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Data X:
9356 9337 10149 9788 9770 9911 9429 8775 10189 10529 9914 9790 9625 9729 10589 9611 9388 9510 9690 8434 9844 10601 9942 10229 9381 9635 11228 9999 10089 11622 10533 9965 11567 11321 11686 11747 10595 10751 12199 11690 10978 11753 10839 10518 12183 11967 12363 12359 12162 12096 14325 12670 13865 13563 12734 12464 13389 13961 14088 13143 13413 13579 15388 13708 14689 14883 13991 13854 14364 15672 15904 14016
Data Y:
14271 14013 15912 14290 14744 14721 13918 13263 15660 15629 15113 14526 15132 14908 16167 14122 13985 14236 13921 12394 15454 16146 15107 14593 14695 14513 17071 15179 15460 17173 15938 15003 18216 17847 18029 17281 16706 16750 18912 17763 16736 18061 16713 16769 19514 19251 19951 19052 19555 19083 22534 18854 19801 20346 18169 19087 20842 21602 22360 20334 21215 20530 23152 20134 21193 21628 20823 20493 22106 24178 24958 21620
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Factor (defining the loop)
Show outliers
TRUE
TRUE
FALSE
Show whiskers
TRUE
TRUE
FALSE
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R Code
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)]) } 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()
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