,]<-fdataobj[lista[[j]]]$data
if (draw) {draw=FALSE;warning("Too few curves in mtrim. The plot is not drawn")}
}
else mtrim$data[j,]=func.mean(fdataobj[lista[[j]]])$data
}
rownames(med$data) <- "FSD.med"
rownames(mtrim$data) <- tr
out <- list(median = med, lmed = k, mtrim = mtrim, ltrim = if (nl==1) unlist(lista) else lista,
dep = dep,name="FSD")
if (scale)
out$dscale = mx
class(out)="depth"
out$trim <- trim
out$name <- "FSD"
out$fdataobj=fdataobj
out$fdataori=fdataori
if (draw) {
plot.depth(out)
}
return(invisible(out))
}
#' @rdname depth.fdata
#' @export
depth.FM=function(fdataobj,fdataori=fdataobj,trim=0.25,scale=FALSE,dfunc="FM1",par.dfunc=list(scale=TRUE),draw=FALSE){
if (!is.fdata(fdataobj)) fdataobj=fdata(fdataobj)
if (!is.fdata(fdataori)) fdataori=fdata(fdataori)
if (is.null(fdataobj)) rownames(fdataobj$data)<-1:nrow(fdataobj$data)
nms<-rownames(fdataobj$data)
#nas<-apply(fd-ataobj$data,1,count.na)
#if (any(nas)) {
# fdataobj$data<-fdataobj$data[!nas,]
# cat("Warning: ",sum(nas)," curves with NA are not used in the calculations \n")
# }
data<-fdataobj[["data"]]
data2<-fdataori[["data"]]
n<-nrow(data)
m<-ncol(data)
m2<-ncol(data2)
n2<-nrow(data2)
d<-matrix(NA,nrow=n,ncol=m)
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.list(dfunc)) dfunc<-dfunc$dfunc
t=fdataobj[["argvals"]]
rtt<-fdataobj[["rangeval"]]
names1<-names2<-names<-fdataobj[["names"]]
names1$main<-"depth.FM median"
Fn<-list()
tr<-paste("FM.tr",trim*100,"\u0025",sep="")
names2$main<- tr
dtt <- diff(t)
eps <- as.double(.Machine[[1]] * 100)
inf <- dtt - eps
sup <- dtt + eps
if (all(dtt > inf) & all(dtt < sup)) { equi = TRUE }
else equi = FALSE
for (i in 1:m) {
if (dfunc %in% c("TD1","Liu1","FM1")){
Fn[[i]]=ecdf(data2[,i])
par.dfunc$x=data[,i]
par.dfunc$Fn=Fn[[i]]
d[,i]=do.call(dfunc,par.dfunc)
}
else {
par.dfunc$x=data[,i]
par.dfunc$xx=data2[,i]
d[,i]=do.call(dfunc,par.dfunc)
}
}
#d<-int.simpson(fdata(d,t,rtt),equi=equi)
d<-apply(d,1,mean)[1:n]
ans<-d
if (scale) { ans=d/max(d)}
names(ans)<-nms
k=which.max(ans)
med=data[k,]
lista=which(ans>=quantile(ans,probs=trim,na.rm=TRUE))
if (n>1) mtrim=apply(data[lista,,drop=FALSE],2,mean,na.rm=TRUE)
else mtrim<-data
med<-fdata(med,t,rtt,names1)
mtrim<-fdata(mtrim,t,rtt,names2)
rownames(med$data)<-"FM.med"
rownames(mtrim$data)<-tr
out=list("median"=med,"lmed"=k,"mtrim"=mtrim,"ltrim"=lista,
"dep"=ans,"Fn"=Fn)
class(out)="depth"
out$trim= out$trim
out$fdataobj=fdataobj
out$fdataori=fdataori
if (draw){
plot.depth(out)
}
return(invisible(out))
}
depth.MB<-function (fdataobj, fdataori = NULL,trim=0.25, scale=FALSE,
draw =FALSE, grayscale = FALSE, band = FALSE, band.limits = NULL, lty = 1,
lwd = 2, col = NULL, cold = NULL, colRef = NULL, ylim = NULL, cex = 1, ...)
{
################################################################################
# Wrapper version of modified band depth (original code from depthTools::MBD)
# adapted from mulitvariate to functioinal case by Manuel Oviedo de la Fuente
################################################################################
if (!is.fdata(fdataobj)) {fdataobj=fdata(fdataobj)}
x<-fdataobj$data
n <- nrow(x)
d <- ncol(x)
x <- as.matrix(x)
tt<-fdataobj$argvals
rtt<-diff(fdataobj$rangeval)
dtt<-diff(tt/rtt)
depth.ori<-NULL
# dtt<-c(0,dtt,0)/sum(dtt)*d
if (length(fdataori) == 0) {
if (ncol(x) == 1) {
x <- t(x)
}
depth <- matrix(0, n,d)
ordered.matrix <- x
if (n > 1) {
for (columns in 1:d) {
if (columns>1 & columns<d)
wei <- .5*dtt[columns]+.5*dtt[columns-1]
else {
if (columns==1) { wei <-.5*dtt[columns]}
else {if (columns==d) wei <- .5*dtt[columns-1]}
}
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,columns] <- index.1 *
(n - (index.2)) + multiplicity * (n - index.2 +
index.1) + choose(multiplicity, 2)
}
depth[, columns] <- depth[, columns]* wei *d
}
depth <- rowSums(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 <- fdataobj[ordering[n:2], ]
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)
plot(fobj, ylim = ylim, type = "l",lty = 0, ...)
for (poly in no.poly:1) {
limit <- band.limits[poly]
no.points <- floor(limit * n)
xx <- t(x[ordering[no.points:1],])
upper <- apply(xx, 1, max)
lower <- apply(xx, 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]
}
}
plot(fobj, type = "l", ylim = ylim,lty = lty, lwd = lwd, col = color[n:2], ...)
}
lines(fdataobj[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 {
if (!is.fdata(fdataori)) fdataori=fdata(fdataori)
xRef<-fdataori$data
xRef <- as.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, n,d)
depth.ori <- matrix(0, n0,d)
ordered.matrix <- xRef
if (n0 > 1) {
for (columns in 1:d) {
if (columns>1 & columns<d)
wei <- .5*dtt[columns]+.5*dtt[columns-1]
else {
if (columns==1) { wei <-.5*dtt[columns]}
else {if (columns==d) wei <- .5*dtt[columns-1]}
}
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,columns] <- (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,columns] <- (index.1 +
multiplicity) * (n0 - index.1 - multiplicity) +
multiplicity * (index.1 + (multiplicity -
1)/2)
}
depth[, columns] <- depth[, columns]* wei *d
depth.ori[, columns] <- depth.ori[, columns]* wei *d
}
depth <- rowSums(depth/(d * choose(n0, 2)))
depth.ori <- rowSums(depth.ori/(d * choose(n0, 2)))
# depth <- depth/(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)
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)
plot(fdataori, 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)
xx<- t(x[ordering[no.points:1],])
upper <- apply(xx, 1, max)
lower <- apply(xx, 1, min)
polygon(c(tt, rev(tt)), c(upper, rev(lower)),
col = color[poly])
}
lines(fdataobj[ordering[1], ], lty = lty, lwd = lwdd,
col = cold)
}
else {
plot(fdataori, 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]
}
}
lines(fdataobj[ordering[n:2], ], lwd = lwd, col = color[n:2],
lty = lty)
lines(fdataobj[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, 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$data)<-"mode.med"
rownames(mtrim$data)<-tr
if (scale) depth<-depth/max(depth)
return(invisible(list("median"=med,"lmed"=ordering[1],ordering=ordering,
"mtrim"=mtrim,"ltrim"=lista,"dep"=depth,"dep.ori"=depth.ori)))
}
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