Nothing
hessian_parallel = function(par,ImpCov,A,S,F,A_fixed,A_est,S_fixed,S_est,lambda,alpha,type){
hesS_out <- matrix(0,length(par),length(par))
h <- 0.0001
# using Cudeck, Klebe, Henly (1993)
add <- matrix(0,length(par),length(par))
diag(add) <- h
vec = seq(1:length(par))
li <- list()
grid <- expand.grid(i=vec,j=vec)
grid <- as.matrix(grid)
for(i in 1:nrow(grid)) li[[i]] <- grid[i,]
snowfall::sfExport("add","par","A","ImpCov","A_fixed","A_est","S","S_fixed","S_est","F","li")
hess_fun <- function(indexI,indexJ,ImpCov,A,S,F,A_fixed,A_est,S_fixed,S_est,add){
ImpCovI = RAMmult((par + add[indexI,]),A,S,F,A_fixed,A_est,S_fixed,S_est)[[1]]
ImpCovJ = RAMmult((par + add[,indexJ]),A,S,F,A_fixed,A_est,S_fixed,S_est)[[1]]
ImpCovII <- (ImpCovI - ImpCov)/h
ImpCovJJ <- (ImpCovJ - ImpCov)/h
0.5 * trace(solve(ImpCov) %*% ImpCovII %*% solve(ImpCov) %*% ImpCovJJ)
}
matrix(unlist(snowfall::sfLapply(li,function(x) hess_fun(indexI=x["i"],indexJ=x["j"],
ImpCov,A,S,F,A_fixed,A_est,S_fixed,S_est,add))),length(par),length(par))
}
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