N<-150 pnum<-N # frame 1 lift<-0.01 colot<-c("red","blue","green","orange") type<-c("gauss","exponential","student") xmax<-9 support<-c(-xmax,xmax) ymax<-0.5 plot(x="",y="",xlim=c(-xmax,xmax),ylim=c(0,ymax),xlab="",ylab="") for (i in 1:length(type)){ func<-type[i] col<-colot[i] pcf<-eval.func.1D(func,N,support=support) dp<-draw.pcf(pcf,pnum=pnum) matpoints(dp$x,dp$y,type="l",xlab="",ylab="",col=col) inde<-which.max(dp$y);text(dp$x[inde],dp$y[inde]+lift,func,col=col) } # frame 2 # gauss lift<-0.02 xmax<-3 ymax<-1 plot(x="",y="",xlim=c(-xmax,xmax),ylim=c(0,ymax),xlab="",ylab="") func<-"gauss" col<-"red" support<-c(-xmax,xmax) pcf<-eval.func.1D(func,N,support=support) dp<-draw.pcf(pcf,pnum=pnum) matpoints(dp$x,dp$y,type="l",xlab="",ylab="",col=col) inde<-which.max(dp$y);text(dp$x[inde],dp$y[inde]+lift,"gauss",col=col) # polynomial func<-"polynomial" g<-1 col<-"blue" pcf<-eval.func.1D(func,N,support=support,g=g) dp<-draw.pcf(pcf,pnum=pnum) matpoints(dp$x,dp$y,type="l",xlab="",ylab="",col=col) inde<-which.max(dp$y);text(dp$x[inde],dp$y[inde]+lift, paste("s=",as.character(g)),col=col) g<-2 col<-"green" pcf<-eval.func.1D(func,N,support=support,g=g) dp<-draw.pcf(pcf,pnum=pnum) matpoints(dp$x,dp$y,type="l",xlab="",ylab="",col=col) inde<-which.max(dp$y);text(dp$x[inde],dp$y[inde]+lift, paste("s=",as.character(g)),col=col) g<-3 col<-"orange" pcf<-eval.func.1D(func,N,support=support,g=g) dp<-draw.pcf(pcf,pnum=pnum) matpoints(dp$x,dp$y,type="l",xlab="",ylab="",col=col) inde<-which.max(dp$y);text(dp$x[inde],dp$y[inde]+lift, paste("s=",as.character(g)),col=col)
# download the file barchart.txt file<-"~/barchart.txt" datamat<-read.table(file=file) dendat<-datamat[,1] low<-datamat[,2] high<-datamat[,3] open<-datamat[,4] aika<-seq(1:length(dendat)) xmin<-1 xmax<-length(dendat) ymin<-min(low) ymax<-max(high) # frame plot(x="",y="",type="n",ylim=c(ymin,ymax),xlab="",ylab="",xlim=c(xmin,xmax), xaxt='n') minnu<-1 vecpit<-minnu/3 x0<-aika-vecpit y0<-open x1<-aika y1<-open segments(x0,y0,x1,y1) x0<-aika+vecpit y0<-dendat x1<-aika y1<-dendat segments(x0,y0,x1,y1) x0<-aika y0<-low x1<-aika y1<-high segments(x0,y0,x1,y1)
N<-150 pnum<-N xmax<-9; support<-c(-xmax,xmax) func<-"gauss" pcf<-eval.func.1D(func,N,support=support) dp<-draw.pcf(pcf,pnum=pnum) func<-"exponential" pcf<-eval.func.1D(func,N,support=support) dp2<-draw.pcf(pcf,pnum=pnum) func<-"student" pcf<-eval.func.1D(func,N,support=support) dp3<-draw.pcf(pcf,pnum=pnum) # frame 1 plot(dp$y,dp2$y,type="l",ylab="exponential",xlab="standard Gaussian",col="red") ma<-max(dp$y,dp2$y) segments(0,0,ma,ma) # frame 2 plot(dp$y,dp3$y,type="l",ylab="Student",xlab="standard Gaussian",col="red") ma<-max(dp$y,dp3$y) segments(0,0,ma,ma)
# download the file aspect.txt file<-"~/aspect.txt" dendat<-read.table(file=file) # frames layout(matrix(c(1,2,3,3), 2, 2, byrow = TRUE),widths=c(1,2,3)) plot(dendat[,1],type="l",xlab="",ylab="SP 500",xaxt="n") plot(dendat[,1],type="l",xlab="",ylab="SP 500",xaxt="n") plot(dendat[,1],type="l",xlab="",ylab="SP 500",xaxt="n")
N<-150 pnum<-N # frame 1 colot<-c("red","blue","green","orange") type<-c("gauss","exponential","student") xmax<-8 support<-c(-xmax,xmax) ymax<-1 plot(x="",y="",xlim=c(-xmax,xmax),ylim=c(0,1),xlab="",ylab="") for (i in 1:length(type)){ func<-type[i] col<-colot[i] pcf<-eval.func.1D(func,N,support=support,distr=TRUE) dp<-draw.pcf(pcf,pnum=pnum) #,dens=FALSE) matpoints(dp$x,dp$y,type="l",xlab="",ylab="",col=col) inde<-floor(2.5*N/4);text(dp$x[inde],dp$y[inde],func,col=col) } # frame 2 lift<-0.02 fac<-0.75 xmax<-2 support<-c(-xmax,xmax) plot(x="",y="",xlim=c(-xmax,xmax),ylim=c(0,1),xlab="",ylab="") func<-"gauss" col<-"red" pcf<-eval.func.1D(func,N,support=support,distr=TRUE) dp<-draw.pcf(pcf,pnum=pnum)#,dens=FALSE) matpoints(dp$x,dp$y,type="l",xlab="",ylab="",col=col) inde<-floor(fac*N);text(dp$x[inde],dp$y[inde]+lift,"gauss",col=col) func<-"polynomial" g<-1 col<-"blue" pcf<-eval.func.1D(func,N,support=support,g=g,distr=TRUE) dp<-draw.pcf(pcf,pnum=pnum)#,dens=FALSE) matpoints(dp$x,dp$y,type="l",xlab="",ylab="",col=col) inde<-floor(fac*N);text(dp$x[inde],dp$y[inde]+lift, paste("s=",as.character(g)),col=col) g<-2 col<-"green" pcf<-eval.func.1D(func,N,support=support,g=g,distr=TRUE) dp<-draw.pcf(pcf,pnum=pnum)#,dens=FALSE) matpoints(dp$x,dp$y,type="l",xlab="",ylab="",col=col) inde<-floor(fac*N);text(dp$x[inde],dp$y[inde]+lift, paste("s=",as.character(g)),col=col) g<-3 col<-"orange" pcf<-eval.func.1D(func,N,support=support,g=g,distr=TRUE) dp<-draw.pcf(pcf,pnum=pnum)#,dens=FALSE) matpoints(dp$x,dp$y,type="l",xlab="",ylab="",col=col) inde<-floor(fac*N);text(dp$x[inde],dp$y[inde]+lift, paste("s=",as.character(g)),col=col)
N<-150 pnum<-N xmax<-9; support<-c(-xmax,xmax) func<-"gauss" pcf<-eval.func.1D(func,N,support=support,distr=TRUE) dp<-draw.pcf(pcf,pnum=pnum) func<-"exponential" pcf<-eval.func.1D(func,N,support=support,distr=TRUE) dp2<-draw.pcf(pcf,pnum=pnum) func<-"student" pcf<-eval.func.1D(func,N,support=support,distr=TRUE) dp3<-draw.pcf(pcf,pnum=pnum) # frame 1 plot(dp2$y,dp$y,type="l",xlab="exponential",ylab="standard Gaussian",col="red") ma<-max(dp$y,dp2$y) segments(0,0,ma,ma) # frame 2 plot(dp3$y,dp$y,type="l",xlab="Student",ylab="standard Gaussian",col="red") ma<-max(dp$y,dp3$y) segments(0,0,ma,ma)
N<-c(60,60) pcf<-sim.data(N=N,type="mulmod") dp<-draw.pcf(pcf) # left frame persp(x=dp$x,y=dp$y,z=dp$z, xlab="coordinate 1",ylab="coordinate 2",zlab="", ticktype="detailed", phi=30,theta=-20) title(sub="perspective plot") # right frame contour(dp$x,dp$y,dp$z, xlab="coordinate 1",ylab="coordinate 2", nlevels=25) title(sub="contour plot")
func<-"gauss" N<-c(32,32) marginal<-"student" r<-0.8 t<-1 nlev<-c(10,50,500) supo<-c(3,4,15) # frame 1 i<-1 nlevel<-nlev[i] yla<-supo[i] ala<--yla support<-c(ala,yla,ala,yla) ef<-pcf.func(func,N,t=c(t,t),support=support,marginal=marginal,r=r) dp<-draw.pcf(ef) contour(dp$x,dp$y,dp$z,nlevel=nlevel) # frame 2 i<-2 nlevel<-nlev[i] yla<-supo[i] ala<--yla support<-c(ala,yla,ala,yla) ef<-pcf.func(func,N,t=c(t,t),support=support,marginal=marginal,r=r) dp<-draw.pcf(ef) contour(dp$x,dp$y,dp$z,nlevel=nlevel) # frame 3 i<-3 nlevel<-nlev[i] yla<-supo[i] ala<--yla support<-c(ala,yla,ala,yla) ef<-pcf.func(func,N,t=c(t,t),support=support,marginal=marginal,r=r) dp<-draw.pcf(ef) contour(dp$x,dp$y,dp$z,nlevel=nlevel)
func<-"gauss" N<-c(32,32) marginal<-"unif" r<-0.2 ef<-pcf.func(func,N,marginal=marginal,r=r) dp<-draw.pcf(ef) # frame 1 persp(dp$x,dp$y,dp$z,theta=-25,phi=40,ticktype="detailed", xlab="",ylab="",zlab="") # frame 2 contour(dp$x,dp$y,dp$z,xlab="",ylab="",nlevels=10) # frame 3 contour(dp$x,dp$y,dp$z,xlab="",ylab="",nlevels=100)
N<-c(100,100) et<-sim.data(N=N,type="fox") luk<-100 dm<-draw.pcf(et,pnum=c(luk,luk)) # Slices parallel to the x-axis d1<-1 slicenum<-9 alaY<--5.5 #et$support[2*d1-1] ylaY<-8 #et$support[2*d1] hop<-(ylaY-alaY)/(slicenum-1) gridiX<-seq(alaY,ylaY,hop) # slices parallel to the y-axis d1<-2 slicenum<-9 alaX<--3 #et$support[2*d1-1] ylaX<-5 #et$support[2*d1] hop<-(ylaX-alaX)/(slicenum-1) gridiY<-seq(alaX,ylaX,hop) # frame 1 contour(dm$x,dm$y,dm$z,nlevels=20) for (i in 1:length(gridiX)) lines(c(-7,9.5),c(gridiX[i],gridiX[i])) # frame 2 contour(dm$x,dm$y,dm$z,nlevels=20) for (i in 1:length(gridiX)) lines(c(gridiY[i],gridiY[i]),c(-10,12))
N<-c(100,100) et<-sim.data(N=N,type="fox") luk<-100 dm<-draw.pcf(et,pnum=c(luk,luk)) # Slices parallel to the x-axis d1<-1 slicenum<-9 alaY<--5.5 #et$support[2*d1-1] ylaY<-8 #et$support[2*d1] hop<-(ylaY-alaY)/(slicenum-1) gridiX<-seq(alaY,ylaY,hop) maxi<-0 for (i in 1:length(gridiX)){ vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) maxi<-max(sl$value,maxi) } # frame 1 i<-1 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 2 i<-2 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 3 i<-3 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 4 i<-4 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 5 i<-5 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 6 i<-6 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 7 i<-7 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 8 i<-8 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 9 i<-9 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5)
N<-c(100,100) et<-sim.data(N=N,type="fox") luk<-100 dm<-draw.pcf(et,pnum=c(luk,luk)) # slices parallel to the y-axis d1<-2 slicenum<-9 alaX<--3 #et$support[2*d1-1] ylaX<-5 #et$support[2*d1] hop<-(ylaX-alaX)/(slicenum-1) gridiY<-seq(alaX,ylaX,hop) maxi<-0 for (i in 1:length(gridiY)){ vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) maxi<-max(sl$value,maxi) } # frame 1 i<-1 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 2 i<-2 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 3 i<-3 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 4 i<-4 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 5 i<-5 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 6 i<-6 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 7 i<-7 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 8 i<-8 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 9 i<-9 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5)
param<-sim.fox() sig<-param$sig M<-param$M p<-param$p N<-c(45,45) theta<-pi/4 support<-c(-8,6,-6,8) et<-pcf.func("mixt",N,sig=sig,M=M,p=p,theta=theta,support=support) dm<-draw.pcf(et,pnum=c(60,60)) # Slices parallel to the x-axis d1<-1 slicenum<-9 alaY<--5 #et$support[2*d1-1] ylaY<-6 #et$support[2*d1] hop<-(ylaY-alaY)/(slicenum-1) gridiX<-seq(alaY,ylaY,hop) # slices parallel to the y-axis d1<-2 slicenum<-9 alaX<--6 #et$support[2*d1-1] ylaX<-5 #et$support[2*d1] hop<-(ylaX-alaX)/(slicenum-1) gridiY<-seq(alaX,ylaX,hop) # frame 1 contour(dm$x,dm$y,dm$z,nlevels=20) for (i in 1:length(gridiX)) lines(c(-9,9.5),c(gridiX[i],gridiX[i])) # frame 2 contour(dm$x,dm$y,dm$z,nlevels=20) for (i in 1:length(gridiX)) lines(c(gridiY[i],gridiY[i]),c(-10,12))
param<-sim.fox() sig<-param$sig M<-param$M p<-param$p N<-c(45,45) theta<-pi/4 support<-c(-8,6,-6,8) et<-pcf.func("mixt",N,sig=sig,M=M,p=p,theta=theta,support=support) dm<-draw.pcf(et,pnum=c(60,60)) # Slices parallel to the x-axis d1<-1 slicenum<-9 alaY<--5 #et$support[2*d1-1] ylaY<-6 #et$support[2*d1] hop<-(ylaY-alaY)/(slicenum-1) gridiX<-seq(alaY,ylaY,hop) maxi<-0 for (i in 1:length(gridiX)){ vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) maxi<-max(sl$value,maxi) } # frame 1 i<-1 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 2 i<-2 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 3 i<-3 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 4 i<-4 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 5 i<-5 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 6 i<-6 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 7 i<-7 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 8 i<-8 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 9 i<-9 vecci<-gridiX[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5)
param<-sim.fox() sig<-param$sig M<-param$M p<-param$p N<-c(45,45) theta<-pi/4 support<-c(-8,6,-6,8) et<-pcf.func("mixt",N,sig=sig,M=M,p=p,theta=theta,support=support) dm<-draw.pcf(et,pnum=c(60,60)) # slices parallel to the y-axis d1<-2 slicenum<-9 alaX<--6 #et$support[2*d1-1] ylaX<-5 #et$support[2*d1] hop<-(ylaX-alaX)/(slicenum-1) gridiY<-seq(alaX,ylaX,hop) maxi<-0 for (i in 1:length(gridiY)){ vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) maxi<-max(sl$value,maxi) } # frame 1 i<-1 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 2 i<-2 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 3 i<-3 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 4 i<-4 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 5 i<-5 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 6 i<-6 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 7 i<-7 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 8 i<-8 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5) # frame 9 i<-9 vecci<-gridiY[i] sl<-slicing(et,vecci,d1=d1) dms<-draw.pcf(sl) plot(dms$x,dms$y,type="l",xlab="",ylab="",ylim=c(0,maxi),cex.axis=1.5)
param<-sim.fox() sig<-param$sig M<-param$M p<-param$p supportx<-c(-4,8) supporty<-c(-10,11) # frame 1 # projection to x-axis Mx<-M[,1] sigx<-sig[,1] N<-100 et<-pcf.func(func="mixt",M=Mx,sig=sigx,p=p,N=N,support=supportx) dm<-draw.pcf(et) plot(dm$x,dm$y,type="l",xlab="",ylab="") # frame 2 # projection to y-axis My<-M[,2] sigy<-sig[,2] et<-pcf.func(func="mixt",M=My,sig=sigy,p=p,N=N,support=supporty) dm<-draw.pcf(et) plot(dm$x,dm$y,type="l",xlab="",ylab="")
d<-3 dproj<-2 dist<-3 height<-sqrt(3)/2 # sqrt(3)/2 = 0.8660254 len<-1/(2*sqrt(3)) # 1/(2*sqrt(3)) = 0.2886751 kor<-sqrt(2/3) # sqrt(2/3) = 0.8164966 moodi<-4 sig<-matrix(1,moodi,dproj) p<-rep(1,moodi)/moodi # Projection to x-y plane. Mxy<-matrix(0,moodi,dproj) Mxy[1,]<-dist*c(1/2,0) Mxy[2,]<-dist*c(-1/2,0) Mxy[3,]<-dist*c(0,height) Mxy[4,]<-dist*c(0,len) N<-c(60,60) M<-Mxy pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) #dmxy<-drawmix(Mxy,sig,p,plkm=60) dmxy<-draw.pcf(pcf,pnum=N) # Projection to x-z plane. Mxz<-matrix(0,moodi,dproj) Mxz[1,]<-dist*c(1/2,0) Mxz[2,]<-dist*c(-1/2,0) Mxz[3,]<-dist*c(0,0) Mxz[4,]<-dist*c(0,kor) #dmxz<-drawmix(Mxz,sig,p,plkm=60) N<-c(60,60) M<-Mxz pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) #dmxy<-drawmix(Mxy,sig,p,plkm=60) dmxz<-draw.pcf(pcf,pnum=N) # Projection to y-z plane. Myz<-matrix(0,moodi,dproj) Myz[1,]<-dist*c(0,0) Myz[2,]<-dist*c(0,0) Myz[3,]<-dist*c(height,0) Myz[4,]<-dist*c(len,kor) N<-c(60,60) M<-Myz pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) #dmxy<-drawmix(Mxy,sig,p,plkm=60) dmyz<-draw.pcf(pcf,pnum=N) # bigger distance dist<-4 Mxy<-matrix(0,moodi,dproj) Mxy[1,]<-dist*c(1/2,0) Mxy[2,]<-dist*c(-1/2,0) Mxy[3,]<-dist*c(0,height) Mxy[4,]<-dist*c(0,len) N<-c(60,60) M<-Mxy pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) #dmxy<-drawmix(Mxy,sig,p,plkm=60) dm<-draw.pcf(pcf,pnum=N) # frame 1 persp(dmxy$x,dmxy$y,dmxy$z,phi=30,theta=130,box=FALSE,col="white") text(-0.3,-0.4,"(a)",cex=1.5) # frame 2 persp(dmxz$x,dmxz$y,dmxz$z,phi=30,theta=130,box=FALSE,col="white") text(-0.3,-0.4,"(b)",cex=1.5) # frame 3 persp(dmyz$x,dmyz$y,dmyz$z,phi=30,theta=130,box=FALSE,col="white") text(-0.3,-0.4,"(c)",cex=1.5) # frame 4 persp(dm$x,dm$y,dm$z,phi=30,theta=130,box=FALSE,col="white") text(-0.3,-0.4,"(d)",cex=1.5)
dist<-4 # determines the distance between vertices of the pentahedron d<-4 moodi<-5 M<-matrix(0,moodi,d) M[1,]<-dist*c(1/2, 0,0,0) M[2,]<-dist*c(-1/2,0,0,0) M[3,]<-dist*c(0,sqrt(3)/2,0,0) M[4,]<-dist*c(0,1/(2*sqrt(3)),sqrt(2/3),0) M[5,]<-dist*c(0,1/(2*sqrt(3)),1/(2*sqrt(6)),sqrt(15/24)) sig<-matrix(1,moodi,d) p0<-1/moodi p<-p0*rep(1,moodi) dist<-4 dproj<-2 sig<-matrix(1,moodi,dproj) # Projection to x-y plane. M<-matrix(0,moodi,dproj) M[1,]<-dist*c(1/2,0) M[2,]<-dist*c(-1/2,0) M[3,]<-dist*c(0,sqrt(3)/2) M[4,]<-dist*c(0,1/(2*sqrt(3))) M[5,]<-dist*c(0,1/(2*sqrt(3))) N<-c(60,60) pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) dmxy<-draw.pcf(pcf,pnum=N) # Projection to x-z plane. M<-matrix(0,moodi,dproj) M[1,]<-dist*c(1/2,0) M[2,]<-dist*c(-1/2,0) M[3,]<-dist*c(0,0) M[4,]<-dist*c(0,sqrt(2/3)) M[5,]<-dist*c(0,1/(2*sqrt(6))) N<-c(60,60) pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) dmxz<-draw.pcf(pcf,pnum=N) # Projection to x-u plane. M<-matrix(0,moodi,dproj) M[1,]<-dist*c(1/2,0) M[2,]<-dist*c(-1/2,0) M[3,]<-dist*c(0,0) M[4,]<-dist*c(0,0) M[5,]<-dist*c(0,sqrt(15/24)) N<-c(60,60) pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) #dmxy<-drawmix(Mxy,sig,p,plkm=60) dmxu<-draw.pcf(pcf,pnum=N) # Projection to y-z plane. M<-matrix(0,moodi,dproj) M[1,]<-dist*c(0,0) M[2,]<-dist*c(0,0) M[3,]<-dist*c(sqrt(3)/2,0) M[4,]<-dist*c(1/(2*sqrt(3)),sqrt(2/3)) M[5,]<-dist*c(1/(2*sqrt(3)),1/(2*sqrt(6))) N<-c(60,60) pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) dmyz<-draw.pcf(pcf,pnum=N) # Projection to y-u plane. M<-matrix(0,moodi,dproj) M[1,]<-dist*c(0,0) M[2,]<-dist*c(0,0) M[3,]<-dist*c(sqrt(3)/2,0) M[4,]<-dist*c(1/(2*sqrt(3)),0) M[5,]<-dist*c(1/(2*sqrt(3)),sqrt(15/24)) N<-c(60,60) pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) dmyu<-draw.pcf(pcf,pnum=N) # Projection to z-u plane. M<-matrix(0,moodi,dproj) M[1,]<-dist*c(0,0) M[2,]<-dist*c(0,0) M[3,]<-dist*c(0,0) M[4,]<-dist*c(sqrt(2/3),0) M[5,]<-dist*c(1/(2*sqrt(6)),sqrt(15/24)) N<-c(60,60) pcf<-pcf.func("mixt",N,sig=sig,M=M,p=p) dmzu<-draw.pcf(pcf,pnum=N) # frame 1 persp(dmxy$x,dmxy$y,dmxy$z,phi=30,theta=130,box=FALSE,col="white") text(-0.3,-0.4,"a)",cex=1.5) # frame 2 persp(dmxz$x,dmxz$y,dmxz$z,phi=30,theta=130,box=FALSE,col="white") text(-0.3,-0.4,"b)",cex=1.5) # frame 3 persp(dmxu$x,dmxu$y,dmxu$z,phi=30,theta=130,box=FALSE,col="white") text(-0.3,-0.4,"c)",cex=1.5) # frame 4 persp(dmyz$x,dmyz$y,dmyz$z,phi=30,theta=130,box=FALSE,col="white") text(-0.3,-0.4,"d)",cex=1.5) # frame 5 persp(dmyu$x,dmyu$y,dmyu$z,phi=30,theta=130,box=FALSE,col="white") text(-0.3,-0.4,"e)",cex=1.5) # frame 6 persp(dmzu$x,dmzu$y,dmzu$z,phi=30,theta=130,box=FALSE,col="white") text(-0.3,-0.4,"f)",cex=1.5)
volball<-function(r,d){ return(r^d*pi^(d/2)/gamma(d/2+1)) } volsphere<-function(d){ return(2*pi^(d/2)/gamma(d/2)) } maksimit<-function(d,type,sig=1,nu=1) { if (type=="gauss"){ maksi<-(2*pi)^(-d/2) } if (type=="bartlett"){ maksi<-sig^{-d}*(volsphere(d)*2/(d*(d+2)))^(-1) } if (type=="student"){ maksi<-gamma((nu+d)/2)/(gamma(nu/2)*(pi*nu)^(d/2)) } if (type=="bartlett2"){ maksi<-(volsphere(d)*2^(1-d)/(d*(d+2)))^(-1) } return(maksi) } voluumit<-function(d,leve,type,sig=1,nu=1) { if (type=="gauss"){ norma<-(2*pi)^{-d/2} radi<-sig*sqrt(-2*log(leve*sig^d/norma)) #sig*sqrt(-2*log(leve)-d*log(2*pi)) } if (type=="bartlett"){ norma<-d*(d+2)/(2*volsphere(d)) radi<-sig*sqrt(1-leve*sig^d/norma) #maksi<-sig^{-d}*(volsphere(d)*2/(d*(d+2)))^(-1) #radi<-sig*sqrt(1-leve/maksi) } if (type=="student"){ norma<-gamma((nu+d)/2)/(gamma(nu/2)*(pi*nu)^(d/2)) radi<-nu*(exp(-2*log(leve/norma)/(d+nu))-1) } if (type=="bartlett2"){ maksi<-(volsphere(d)*2^(1-d)/(d*(d+2)))^(-1) radi<-sqrt(1-leve/maksi)/2 } volu<-volball(radi,d) return(list(volu=volu,radi=radi)) } volugene<-function(d,lnum,type,epsi=NULL,sig=1,nu=1) { maksi<-maksimit(d,type,sig=sig,nu=nu) if (is.null(epsi)){ step<-maksi/(lnum) minni<-step } else{ minni<-epsi step<-(maksi-minni)/lnum } levels<-seq(minni,(maksi),step) maksivol<-voluumit(d,levels[1],type,sig=sig,nu=nu)$volu x<-matrix(0,2*lnum,1) y<-matrix(0,2*lnum,1) x[1]<-0 x[2*lnum]<-maksivol y[1]<-levels[1] y[2*lnum]<-y[1] for (i in 2:(lnum-1)){ volpre<-voluumit(d,levels[i-1],type,sig=sig,nu=nu)$volu volnyk<-voluumit(d,levels[i],type,sig=sig,nu=nu)$volu erotus<-volpre-volnyk x[i]<-x[i-1]+erotus/2 x[2*lnum-i+1]<-x[2*lnum-i+2]-erotus/2 y[i]<-levels[i] y[2*lnum-i+1]<-y[i] } x[lnum]<-maksivol/2 x[lnum+1]<-maksivol/2 y[lnum]<-levels[lnum] y[lnum+1]<-levels[lnum] return(list(x=x,y=y)) #plot(x,y,type="l") } d<-1 type<-"bartlett" sig<-1 mak<-maksimit(d,type,sig=sig) lkm<-100 step<-mak/lkm leve<-seq(step,mak-step,step) vol<-voluumit(d,leve,type,sig=sig) vg<-volugene(d,lnum=1000,type=type,sig=sig) # frame 1 plot(leve,vol$volu,type="l",xlab="level",ylab="volume") # frame 2 plot(vol$volu,leve,type="l",xlab="volume",ylab="level") # frame 3 plot(vg$x,vg$y,type="l",xlab="volume",ylab="level")
dime<-seq(1,20,1) r<-1/2 eka<-volball(r,dime) r<-1 toka<-volball(r,dime) # frame plot(dime,toka,type="b",xlab="dimension",ylab="volume") matpoints(dime,eka,type="b") text(9.5,4,"r=1") text(4,0.8,"r=0.5")
plotunivol<-function(R,dimet,type,gnum=1000,sig=1,nu=1,inde=round(gnum/2)) { xmax<-0 ymax<-0 for (i in 1:length(dimet)){ d<-dimet[i] rp<-tailfunc(R,d,type,gnum=gnum,sig=sig,nu=nu) x<-rp$volu y<-rp$level xmax<-max(xmax,x) ymax<-max(ymax,y) } plot(x="",y="",xlim=c(0,xmax),ylim=c(0,ymax),xlab="volume",ylab="level") for (i in 1:length(dimet)){ d<-dimet[i] rp<-tailfunc(R,d,type,gnum=gnum,sig=sig,nu=nu) x<-rp$volu y<-rp$level sy<-symme(x,y) xp<-sy$x/2 yp<-sy$y matpoints(xp,yp,type="l",xlab="volume",ylab="level") text(xp[inde],yp[inde],paste("d=",as.character(dimet[i]))) } } symme<-function(x,y) { x11<-x[length(x)]-x x1<-x11[length(x11):1] x2<-x+x[length(x)] x3<-c(x1,x2) y1<-y[length(y):1] y3<-c(y1,y) return(list(x=x3,y=y3)) } # frame 1 type<-"bartlett" gnum<-1000 sig<-1 R<-1 dimet<-c(1,3,5,7,9) plotunivol(R,dimet,type,gnum=gnum,inde=700) # frame 2 sig<-1/2 R<-1/2 dimet<-c(1,3,5) plotunivol(R,dimet,type,gnum=gnum,sig=sig,nu=nu,inde=700) # frame 3 type<-"gauss" gnum<-1000 sig<-1 R<-5 dimet<-c(1:2) plotunivol(R,dimet,type,gnum=gnum,inde=700) # frame 4 type<-"student" nu<-1 R<-10 dimet<-c(1:2) plotunivol(R,dimet,type,gnum=gnum,inde=700,nu=nu)
plotradi<-function(R,type,gnum=1000,sig=1,nu=1,d=d) { rp<-tailfunc(R,d,type,gnum=gnum,sig=sig,nu=nu) x<-rp$radi y<-rp$levelnorma sy<-symme(x,y) xp<-sy$x yp<-sy$y plot(x=xp,y=yp,xlab="radius",ylab="normalized level",type="l") } plotmanyradi<-function(R,dimet,type,gnum=1000,sig=1,nu=1,inde=round(gnum/2)) { xmax<-0 ymax<-0 for (i in 1:length(dimet)){ d<-dimet[i] rp<-tailfunc(R,d,type,gnum=gnum,sig=sig,nu=nu) x<-rp$radi y<-rp$levelnorma xmax<-max(xmax,x) ymax<-max(ymax,y) } plot(x="",y="",xlim=c(-xmax,xmax),ylim=c(0,ymax), xlab="radius",ylab="normalized level") for (i in 1:length(dimet)){ d<-dimet[i] rp<-tailfunc(R,d,type,gnum=gnum,sig=sig,nu=nu) x<-rp$radi y<-rp$levelnorma sy<-symme(x,y) xp<-sy$x-R yp<-sy$y matpoints(xp,yp,type="l",xlab="volume",ylab="level") text(xp[inde],yp[inde],paste("d=",as.character(dimet[i]))) } } # frame 1 d<-1 type<-"bartlett" R<-1 rp<-tailfunc(R,d,type,gnum=gnum,sig=sig,nu=nu) x<-rp$radi y<-rp$levelnorma sy<-symme(x,y) xp<-sy$x-1 yp<-sy$y type<-"gauss" R<-3.5 rp<-tailfunc(R,d,type,gnum=gnum,sig=sig,nu=nu) x<-rp$radi y<-rp$levelnorma sy<-symme(x,y) xp2<-sy$x-R yp2<-sy$y plot(x="",y="",xlim=c(-R,R),ylim=c(0,0.8),xlab="radius",ylab="normalized level") matpoints(xp,yp,type="l",xlab="volume",ylab="level") matpoints(xp2,yp2,type="l",xlab="volume",ylab="level") # frame 2 type<-"student" R<-10 dimet<-c(1:3) nu<-1 plotmanyradi(R,dimet,type,nu=nu,inde=800)
plotquantile<-function(R,dimet,type,gnum=1000,sig=1,nu=1, inde=round(gnum/2)) { coln<-length(dimet) rown<-gnum xm<-matrix(0,rown,coln) ym<-matrix(0,rown,coln) for (i in 1:length(dimet)){ d<-dimet[i] rp<-tailfunc(R,d,type,gnum=gnum,sig=sig,nu=1) xm[,i]<-rp$proba ym[,i]<-rp$volu } matplot(xm,ym,type="l",xlab="probability",ylab="volume") for (i in 1:length(dimet)) text(xm[inde,i],ym[inde,i],paste("d=",as.character(dimet[i]))) } # frame 1 type<-"bartlett" gnum<-1000 R<-1 dimet<-c(1,3,5,7,9) plotquantile(R,dimet,type,gnum=gnum,inde=900) # frame 2 R<-0.5 sig<-0.5 dimet<-c(1,3,5) plotquantile(R,dimet,type,gnum=gnum,sig=sig,inde=700) # frame 3 type<-"gauss" gnum<-1000 sig<-1 R<-6 dimet<-c(1:2) plotquantile(R,dimet,type,gnum=gnum,inde=700) # frame 4 type<-"student" gnum<-1000 sig<-1 R<-10 nu<-1 dimet<-c(1:2) plotquantile(R,dimet,type,gnum=gnum,inde=700,nu=nu)
plotquantile.norm<-function(R,dimet,type,gnum=1000,sig=1,nu=1, inde=round(gnum/2),textdim=length(dimet)) { coln<-length(dimet) rown<-gnum xm<-matrix(0,rown,coln) ym<-matrix(0,rown,coln) for (i in 1:length(dimet)){ d<-dimet[i] rp<-tailfunc(R,d,type,gnum=gnum,sig=sig,nu=nu) xm[,i]<-rp$proba ym[,i]<-rp$radi } matplot(xm,ym,type="l",xlab="probability",ylab="radius") for (i in 1:textdim) text(xm[inde,i],ym[inde,i],paste("d=",as.character(dimet[i]))) } gnum<-1000 dimet<-c(1:20) # frame 1 type<-"bartlett" R<-1 plotquantile.norm(R,dimet,type,gnum=gnum,inde=700,textdim=5) # frame 2 type<-"gauss" R<-6 plotquantile.norm(R,dimet,type,gnum=gnum,inde=300,textdim=5) # frame 3 type<-"student" R<-20 nu<-1 plotquantile.norm(R,dimet,type,gnum=gnum,inde=300,textdim=5,nu=nu)
plotdistri.norm<-function(R,dimet,type,gnum=1000,sig=1,nu=nu, inde=round(gnum/2),textdim=length(dimet)) { coln<-length(dimet) rown<-gnum xm<-matrix(0,rown,coln) ym<-matrix(0,rown,coln) for (i in 1:length(dimet)){ d<-dimet[i] rp<-tailfunc(R,d,type,gnum=gnum,sig=sig,nu=1) xm[,i]<-rp$radi ym[,i]<-rp$proba } matplot(xm,ym,type="l",ylab="probability",xlab="radius") for (i in 1:textdim) text(xm[inde,i],ym[inde,i],paste("d=",as.character(dimet[i]))) } # frame 1 type<-"bartlett" R<-1 plotdistri.norm(R,dimet,type,gnum=gnum,inde=700,textdim=5) # frame 2 type<-"gauss" R<-6 plotdistri.norm(R,dimet,type,gnum=gnum,inde=300,textdim=5) # frame 3 type<-"student" R<-20 nu<-1 plotdistri.norm(R,dimet,type,gnum=gnum,inde=300,textdim=5,nu=nu)