nrows=72
ncols=36
ntime = 1341    #Jan 1900 - Sep 2011
ntimep = 1332   # Jan 1900 - Dec 2010
nglobe = nrows*ncols

nyrs = ntimep/12	#1900 - 2010 
N = nrows*ncols


### Lat - Long grid..

locs=matrix(scan("http://civil.colorado.edu/~balajir/CVEN6833/R-sessions/session2/files-4HW2/sst-lat-long.txt"), ncol=2, byrow=T)
ygrid=seq(-87.5,87.5,by=5)
ny=length(ygrid)

xgrid=seq(27.5,382.5,by=5)
#xgrid[xgrid > 180]=xgrid[xgrid > 180]-360	#longitude on 0-360 grid if needed
xgrid[xgrid > 180]=xgrid[xgrid > 180]
nx=length(xgrid)

xygrid=matrix(0,nrow=nx*ny,ncol=2)

i=0
for(iy in 1:ny){
for(ix in 1:nx){
i=i+1
xygrid[i,1]=ygrid[iy]
xygrid[i,2]=xgrid[ix]
}

}

# REad Kaplan SST data..


#data=readBin("http://civil.colorado.edu/~balajir/CVEN6833/R-sessions/session2/files-HW2/Kaplan-SST-Jan1900-Sep2011.r4",what="numeric", n=( nrows * ncols * ntime), size=4,endian="swap")
data=readBin("Kaplan-SST-Jan1900-Sep2011.r4",what="numeric", n=( nrows * ncols * ntime), size=4,endian="swap")


data <- array(data = data, dim=c( nrows, ncols, ntime ) )


data1=data[,,1]
	

# the lat -long data grid..

index=1:(nx*ny)

index1=index[data1 < 20]	# only non-missing data.
xygrid1=xygrid[index1,]
x1=xygrid1[,2]

#x1[x1 < 0]= x1[x1 < 0] + 360
#xygrid1[,2]=x1

nsites=length(index1)
data2=data1[index1]

### SSTdata matrix - rows are months annd columns are locations
sstdata=matrix(NA,nrow=ntimep, ncol=nsites)


for(i in 1:ntimep){
data1=data[,,i]
index1=index[data1 < 20]
data2=data1[index1]
sstdata[i,]=data2
}

indexgrid = index1
rm("data")	#remove the object data to clear up space


### If you want annual data 
## create annual average data
nyrs1=ntimep/12
sstanavg = matrix(0,nrow=nyrs1, ncol=nsites)

for(i in 1:nsites){
xx=t(matrix(t(sstdata[,i]),nrow=12))
sstanavg[,i]=apply(xx,1,mean)

}

## write out the grid locations..
write(t(xygrid1),file="kaplan-sst-locs.txt",ncol=2)


###################### PCA 
## You can do the same with the monthly SST data sstdata

#get variance matrix..
zs=var(sstanavg)

#do an Eigen decomposition..
zsvd=svd(zs)

#Principal Components...
pcs=t(t(zsvd$u) %*% t(sstanavg))

#Eigen Values.. - fraction variance 
lambdas=(zsvd$d/sum(zsvd$d))

plot(1:40, lambdas[1:40], type="l", xlab="Modes", ylab="Frac. Var. explained")
points(1:40, lambdas[1:40], col="red")


#plots..
#plot the first spatial component or Eigen Vector pattern..
library(maps)
library(akima)
library(fields)


# the data is on a grid so fill the entire globaal grid with NaN and then populate the ocean grids with
# the Eigen vector
xlong = sort(unique(xygrid[,2]))
ylat = sort(unique(xygrid[,1]))
zfull = rep(NaN,nglobe)   #also equal 72*36
zfull[indexgrid]=zsvd$u[,1]
zmat = matrix(zfull,nrow=nrows,ncol=ncols)

image.plot(xlong,ylat,zmat,ylim=range(-40,70))
contour(xlong,ylat,(zmat),ylim=range(-40,70),add=TRUE,nlev=6,lwd=2)
map("world2",add=T)
#world(add=TRUE,shift=TRUE)


### Similarly plot the other two Eigen vectors..


################## If you wish to remove a component from the data, say first component.
####

nmodes = length(zsvd$u[1,])   # number of modes
nkeep = c(1)		# modes to keep, here we keep the first mode. If more then
			# nkeep=c(1,2,3) etc..
E = matrix(0,nrow=nmodes,ncol=nmodes)
E[,nkeep]=zsvd$u[,nkeep]
sstanavgkeep = pcs %*% t(E)

sstanrem = sstanavg - sstanavgkeep

## Now perform PCA on sstanrem