nrows=72
ncols=36
ntime = 111    #JJAS 1900 - JJAS 2010
ntimep = 111   # JJAS 1900 - JJAS 2010
N = nrows*ncols


### Lat - Long grid..

locs=matrix(scan("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("Kaplan-SST-JJAS1900-JJAS2011.r4",what="numeric", n=( nrows * ncols * ntime), size=4,endian="swap")


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


data1=data[,,1]
# Missing value is NaN, put it to a large number..
data1[data1 == "NaN"]=1e+30	

# 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)	# locations with data -i.e. global locations
data2=data1[index1]

### SSTdata matrix - rows are years and columns are locations on the globe with data
sstdata=matrix(NA,nrow=ntimep, ncol=nsites)


for(i in 1:ntimep){
data1=data[,,i]
data1[data1 == "NaN"]=1e+30	
index1=index[data1 < 20]
data2=data1[index1]
sstdata[i,]=data2
}

## Index of locations corresponding to Pacific Tropic
xlongs = xygrid[,2]
ylats = xygrid[,1]
indextrop = index[data1 < 20 & ylats >= -20 & ylats <= 20 & xlongs >= 105 & xlongs <= 290]

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

### Tropical Pacific Ocean
xlongs = xygrid1[,2]
ylats = xygrid1[,1]
xlong = xlongs[ylats >= -20 & ylats <= 20 & xlongs >= 105 & xlongs <= 290]
ylat = ylats[ylats >= -20 & ylats <= 20 & xlongs >= 105 & xlongs <= 290]
index1=1:length(xlongs)
index = index1[ylats >= -20 & ylats <= 20 & xlongs >= 105 & xlongs <= 290]

### Tropical seasonal average.. - the data already is seasonal average
sstanavgtrop = sstdata[,index]

xygridp=cbind(ylat,xlong)

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


###################### PCA 
## PCA on the seasonal SST for the Trop. Pacific Ocean

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

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

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

#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]))
nrows=72
ncols=36
nglobe = length(xlong)*length(ylat)   # also equal to 72*36

zfull = rep(NaN,nglobe)
zfull[indextrop]=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)
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