# 2014-03-31
# 
# example of covariance matrix 
#
# clear memory
rm(list=ls())
# reset the plot window to full sized plot
par(mfrow=c(1,1))
source("scripts/loadano2.R")



month<-"Jan"
# Station 1

x1<-loadano2(station="USW00014750",state="NY",month=month,start=1950,end=2012)
# Station 2
x2<-loadano2(station="USW00094728",state="NY",month=month,start=1950,end=2012)


xm1<-mean(x1$ano)
xm2<-mean(x2$ano)

x1$ano<-x1$ano-xm1
x2$ano<-x2$ano-xm2

# forming a matrix from existing vectors of same dimension
# (length(x1$ano)==length(x2$ano))

X<-cbind(x1$ano,x2$ano)
N<-length(x1$ano)
# R for the advanced: special string creation from a vector
res<-paste(dim(X),collapse=' x ')

print(paste("dimension of the matrix X: (",res,")",sep=''))

# matrix multiplication in R %*%
# transpose of a matrix t()
Sxx<-t(X)%*%X
res<-paste(dim(Sxx),collapse=' x ')
print(paste("dimension of the matrix Sxx: (",res,")",sep=''))
Cxx<-1/(N-1)*Sxx

print(Cxx)


plot(x1$ano,x2$ano)



# fitted regression line is now 
# (centered data => intercept = 0)

bfit<-cor(x1$ano,x2$ano)*sd(x2$ano)/sd(x2$ano)

lines(x1$ano,bfit*x1$ano,col=5)