rm(list=ls())
read.table("datenb3.txt",header=TRUE)->tab

t<-tab[,1]
y<-tab[,2]

plot(t,y,pch=16,cex=0.5)
curve(10*(5*x^4-7*x^3+2*x^2)+4*x,0,1,add=TRUE,col=2)
lines(ksmooth(t,y,kernel="normal",bandwidth=0.2),col=3,lwd=2)
lines(ksmooth(t,y,kernel="normal",bandwidth=0.05),col=4,lwd=2)
lines(ksmooth(t,y,kernel="normal",bandwidth=0.5),col=5,lwd=2)
legend("topleft",legend=c("echte Kurve", "bw=0.2","bw=0.05","bw=0.5"),col=2:5,lwd=c(1,rep(2,3)))

library(KernSmooth)
plot(t,y,pch=16,cex=0.5)
curve(10*(5*x^4-7*x^3+2*x^2)+4*x,0,1,add=TRUE,col=2)
lines(locpoly(t,y,bandwidth=0.05),lwd=2,col=3)
lines(locpoly(t,y,bandwidth=0.1),lwd=2,col=4)
lines(locpoly(t,y,bandwidth=0.2),lwd=2,col=5)
lines(locpoly(t,y,bandwidth=0.5),lwd=2,col=6)
legend("topleft",legend=c("echte Kurve", "bw=0.05","bw=0.1","bw=0.2",bw=0.5),col=2:6,lwd=c(1,rep(2,4)))

### Aufg 3

n<-length(y)

#alles zusammen, mit wenige Stützstellen
cv<-c()
ha<-seq(0.02,0.2,by=0.02)
par(mfrow=c(1,3))
cvall<-matrix(NA,length(ha),3)
for (deg in 1:3){
	for (k in 1:length(ha)){
		hatm<-rep(NA,n)
			for (i in 1:n){
			datenm<-cbind(t[-i],y[-i])
			fitm<-locpoly(datenm[,1],datenm[,2],bandwidth=ha[k],gridsize=101,range.x=c(0,1),degree=deg)
			#lines(fitm)
			hatm[i]<-fitm$y[i]
		}
	cv[k]<-1/n*sum((y-hatm)^2)
	}
	cvall[,deg]<-cv
	plot(ha,cvall[,deg])
	lines(ha,cvall[,deg],col=2)
}


# Genauer:
# für deg=1
ha<-seq(0.045,0.06,by=0.001)
for (k in 1:length(ha)){
	hatm<-rep(NA,n)
	for (i in 1:n){
		datenm<-cbind(t[-i],y[-i])
		fitm<-locpoly(datenm[,1],datenm[,2],bandwidth=ha[k],gridsize=101,range.x=c(0,1),degree=1)
		hatm[i]<-fitm$y[i]
	}
cv[k]<-1/n*sum((y-hatm)^2)
}

h1<-ha[which.min(cv)]
h1

#für deg=2
ha<-seq(0.09,0.11,by=0.001)
for (k in 1:length(ha)){
	hatm<-rep(NA,n)
	for (i in 1:n){
		datenm<-cbind(t[-i],y[-i])
		fitm<-locpoly(datenm[,1],datenm[,2],bandwidth=ha[k],gridsize=101,range.x=c(0,1),degree=2)
		#lines(fitm)
		hatm[i]<-fitm$y[i]
	}
cv[k]<-1/n*sum((y-hatm)^2)
}
h2<-ha[which.min(cv)]
h2

# für deg=3
ha<-seq(0.1,0.13,by=0.001)
for (k in 1:length(ha)){
	hatm<-rep(NA,n)
	for (i in 1:n){
		datenm<-cbind(t[-i],y[-i])
		fitm<-locpoly(datenm[,1],datenm[,2],bandwidth=ha[k],gridsize=101,range.x=c(0,1),degree=3)
		#lines(fitm)
		hatm[i]<-fitm$y[i]
	}
cv[k]<-1/n*sum((y-hatm)^2)
}
h3<-ha[which.min(cv)]
h3



plot(t,y,pch=16,cex=0.5)
curve(10*(5*x^4-7*x^3+2*x^2)+4*x,0,1,add=TRUE,col=2)
lines(locpoly(t,y,bandwidth=h1),lwd=2,col=3)
lines(locpoly(t,y,bandwidth=h2,degree=2),lwd=2,col=4)
lines(locpoly(t,y,bandwidth=h3,degree=3),lwd=2,col=5)
legend("topleft",legend=c("echte Kurve","1. Grad", "2. Grad", "3. Grad"),col=2:5,lwd=c(1,rep(2,3)))