```
Sigma_i = function(i,Y_na,Y.hat.matrix){
days = which(!is.na(Y_na[i,]))
Sigma_ii = matrix(NA, nrow = length(days), ncol = length(days))
for ( l in days){
for ( s in days){
no_na_l = which(!is.na(Y_na[,l]))
no_na_s = which(!is.na(Y_na[,s]))
#find the common plants that have both the lth time and the sth time(no NA)
elements = Reduce(intersect, list(no_na_l,no_na_s))
temp = c(NA,length(elements))
for (k in 1: length(elements)){
temp[k] = (Y_na[elements[k],l]-Y.hat.matrix[elements[k],l])*((Y_na[elements[k],s]-Y.hat.matrix[elements[k],s]))
}
sum_temp = sum(temp)
#if(length(elements)<10)
#print(length(elements))
cov_ls = (1/(length(elements)-1))*sum_temp
Sigma_ii[which(days==l),which(days==s)] = cov_ls
}
}
return(Sigma_ii)
}
```

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