Bagplot - Free Statistics and Forecasting Software (Calculators) v.1.2.1

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the Bagplot for a bivariate data set.
Peter Wolf describes the Bagplot as follows: A bagplot is a bivariate generalization of the well known boxplot. It has been proposed by Rousseeuw, Ruts, and Tukey. In the bivariate case the box of the boxplot changes to a convex polygon, the bag of bagplot. In the bag are 50 percent of all points. The fence separates points within the fence from points outside. It is computed by increasing the the bag. The loop is defined as the convex hull containing all points inside the fence. If all points are on a straight line you get a classical boxplot.
(source: Peter Wolf and Uni Bielefeld, 2007, *aplpack: Another Plot PACKage: stem.leaf, bagplot, faces, spin3R, ...*, R package version 1.1.1, http://www.wiwi.uni-bielefeld.de/~wolf/software/aplpack

This R module is based on the following original R code: http://addictedtor.free.fr/graphiques/graphcode.php?graph=112
Enter (or paste) your data delimited by hard returns.
Send output to:


Data X (click to load default data)
1178 2141 2238 2685 4341 5376 4478 6404 4617 3024 1897 2075 1351 2211 2453 3042 4765 4992 4601 6266 4812 3159 1916 2237 1595 2453 2226 3597 4706 4974 5756 5493 5004 3225 2006 2291 1588 2105 2191 3591 4668 4885 5822 5599 5340 3082 2010 2301 1514 1979 2480 3499 4676 5585 5610 5796 6199 3030 1930 2552

Data Y:
476049 474605 470439 461251 454724 455626 516847 525192 522975 518585 509239 512238 519164 517009 509933 509127 500857 506971 569323 579714 577992 565464 547344 554788 562325 560854 555332 543599 536662 542722 593530 610763 612613 611324 594167 595454 590865 589379 584428 573100 567456 569028 620735 628884 628232 612117 595404 597141 593408 590072 579799 574205 572775 572942 619567 625809 619916 587625 565742 557274


Sample Range: (leave blank to include all observations)
From:
To:

Factor (defining the loop)


Show outliers


Show whiskers


Chart options
Width:
Height:
Title:
Label y-axis:
Label x-axis:
Source code of R module
par1 <- as.numeric(par1) #factor
if (par2 == "TRUE") par2 <- TRUE else par2 <- FALSE
if (par3 == "TRUE") par3 <- TRUE else par3 <- FALSE
library(rpart)
compute.bagplot<-function(x,y,
factor=3, # expanding factor for bag to get the loop
approx.limit=300, # limit
dkmethod=2, # in 1:2; there are two methods for approximating the bag
precision=1, # controls precisionn of computation
verbose=FALSE,debug.plots="no" # tools for debugging
){
win<-function(dx,dy){  atan2(y=dy,x=dx) }
out.of.polygon<-function(xy,pg){
if(nrow(pg)==1) return(pg)
pgcenter<-apply(pg,2,mean)
pg<-cbind(pg[,1]-pgcenter[1],pg[,2]-pgcenter[2])
xy<-cbind(xy[,1]-pgcenter[1],xy[,2]-pgcenter[2])
extr<-rep(FALSE,nrow(xy))
for(i in seq(nrow(xy))){
alpha<-sort((win(xy[i,1]-pg[,1],xy[i,2]-pg[,2]))%%(2*pi))
extr[i]<-pi<max(diff(alpha)) |
pi<(alpha[1]+2*pi-alpha[length(alpha)])
}
print(extr)
}
cut.z.pg<-function(zx,zy,p1x,p1y,p2x,p2y){
a2<-(p2y-p1y)/(p2x-p1x); a1<-zy/zx
sx<-(p1y-a2*p1x)/(a1-a2); sy<-a1*sx
sxy<-cbind(sx,sy)
h<-any(is.nan(sxy))||any(is.na(sxy))||any(Inf==abs(sxy))
if(h){
if(!exists("verbose")) verbose<-FALSE
if(verbose) cat("special")
h<-0==(a1-a2) & sign(zx)==sign(p1x)
sx<-ifelse(h,p1x,sx); sy<-ifelse(h,p1y,sy)
h<-0==(a1-a2) & sign(zx)!=sign(p1x)
sx<-ifelse(h,p2x,sx); sy<-ifelse(h,p2y,sy)
h<-p1x==p2x & zx!=p1x & p1x!=0
sx<-ifelse(h,p1x,sx); sy<-ifelse(h,zy*p1x/zx,sy)
h<-p1x==p2x & zx!=p1x & p1x==0
sx<-ifelse(h,p1x,sx); sy<-ifelse(h,0,sy)
h<-p1x==p2x & zx==p1x & p1x==0 & sign(zy)==sign(p1y)
sx<-ifelse(h,p1x,sx); sy<-ifelse(h,p1y,sy)
h<-p1x==p2x & zx==p1x & p1x==0 & sign(zy)!=sign(p1y)
sx<-ifelse(h,p1x,sx); sy<-ifelse(h,p2y,sy)
h<-zx==p1x & zy==p1y; sx<-ifelse(h,p1x,sx); sy<-ifelse(h,p1y,sy)
h<-zx==p2x & zy==p2y; sx<-ifelse(h,p2x,sx); sy<-ifelse(h,p2y,sy)
h<-zx==0 & zy==0; sx<-ifelse(h,0,sx); sy<-ifelse(h,0,sy)
sxy<-cbind(sx,sy)
} # end of special cases
if(!exists("debug.plots")) debug.plots<-"no"
if(debug.plots=="all"){
segments(sxy[,1],sxy[,2],zx,zy,col="red")
segments(0,0,sxy[,1],sxy[,2],type="l",col="green",lty=2)
points(sxy,col="red")
}
return(sxy)
}
find.cut.z.pg<-function(z,pg,center=c(0,0),debug.plots="no"){
if(!is.matrix(z)) z<-rbind(z)
if(1==nrow(pg)) return(matrix(center,nrow(z),2,TRUE))
n.pg<-nrow(pg); n.z<-nrow(z)
z<-cbind(z[,1]-center[1],z[,2]-center[2])
pgo<-pg; pg<-cbind(pg[,1]-center[1],pg[,2]-center[2])
if(!exists("debug.plots")) debug.plots<-"no"
if(debug.plots=="all"){plot(rbind(z,pg,0),bty="n"); points(z,pch="p")
lines(c(pg[,1],pg[1,1]),c(pg[,2],pg[1,2]))}
apg<-win(pg[,1],pg[,2])
apg[is.nan(apg)]<-0; a<-order(apg); apg<-apg[a]; pg<-pg[a,]
az<-win(z[,1],z[,2])
segm.no<-apply((outer(apg,az,"<")),2,sum)
segm.no<-ifelse(segm.no==0,n.pg,segm.no)
next.no<-1+(segm.no %% length(apg))
cuts<-cut.z.pg(z[,1],z[,2],pg[segm.no,1],pg[segm.no,2],
pg[next.no,1],pg[next.no,2])
cuts<-cbind(cuts[,1]+center[1],cuts[,2]+center[2])
return(cuts)
}
hdepth.of.points<-function(tp,n){
n.tp<-nrow(tp)
tphdepth<-rep(0,n.tp); dpi<-2*pi-0.000001
minusplus<-c(rep(-1,n),rep(1,n))
for(j in 1:n.tp) {
dx<-tp[j,1]-xy[,1]; dy<-tp[j,2]-xy[,2]
a<-win(dx,dy)+pi; h<-a<10;a<-a[h]; ident<-sum(!h)
init<-sum(a < pi); a.shift<-(a+pi) %% dpi
h<-cumsum(minusplus[order(c(a,a.shift))])
tphdepth[j]<-init+min(h)+1
}
tphdepth
}
expand.hull<-function(pg,k){
resolution<-floor(20*precision)
pg0<-xy[hdepth==1,]
pg0<-pg0[chull(pg0[,1],pg0[,2]),]
end.points<-find.cut.z.pg(pg,pg0,center=center,debug.plots=debug.plots)
lam<-((0:resolution)^1)/resolution^1
pg.new<-pg
for(i in 1:nrow(pg)){
tp<-cbind(pg[i,1]+lam*(end.points[i,1]-pg[i,1]),
pg[i,2]+lam*(end.points[i,2]-pg[i,2]))
hd.tp<-hdepth.of.points(tp,nrow(xy))
ind<-max(sum(hd.tp>=k),1)
if(ind<length(hd.tp)){  # hd.tp[ind]>k &&
tp<-cbind(tp[ind,1]+lam*(tp[ind+1,1]-tp[ind,1]),
tp[ind,2]+lam*(tp[ind+1,2]-tp[ind,2]))
hd.tp<-hdepth.of.points(tp,nrow(xy))
ind<-max(sum(hd.tp>=k),1)
}
pg.new[i,]<-tp[ind,]
}
pg.new<-pg.new[chull(pg.new[,1],pg.new[,2]),]
pg.add<-0.5*(pg.new+rbind(pg.new[-1,],pg.new[1,]))
end.points<-find.cut.z.pg(pg,pg0,center=center)
for(i in 1:nrow(pg.add)){
tp<-cbind(pg.add[i,1]+lam*(end.points[i,1]-pg.add[i,1]),
pg.add[i,2]+lam*(end.points[i,2]-pg.add[i,2]))
hd.tp<-hdepth.of.points(tp,nrow(xy))
ind<-max(sum(hd.tp>=k),1)
if(ind<length(hd.tp)){ # hd.tp[ind]>k &&
tp<-cbind(tp[ind,1]+lam*(tp[ind+1,1]-tp[ind,1]),
tp[ind,2]+lam*(tp[ind+1,2]-tp[ind,2]))
hd.tp<-hdepth.of.points(tp,nrow(xy))
ind<-max(sum(hd.tp>=k),1)
}
pg.add[i,]<-tp[ind,]
}
pg.new<-rbind(pg.new,pg.add)
pg.new<-pg.new[chull(pg.new[,1],pg.new[,2]),]
}
cut.p.sl.p.sl<-function(xy1,m1,xy2,m2){
sx<-(xy2[2]-m2*xy2[1]-xy1[2]+m1*xy1[1])/(m1-m2)
sy<-xy1[2]-m1*xy1[1]+m1*sx
if(!is.nan(sy)) return( c(sx,sy) )
if(abs(m1)==Inf) return( c(xy1[1],xy2[2]+m2*(xy1[1]-xy2[1])) )
if(abs(m2)==Inf) return( c(xy2[1],xy1[2]+m1*(xy2[1]-xy1[1])) )
}
pos.to.pg<-function(z,pg,reverse=FALSE){
if(reverse){
int.no<-apply(outer(pg[,1],z[,1],">="),2,sum)
zy.on.pg<-pg[int.no,2]+pg[int.no,3]*(z[,1]-pg[int.no,1])
}else{
int.no<-apply(outer(pg[,1],z[,1],"<="),2,sum)
zy.on.pg<-pg[int.no,2]+pg[int.no,3]*(z[,1]-pg[int.no,1])
}
ifelse(z[,2]<zy.on.pg, "lower","higher")
}
xydata<-if(missing(y)) x else cbind(x,y)
if(is.data.frame(xydata)) xydata<-as.matrix(xydata)
very.large.data.set<-nrow(xydata)>approx.limit
if(!exists(".Random.seed")) set.seed(13)
save.seed<-.Random.seed
if(very.large.data.set){
ind<-sample(seq(nrow(xydata)),size=approx.limit)
xy<-xydata[ind,]
} else xy<-xydata
n<-nrow(xy)
points.in.bag<-floor(n/2)
assign(".Random.seed",save.seed,env=.GlobalEnv)
if(verbose) cat("end of initialization")
prdata<-prcomp(xydata)
is.one.dim<-(min(prdata[[1]])/max(prdata[[1]]))<0.0001
if(is.one.dim){
if(verbose) cat("data set one dimensional")
center<-colMeans(xydata)
res<-list(xy=xy,xydata=xydata,prdata=prdata,is.one.dim=is.one.dim,center=center)
class(res)<-"bagplot"
return(res)
}
if(verbose) cat("data not linear")
dx<-(outer(xy[,1],xy[,1],"-"))
dy<-(outer(xy[,2],xy[,2],"-"))
alpha<-atan2(y=dy,x=dx); diag(alpha)<-1200
for(j in 1:n) alpha[,j]<-sort(alpha[,j])
alpha<-alpha[-n,] ; m<-n-1
if(debug.plots=="all"){
plot(xy,bty="n"); xdelta<-abs(diff(range(xy[,1]))); dx<-xdelta*.3
for(j in 1:n) {
p<-xy[j,]; dy<-dx*tan(alpha[,j])
segments(p[1]-dx,p[2]-dy,p[1]+dx,p[2]+dy,col=j)
text(p[1]-xdelta*.02,p[2],j,col=j)
}
}
if(verbose) print("end of computation of angles")
hdepth<-rep(0,n); dpi<-2*pi-0.000001
minusplus<-c(rep(-1,m),rep(1,m))
for(j in 1:n) {
a<-alpha[,j]+pi; h<-a<10; a<-a[h]; init<-sum(a < pi) # hallo
a.shift<-(a+pi) %% dpi
h<-cumsum(minusplus[order(c(a,a.shift))])
hdepth[j]<-init+min(h)+1 #  or do we have to count identical points?:
}
if(verbose){print("end of computation of hdepth:"); print(hdepth)}
if(debug.plots=="all"){
plot(xy,bty="n")
xdelta<-abs(diff(range(xy[,1]))); dx<-xdelta*.1
for(j in 1:n) {
a<-alpha[,j]+pi; a<-a[a<10]; init<-sum(a < pi)
a.shift<-(a+pi) %% dpi
h<-cumsum(minusplus[ao<-(order(c(a,a.shift)))])
no<-which((init+min(h)) == (init+h))[1]
p<-xy[j,]; dy<-dx*tan(alpha[,j])
segments(p[1]-dx,p[2]-dy,p[1]+dx,p[2]+dy,col=j,lty=3)
dy<-dx*tan(c(sort(a),sort(a))[no])
segments(p[1]-5*dx,p[2]-5*dy,p[1]+5*dx,p[2]+5*dy,col="black")
text(p[1]-xdelta*.02,p[2],hdepth[j],col=1,cex=2.5)
}
}
hd.table<-table(sort(hdepth))
d.k<-cbind(dk=rev(cumsum(rev(hd.table))),
k =as.numeric(names(hd.table)))
k.1<-sum(points.in.bag<d.k[,1])
if(nrow(d.k)>1){
k<-d.k[k.1+1,2]
} else {
k<-d.k[k.1,2]
}
if(verbose){cat("counts of members of dk:"); print(hd.table)}
if(verbose){cat("end of computation of k, k=",k)}
center<-apply(xy[which(hdepth==max(hdepth)),,drop=FALSE],2,mean)
hull.center<-NULL
if(10<nrow(xy)&&length(hd.table)>2){
n.p<-floor(c(32,16,8)[1+(n>50)+(n>200)]*precision)
cands<-xy[rev(order(hdepth))[1:6],]
cands<-cands[chull(cands[,1],cands[,2]),]; n.c<-nrow(cands)
xyextr<-rbind(apply(cands,2,min),apply(cands,2,max))
h1<-seq(xyextr[1,1],xyextr[2,1],length=n.p)
h2<-seq(xyextr[1,2],xyextr[2,2],length=n.p)
tp<-cbind(matrix(h1,n.p,n.p)[1:n.p^2],
matrix(h2,n.p,n.p,TRUE)[1:n.p^2])
tphdepth<-hdepth.of.points(tp,n)
hull.center<-tp[which(tphdepth>=(max(tphdepth))),,drop=FALSE]
center<-apply(hull.center,2,mean)
cands<-hull.center[chull(hull.center[,1],hull.center[,2]),,drop=F]
xyextr<-rbind(apply(cands,2,min),apply(cands,2,max))
xydel<-(xyextr[2,]-xyextr[1,])/n.p
xyextr<-rbind(xyextr[1,]-xydel,xyextr[2,]+xydel)
h1<-seq(xyextr[1,1],xyextr[2,1],length=n.p)
h2<-seq(xyextr[1,2],xyextr[2,2],length=n.p)
tp<-cbind(matrix(h1,n.p,n.p)[1:n.p^2],
matrix(h2,n.p,n.p,TRUE)[1:n.p^2])
tphdepth<-hdepth.of.points(tp,n)
hull.center<-tp[which(tphdepth>=max(tphdepth)),,drop=FALSE]
center<-apply(hull.center,2,mean)
hull.center<-hull.center[chull(hull.center[,1],hull.center[,2]),]
if(verbose){cat("hull.center",hull.center); print(table(tphdepth)) }
}
if(verbose) cat("center depth:",hdepth.of.points(rbind(center),n))
if(verbose){print("end of computation of center"); print(center)}
if(dkmethod==1){
xyi<-xy[hdepth>=k,,drop=FALSE]
pdk<-xyi[chull(xyi[,1],xyi[,2]),,drop=FALSE]
xyo<-xy[hdepth>=(k-1),,drop=FALSE]
pdk.1<-xyo[chull(xyo[,1],xyo[,2]),,drop=FALSE]
if(verbose)cat("hull computed:")
if(debug.plots=="all"){
plot(xy,bty="n")
h<-rbind(pdk,pdk[1,]); lines(h,col="red",lty=2)
h<-rbind(pdk.1,pdk.1[1,]);lines(h,col="blue",lty=3)
points(center[1],center[2],pch=8,col="red")
}
exp.dk<-expand.hull(pdk,k)
exp.dk.1<-expand.hull(exp.dk,k-1) # pdk.1,k-1,20)
}else{
num<-floor(c(417,351,171,85,67,43)[sum(n>c(1,50,100,150,200,250))]*precision)
num.h<-floor(num/2); angles<-seq(0,pi,length=num.h)
ang<-tan(pi/2-angles)
xym<-apply(xy,2,mean); xysd<-apply(xy,2,sd)
xyxy<-cbind((xy[,1]-xym[1])/xysd[1],(xy[,2]-xym[2])/xysd[2])
kkk<-k
ia<-1; a<-angles[ia]; xyt<-xyxy%*%c(cos(a),-sin(a)); xyto<-order(xyt)
ind.k <-xyto[kkk]; cutp<-c(xyxy[ind.k,1],-10)
dxy<-diff(range(xyxy))
pg<-rbind(c(cutp[1],-dxy,Inf),c(cutp[1],dxy,NA))
ind.kk<-xyto[n+1-kkk]; cutpl<-c(xyxy[ind.kk,1],10)
pgl<-rbind(c(cutpl[1],dxy,Inf),c(cutpl[1],-dxy,NA))
if(debug.plots=="all"){ plot(xyxy,type="p",bty="n")
}
for(ia in seq(angles)[-1]){
a<-angles[ia]; angtan<-ang[ia]; xyt<-xyxy%*%c(cos(a),-sin(a)); xyto<-order(xyt)
ind.k <-xyto[kkk]; ind.kk<-xyto[n+1-kkk]; pnew<-xyxy[ind.k,]; pnewl<-xyxy[ind.kk,]
if(debug.plots=="all") points(pnew[1],pnew[2],col="red")
if(abs(angtan)>1e10){  ###  cat("y=c case")
pg.no<-sum(pg[,1]<pnew[1])
cutp<-c(pnew[1],pg[pg.no,2]+pg[pg.no,3]*(pnew[1]-pg[pg.no,1]))
pg.nol<-sum(pgl[,1]>=pnewl[1])
cutpl<-c(pnewl[1],pgl[pg.nol,2]+pgl[pg.nol,3]*(pnewl[1]-pgl[pg.nol,1]))
}else{    ### cat("normal case")
pg.inter<-pg[,2]-angtan*pg[,1]; pnew.inter<-pnew[2]-angtan*pnew[1]
pg.no<-sum(pg.inter<pnew.inter)
cutp<-cut.p.sl.p.sl(pnew,ang[ia],pg[pg.no,1:2],pg[pg.no,3])
pg.interl<-pgl[,2]-angtan*pgl[,1]; pnew.interl<-pnewl[2]-angtan*pnewl[1]
pg.nol<-sum(pg.interl>pnew.interl)
cutpl<-cut.p.sl.p.sl(pnewl,angtan,pgl[pg.nol,1:2],pgl[pg.nol,3])
}
pg<-rbind(pg[1:pg.no,],c(cutp,angtan),c(cutp[1]+dxy, cutp[2]+angtan*dxy,NA))
pgl<-rbind(pgl[1:pg.nol,],c(cutpl,angtan),c(cutpl[1]-dxy, cutpl[2]-angtan*dxy,NA))
if(debug.plots=="all"){
points(pnew[1],pnew[2],col="red")
hx<-xyxy[ind.k,c(1,1)]; hy<-xyxy[ind.k,c(2,2)]
segments(hx,hy,c(10,-10),hy+ang[ia]*(c(10,-10)-hx),lty=2)
points(cutpl[1],cutpl[2],col="red")
hx<-xyxy[ind.kk,c(1,1)]; hy<-xyxy[ind.kk,c(2,2)]
segments(hx,hy,c(10,-10),hy+ang[ia]*(c(10,-10)-hx),lty=2)
}
}
pg<-pg[-nrow(pg),][-1,,drop=F]; pgl<-pgl[-nrow(pgl),][-1,,drop=FALSE]
indl<-pos.to.pg(pgl,pg); indu<-pos.to.pg(pg,pgl,TRUE)
npg<-nrow(pg); npgl<-nrow(pgl)
rnuml<-rnumu<-lnuml<-lnumu<-0; sl<-pg[1,1:2]; sr<-pgl[1,1:2]
if(indl[1]=="higher"&indu[npg]=="lower"){
rnuml<-which(indl=="lower")[1]-1; xyl<-pgl[rnuml,] #
rnumu<-which(rev(indu=="higher"))[1]; xyu<-pg[npg+1-rnumu,] #
sr<-cut.p.sl.p.sl(xyl[1:2],xyl[3],xyu[1:2],xyu[3])
}
if(indl[npgl]=="higher"&indu[1]=="lower"){
lnuml<-which(rev(indl=="lower"))[1]; xyl<-pgl[npgl+1-lnuml,] #
lnumu<-which(indu=="higher")[1]-1; xyu<-pg[lnumu,] #?
sl<-cut.p.sl.p.sl(xyl[1:2],xyl[3],xyu[1:2],xyu[3])
}
pgl<-pgl[(rnuml+1):(npgl-lnuml),1:2,drop=FALSE]
pg <-pg [(lnumu+1):(npg -rnumu),1:2,drop=FALSE]
pg<-rbind(pg,sr,pgl,sl)
pg<-pg[chull(pg[,1],pg[,2]),]
if(debug.plots=="all") lines(rbind(pg,pg[1,]),col="red")
exp.dk<-cbind(pg[,1]*xysd[1]+xym[1],pg[,2]*xysd[2]+xym[2])
if(kkk>1) kkk<-kkk-1
ia<-1; a<-angles[ia]; xyt<-xyxy%*%c(cos(a),-sin(a)); xyto<-order(xyt)
ind.k <-xyto[kkk]; cutp<-c(xyxy[ind.k,1],-10)
dxy<-diff(range(xyxy))
pg<-rbind(c(cutp[1],-dxy,Inf),c(cutp[1],dxy,NA))
ind.kk<-xyto[n+1-kkk]; cutpl<-c(xyxy[ind.kk,1],10)
pgl<-rbind(c(cutpl[1],dxy,Inf),c(cutpl[1],-dxy,NA))
if(debug.plots=="all"){ plot(xyxy,type="p",bty="n")
}
for(ia in seq(angles)[-1]){
a<-angles[ia]; angtan<-ang[ia]; xyt<-xyxy%*%c(cos(a),-sin(a)); xyto<-order(xyt)
ind.k <-xyto[kkk]; ind.kk<-xyto[n+1-kkk]; pnew<-xyxy[ind.k,]; pnewl<-xyxy[ind.kk,]
if(debug.plots=="all") points(pnew[1],pnew[2],col="red")
if(abs(angtan)>1e10){  ###  cat("y=c case")
pg.no<-sum(pg[,1]<pnew[1])
cutp<-c(pnew[1],pg[pg.no,2]+pg[pg.no,3]*(pnew[1]-pg[pg.no,1]))
pg.nol<-sum(pgl[,1]>=pnewl[1])
cutpl<-c(pnewl[1],pgl[pg.nol,2]+pgl[pg.nol,3]*(pnewl[1]-pgl[pg.nol,1]))
}else{    ### cat("normal case")
pg.inter<-pg[,2]-angtan*pg[,1]; pnew.inter<-pnew[2]-angtan*pnew[1]
pg.no<-sum(pg.inter<pnew.inter)
cutp<-cut.p.sl.p.sl(pnew,ang[ia],pg[pg.no,1:2],pg[pg.no,3])
pg.interl<-pgl[,2]-angtan*pgl[,1]; pnew.interl<-pnewl[2]-angtan*pnewl[1]
pg.nol<-sum(pg.interl>pnew.interl)
cutpl<-cut.p.sl.p.sl(pnewl,angtan,pgl[pg.nol,1:2],pgl[pg.nol,3])
}
pg<-rbind(pg[1:pg.no,],c(cutp,angtan),c(cutp[1]+dxy, cutp[2]+angtan*dxy,NA))
pgl<-rbind(pgl[1:pg.nol,],c(cutpl,angtan),c(cutpl[1]-dxy, cutpl[2]-angtan*dxy,NA))
if(debug.plots=="all"){
points(pnew[1],pnew[2],col="red")
hx<-xyxy[ind.k,c(1,1)]; hy<-xyxy[ind.k,c(2,2)]
segments(hx,hy,c(10,-10),hy+ang[ia]*(c(10,-10)-hx),lty=2)
points(cutpl[1],cutpl[2],col="red")
hx<-xyxy[ind.kk,c(1,1)]; hy<-xyxy[ind.kk,c(2,2)]
segments(hx,hy,c(10,-10),hy+ang[ia]*(c(10,-10)-hx),lty=2)
}
}
pg<-pg[-nrow(pg),][-1,,drop=F]; pgl<-pgl[-nrow(pgl),][-1,,drop=FALSE]
indl<-pos.to.pg(pgl,pg); indu<-pos.to.pg(pg,pgl,TRUE)
npg<-nrow(pg); npgl<-nrow(pgl)
rnuml<-rnumu<-lnuml<-lnumu<-0; sl<-pg[1,1:2]; sr<-pgl[1,1:2]
if(indl[1]=="higher"&indu[npg]=="lower"){
rnuml<-which(indl=="lower")[1]-1; xyl<-pgl[rnuml,] #
rnumu<-which(rev(indu=="higher"))[1]; xyu<-pg[npg+1-rnumu,] #
sr<-cut.p.sl.p.sl(xyl[1:2],xyl[3],xyu[1:2],xyu[3])
}
if(indl[npgl]=="higher"&indu[1]=="lower"){
lnuml<-which(rev(indl=="lower"))[1]; xyl<-pgl[npgl+1-lnuml,] #
lnumu<-which(indu=="higher")[1]-1; xyu<-pg[lnumu,] #?
sl<-cut.p.sl.p.sl(xyl[1:2],xyl[3],xyu[1:2],xyu[3])
}
pgl<-pgl[(rnuml+1):(npgl-lnuml),1:2,drop=FALSE]
pg <-pg [(lnumu+1):(npg -rnumu),1:2,drop=FALSE]
pg<-rbind(pg,sr,pgl,sl)
pg<-pg[chull(pg[,1],pg[,2]),]
if(debug.plots=="all") lines(rbind(pg,pg[1,]),col="red")
exp.dk.1<-cbind(pg[,1]*xysd[1]+xym[1],pg[,2]*xysd[2]+xym[2])
}
lambda<-if(nrow(d.k)==1) 0.5 else
(n/2-d.k[k.1+1,1])/(d.k[k.1,1]-d.k[k.1+1,1])
if(verbose) cat("lambda",lambda)
cut.on.pdk.1<-find.cut.z.pg(exp.dk,  exp.dk.1,center=center)
cut.on.pdk  <-find.cut.z.pg(exp.dk.1,exp.dk,  center=center)
h1<-(1-lambda)*exp.dk+lambda*cut.on.pdk.1
h2<-(1-lambda)*cut.on.pdk+lambda*exp.dk.1
h<-rbind(h1,h2); hull.bag<-h[chull(h[,1],h[,2]),]
if(verbose)cat("bag completed:") #if(verbose)print(hull.bag)
if(debug.plots=="all"){   lines(hull.bag,col="red") }
hull.loop<-cbind(hull.bag[,1]-center[1],hull.bag[,2]-center[2])
hull.loop<-factor*hull.loop
hull.loop<-cbind(hull.loop[,1]+center[1],hull.loop[,2]+center[2])
if(verbose) cat("loop computed")
if(!very.large.data.set){
pxy.bag    <-xydata[hdepth>= k   ,,drop=FALSE]
pkt.cand   <-xydata[hdepth==(k-1),,drop=FALSE]
pkt.not.bag<-xydata[hdepth< (k-1),,drop=FALSE]
if(length(pkt.cand)>0){
outside<-out.of.polygon(pkt.cand,hull.bag)
if(sum(!outside)>0)
pxy.bag    <-rbind(pxy.bag,     pkt.cand[!outside,])
if(sum( outside)>0)
pkt.not.bag<-rbind(pkt.not.bag, pkt.cand[ outside,])
}
}else {
extr<-out.of.polygon(xydata,hull.bag)
pxy.bag    <-xydata[!extr,]
pkt.not.bag<-xydata[extr,,drop=FALSE]
}
if(length(pkt.not.bag)>0){
extr<-out.of.polygon(pkt.not.bag,hull.loop)
pxy.outlier<-pkt.not.bag[extr,,drop=FALSE]
if(0==length(pxy.outlier)) pxy.outlier<-NULL
pxy.outer<-pkt.not.bag[!extr,,drop=FALSE]
}else{
pxy.outer<-pxy.outlier<-NULL
}
if(verbose) cat("points of bag, outer points and outlier identified")
hull.loop<-rbind(pxy.outer,hull.bag)
hull.loop<-hull.loop[chull(hull.loop[,1],hull.loop[,2]),]
if(verbose) cat("end of computation of loop")
assign(".Random.seed",save.seed,env=.GlobalEnv)
res<-list(
center=center,
pxy.bag=pxy.bag,
pxy.outer=if(length(pxy.outer)>0) pxy.outer else NULL,
pxy.outlier=if(length(pxy.outlier)>0) pxy.outlier else NULL,
hull.center=hull.center,
hull.bag=hull.bag,
hull.loop=hull.loop,
hdepths=hdepth,
is.one.dim=is.one.dim,
prdata=prdata,
xy=xy,xydata=xydata
)
if(verbose) res<-c(res,list(exp.dk=exp.dk,exp.dk.1=exp.dk.1,hdepth=hdepth))
class(res)<-"bagplot"
return(res)
}
plot.bagplot<-function(bagplot.obj,
show.outlier=TRUE,# if TRUE outlier are shown
show.whiskers=TRUE, # if TRUE whiskers are shown
show.looppoints=TRUE, # if TRUE points in loop are shown
show.bagpoints=TRUE, # if TRUE points in bag are shown
show.loophull=TRUE, # if TRUE loop is shown
show.baghull=TRUE, # if TRUE bag is shown
add=FALSE, # if TRUE graphical elements are added to actual plot
pch=16,cex=.4,..., # to define further parameters of plot
verbose=FALSE # tools for debugging
){
win<-function(dx,dy){  atan2(y=dy,x=dx) }
cut.z.pg<-function(zx,zy,p1x,p1y,p2x,p2y){
a2<-(p2y-p1y)/(p2x-p1x); a1<-zy/zx
sx<-(p1y-a2*p1x)/(a1-a2); sy<-a1*sx
sxy<-cbind(sx,sy)
h<-any(is.nan(sxy))||any(is.na(sxy))||any(Inf==abs(sxy))
if(h){
if(!exists("verbose")) verbose<-FALSE
if(verbose) cat("special")
h<-0==(a1-a2) & sign(zx)==sign(p1x)
sx<-ifelse(h,p1x,sx); sy<-ifelse(h,p1y,sy)
h<-0==(a1-a2) & sign(zx)!=sign(p1x)
sx<-ifelse(h,p2x,sx); sy<-ifelse(h,p2y,sy)
h<-p1x==p2x & zx!=p1x & p1x!=0
sx<-ifelse(h,p1x,sx); sy<-ifelse(h,zy*p1x/zx,sy)
h<-p1x==p2x & zx!=p1x & p1x==0
sx<-ifelse(h,p1x,sx); sy<-ifelse(h,0,sy)
h<-p1x==p2x & zx==p1x & p1x==0 & sign(zy)==sign(p1y)
sx<-ifelse(h,p1x,sx); sy<-ifelse(h,p1y,sy)
h<-p1x==p2x & zx==p1x & p1x==0 & sign(zy)!=sign(p1y)
sx<-ifelse(h,p1x,sx); sy<-ifelse(h,p2y,sy)
h<-zx==p1x & zy==p1y; sx<-ifelse(h,p1x,sx); sy<-ifelse(h,p1y,sy)
h<-zx==p2x & zy==p2y; sx<-ifelse(h,p2x,sx); sy<-ifelse(h,p2y,sy)
h<-zx==0 & zy==0; sx<-ifelse(h,0,sx); sy<-ifelse(h,0,sy)
sxy<-cbind(sx,sy)
} # end of special cases
if(!exists("debug.plots")) debug.plots<-"no"
if(debug.plots=="all"){
segments(sxy[,1],sxy[,2],zx,zy,col="red")
segments(0,0,sxy[,1],sxy[,2],type="l",col="green",lty=2)
points(sxy,col="red")
}
return(sxy)
}
find.cut.z.pg<-function(z,pg,center=c(0,0),debug.plots="no"){
if(!is.matrix(z)) z<-rbind(z)
if(1==nrow(pg)) return(matrix(center,nrow(z),2,TRUE))
n.pg<-nrow(pg); n.z<-nrow(z)
z<-cbind(z[,1]-center[1],z[,2]-center[2])
pgo<-pg; pg<-cbind(pg[,1]-center[1],pg[,2]-center[2])
if(!exists("debug.plots")) debug.plots<-"no"
if(debug.plots=="all"){plot(rbind(z,pg,0),bty="n"); points(z,pch="p")
lines(c(pg[,1],pg[1,1]),c(pg[,2],pg[1,2]))}
apg<-win(pg[,1],pg[,2])
apg[is.nan(apg)]<-0; a<-order(apg); apg<-apg[a]; pg<-pg[a,]
az<-win(z[,1],z[,2])
segm.no<-apply((outer(apg,az,"<")),2,sum)
segm.no<-ifelse(segm.no==0,n.pg,segm.no)
next.no<-1+(segm.no %% length(apg))
cuts<-cut.z.pg(z[,1],z[,2],pg[segm.no,1],pg[segm.no,2],
pg[next.no,1],pg[next.no,2])
cuts<-cbind(cuts[,1]+center[1],cuts[,2]+center[2])
return(cuts)
}
for(i in seq(along=bagplot.obj))
eval(parse(text=paste(names(bagplot.obj)[i],"<-bagplot.obj[[",i,"]]")))
if(is.one.dim){
if(verbose) cat("data set one dimensional")
prdata<-prdata[[2]];
trdata<-xydata%*%prdata; ytr<-mean(trdata[,2])
boxplotres<-boxplot(trdata[,1],plot=FALSE)
dy<-0.1*diff(range(stats<-boxplotres$stats))
dy<-0.05*mean(c(diff(range(xydata[,1])),
diff(range(xydata[,2]))))
segtr<-rbind(cbind(stats[2:4],ytr-dy,stats[2:4],ytr+dy),
cbind(stats[c(2,2)],ytr+c(dy,-dy),
stats[c(4,4)],ytr+c(dy,-dy)),
cbind(stats[c(2,4)],ytr,stats[c(1,5)],ytr))
segm<-cbind(segtr[,1:2]%*%t(prdata),
segtr[,3:4]%*%t(prdata))
if(!add) plot(xydata,type="n",bty="n",pch=16,cex=.2,...)
extr<-c(min(segm[6,3],segm[7,3]),max(segm[6,3],segm[7,3]))
extr<-extr+c(-1,1)*0.000001*diff(extr)
xydata<-xydata[xydata[,1]<extr[1] |
xydata[,1]>extr[2],,drop=FALSE]
if(0<nrow(xydata))points(xydata[,1],xydata[,2],pch=pch,cex=cex)
segments(segm[,1],segm[,2],segm[,3],segm[,4],)
return("one dimensional boxplot plottet")
}
if(!add) plot(xydata,type="n",pch=pch,cex=cex,bty="n",...)
if(verbose) text(xy[,1],xy[,2],paste(as.character(hdepth)),cex=2)
if(show.loophull){ # fill loop
h<-rbind(hull.loop,hull.loop[1,]); lines(h[,1],h[,2],lty=1)
polygon(hull.loop[,1],hull.loop[,2],col="#aaccff")
}
if(show.looppoints && length(pxy.outer)>0){ # points in loop
points(pxy.outer[,1],pxy.outer[,2],col="#3355ff",pch=pch,cex=cex)
}
if(show.baghull){ # fill bag
h<-rbind(hull.bag,hull.bag[1,]); lines(h[,1],h[,2],lty=1)
polygon(hull.bag[,1],hull.bag[,2],col="#7799ff")
}
if(show.bagpoints && length(pxy.bag)>0){ # points in bag
points(pxy.bag[,1],pxy.bag[,2],col="#000088",pch=pch,cex=cex)
}
if(show.whiskers && length(pxy.outer)>0){
debug.plots<-"not"
pkt.cut<-find.cut.z.pg(pxy.outer,hull.bag,center=center)
segments(pxy.outer[,1],pxy.outer[,2],pkt.cut[,1],pkt.cut[,2],col="red")
}
if(show.outlier && length(pxy.outlier)>0){ # points in loop
points(pxy.outlier[,1],pxy.outlier[,2],col="red",pch=pch,cex=cex)
}
if(exists("hull.center")&&length(hull.center)>2){
h<-rbind(hull.center,hull.center[1,]); lines(h[,1],h[,2],lty=1)
polygon(hull.center[,1],hull.center[,2],col="orange")
}
points(center[1],center[2],pch=8,col="red")
if(verbose){
h<-rbind(exp.dk,exp.dk[1,]); lines(h,col="blue",lty=2)
h<-rbind(exp.dk.1,exp.dk.1[1,]); lines(h,col="black",lty=2)
if(exists("tphdepth"))
text(tp[,1],tp[,2],as.character(tphdepth),col="green")
text(xy[,1],xy[,2],paste(as.character(hdepth)),cex=2)
points(center[1],center[2],pch=8,col="red")
}
"bagplot plottet"
}
bagplot<-function(x,y,
factor=3, # expanding factor for bag to get the loop
approx.limit=300, # limit
show.outlier=TRUE,# if TRUE outlier are shown
show.whiskers=TRUE, # if TRUE whiskers are shown
show.looppoints=TRUE, # if TRUE points in loop are shown
show.bagpoints=TRUE, # if TRUE points in bag are shown
show.loophull=TRUE, # if TRUE loop is shown
show.baghull=TRUE, # if TRUE bag is shown
create.plot=TRUE, # if TRUE a plot is created
add=FALSE, # if TRUE graphical elements are added to actual plot
pch=16,cex=.4,..., # to define further parameters of plot
dkmethod=2, # in 1:2; there are two methods for approximating the bag
precision=1, # controls precisionn of computation
verbose=FALSE,debug.plots="" # tools for debugging
){
bo<-compute.bagplot(x=x,y=y,factor=factor,approx.limit=approx.limit,
dkmethod=dkmethod,precision=precision,
verbose=verbose,debug.plots=debug.plots)
if(create.plot){
plot(bo,
show.outlier=show.outlier,
show.whiskers=show.whiskers,
show.looppoints=show.looppoints,
show.bagpoints=show.bagpoints,
show.loophull=show.loophull,
show.baghull=show.baghull,
add=add,pch=pch,cex=cex,...,
verbose=verbose
)
}
}
bitmap(file="test1.png")
bagplot(x=x, y=y, verbose=F, factor=par1, show.outlier=par2, show.whiskers=par3, show.baghull=T, dkmethod=2, show.loophull=T, precision=1, xlab=xlab, ylab=ylab, main=main)
box()
dev.off()
::Free Statistics and Forecasting Software::

:: Bagplot - Free Statistics Software (Calculator) ::
