ssab = function(yy,M)
{

#### SSA 

N = length(yy)

m1 = M-1
Np = N-M+1
Np1 = Np+1

## create the lagged matrix
topl = matrix(0,Np,M)
for(i in 1:M){
i1=i-1+1
i2 = Np+i-1
topl[,i]=yy[i1:i2]
}

#zz=scale(topl)

zs=var(topl)
zsvd = svd(zs)

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

### PCs
At = topl %*% zsvd$u


#### Reconstructed Components RCs
Rpc = matrix(0,N,M)

for(ipc in 1:M){

## t = 1,M-1  mt = 1/t; lt = 1, ut =t
lt=1
m1 = M-1

for(i in 1:m1){

i1 = i-lt+1
i2 = i-i+1

Rpc[i,ipc] = sum(At[i1:i2,ipc]*zsvd$u[lt:i,ipc])/i

}

### t = M, N', mt = 1/M, lt = 1, ut = M
lt=1
ut=M

for(i in M:Np){

i1 = i-lt+1
i2 = i-M+1

Rpc[i,ipc] = sum(At[i1:i2,ipc]*zsvd$u[lt:ut,ipc])/M

}


### t = N'+1, N, mt = 1/(N-t+1), lt = t-N+M, ut = M
lt=1
ut=M

for(i in Np1:N){
lt = i-N+M
i1 = i-lt+1
i2 = i-M+1
mt = (N-i+1)

Rpc[i,ipc] = sum(At[i1:i2,ipc]*zsvd$u[lt:ut,ipc])/mt

}

}


out=c()
out$lambdas = lambdas
out$eof = zsvd$u
out$At = At
out$Rpc = Rpc

as.list(out)


}