# NOTE: THIS FILE CONTAINS ERRORS AND HAS BEEN SUPERCEDED BY R_les_proxy.txt
# WE ARE GRATEFUL TO MCSHANE AND WYNER FOR NOTICING THEM. (DEC 16 2010).

# Calculate proxy PC log eigenvalue spectrum
# cf. Mann et al (2007, JGR), Wilks (2006)

pc_hat <- list(NULL) 
pc_var <- list(NULL)  
sd_res <- list(NULL)  

# normalise eigenvalues (saved arrays are sqrt(eigenvalue)), to the power of 4 to get eigenvalues^2

pc_var[[1]] = pc_sdev_orig^4
pc_var[[2]] = pc_sdev_correct^4
pc_var[[3]] = pc_sdev_correct_notilj^4

for (i in 1:3){
pc_var[[i]] = pc_var[[i]]/sum(pc_var[[i]])
}

# fit line to lowest half of log spectrum
for (i in 1:3){
  nhalf=floor(length(pc_var[[i]]))
  mylm <- lm(log(pc_var[[i]][1:nhalf])~., data=data.frame(x=1:nhalf))
  pc_hat[[i]] <- predict(mylm, data.frame(x=1:nhalf))
  sd_res[[i]] <- sd(residuals(mylm))
}

# plot points and lines
pdf(pdffile, width=7, height=7)

plot(1:40,0.01*1:40,type="n", xlab="Eigenvalue number", ylab="Variance explained", ylim=c(0.002,0.5), xlim=c(0,40), col="grey", main="Eigenvalue spectrum", cex.main=0.8, log="y", yaxs="i",xaxs="i")

for (i in 1:3){
  nhalf=floor(length(pc_var[[i]]))
  points(pc_var[[i]][1:nhalf],col=i,pch=i)
  lines(exp(pc_hat[[i]][1:nhalf]),col=i)
}

legend(15,0.1,legend=c("MW network (93 proxies)","Correct proxies (57)","Correct proxies (no Tiljander) (55)"),pch=c(1,2,3),col=c(1,2,3))

dev.off()

# using tolerance and criteria estimate PCs to be retained.
# retain if log(eigenvalue) is greater than the fit plus a tolerance (1 sd residuals)
print("Use Log Eigenvalue criteria...")
for (i in 1:3){
  print(paste("For network ",i," retain ",sum(pc_var[[1]][1:20] > exp(pc_hat[[1]][1:20]+sd_res[[i]]))," PCs",sep=""))
}

# Alternatively...
print("Or Cumulative Percent Variance explained > 50%...")
for (i in 1:3){
  n=0
  for (j in 1:10) { if (sum(pc_var[[i]][1:j]) < 0.5) {n=n+1} }
  print(paste("For network ",i," retain ",n+1," PCs",sep=""))
}




#