# example from the correlation matrix
# Jun tavg stations USW00014771 USW00094728
# correlation matrix

rm(list=ls())
source("scripts/myfunctions.R")





# covariance matrix between USW00014771 and USW00094728
# tavg June monthly mean anomalies

C<-matrix(c(1.4732,0.7530,0.7530,1.1516),2,2)

# eigenvectors
# e1=c(1.502,-0.8683)
# e2=c(-0.8683,1.5019)



# find the direction where input (black) 
# and output vector (red) have same direction

#plot_vector(x)
# as a test criterion I us the scaling factors 
# if the x component of the new vector 
# and the y component are stretched/squeezed by the same factor
# the ratio l1/l2 will be 1.0
print(" input angle, vector x-coordinate, y-coordinate, scaling ratio")
for (i in seq(0,360,10)) {	
  phi<-i/180.0*pi
  print(paste("test vector in direction of phi= ",round(phi/pi*180.,2)))
  x<-c(cos(phi),sin(phi))	
  y<-C%*%x
  # when
  l1<-y[1]/x[1]
  l2<-y[2]/x[2]
  print(paste(i,x[1],x[2],l1/l2))
  plot(c(-3,3),c(-3,3),typ='n',xlab='x1',ylab='x2')
  plot_vector(x,col=1)
  plot_vector(y,col=2)
  res<-readline("enter for next testing the next direction ('q' for exit)")
  if (res=='q') {break}
}