rm(list=ls())
library(fda)
attach(growth)

#a
gr<-cbind(growth$hgtm,growth$hgtf)
length(apply(gr,1,mean)->mif)

wach<-gr
for (i in 1:93)
wach[,i]<-gr[,i]-mif


#b
base<-create.bspline.basis(nbasis=12,rangeval=c(1,18))
plot(base, col=rainbow(12))

#c
Data2fd(age,mif,base)->meanf
plot(meanf)

Data2fd(age,wach,base)->wachfd
plot(wachfd)

v<-(meanf+wachfd[1])
plot(v)

#d
gfda<-pca.fd(wachfd,nharm=10)
plot(gfda)

#e
str(gfda)
koef<-gfda$scores
antvar<-gfda$varprop
cumsum(antvar)
harmfd<-gfda$harmonics

#f
par(mfrow=c(2,1),ask=TRUE)
for (i in 1:4){
plot(harmfd[i])
plot(meanf,ylim=c(70,190),lty=3,col="gray")
lines(meanf+20*harmfd[i])
lines(meanf-20*harmfd[i])
}

# besser
a<-rep(0,4)
for (i in 1:4)
a[i]<-sd(koef[,i])
a
par(mfrow=c(2,1),ask=TRUE)
for (i in 1:4){
plot(harmfd[i])
plot(meanf,ylim=c(70,190),lty=3,col="gray")
lines(meanf+a[i]*harmfd[i])
lines(meanf-a[i]*harmfd[i])
}

# g

dim(koef)

n=93
par(mfrow=c(1,2))
plot(c(1,18),c(70,200),type="n")
matlines(age,gr,lty=1)
plot(c(1,18),c(70,200),type="n")
for (i in 1:n)
	lines(meanf+koef[i,1]*harmfd[1],col=i)

par(mfrow=c(1,2))
plot(c(1,18),c(70,200),type="n")
matlines(age,gr,lty=1)
plot(c(1,18),c(70,200),type="n")
for (i in 1:n)
	lines(meanf+koef[i,1]*harmfd[1]+koef[i,2]*harmfd[2],col=i)

par(mfrow=c(1,2))
plot(c(1,18),c(70,200),type="n")
matlines(age,gr,lty=1,col=rainbow(93))
plot(c(1,18),c(70,200),type="n")
for (i in 1:n)
	lines(meanf+koef[i,1]*harmfd[1]+koef[i,2]*harmfd[2]+koef[i,3]*harmfd[3],col=rainbow(93)[i])


#h
plot(koef[,1:2])
kmeans(koef[,1:2],centers=2,nstart=3)->km
plot(koef[,1:2],col=km$cluster,pch=c(rep(16,39),rep(17,54)))

# weil "Euklidischer Norm"
plot(koef[,1:2],col=km$cluster,pch=16,asp=1)

# entweder muss man bezüglich einen anderen Abstand "gruppieren",
# oder die werte erst normieren
u<-koef[,1]/sd(koef[,1])
v<-koef[,2]/sd(koef[,2])
cbind(u,v)->uv
kmeans(uv,centers=2,nstart=3)->km
plot(uv,col=km$cluster,pch=c(rep(16,39),rep(17,54)),cex=1.5)
km$cluster