hess_ramParallel = function(par,ImpCov,SampCov,Areg,Sreg,A,S,F){
#?sfClusterApplyLB
#sfClusterApplyLB(index, simulationIteration, n, rho, g, h, pv, het=F)
hess.out <- matrix(0,length(par),length(par))
# get rid of
#Areg = A.est
#Sreg= S.est
#ImpCov = out$imp_cov
#SampCov=S1
B = solve(diag(nrow(A)) - Areg)
C = diag(nrow(ImpCov)) - solve(ImpCov) %*% SampCov
E = B %*% Sreg %*% t(B)
vec = seq(1:length(par))
li <- list()
grid <- expand.grid(i=vec,j=vec)
grid <- as.matrix(grid)
for(i in 1:nrow(grid)) li[[i]] <- grid[i,]
snowfall::sfExport("Areg","A","ImpCov","SampCov","B","C","E","S","li")
hess_fun <- function(indexI,indexJ,Areg,A,ImpCov,SampCov,B,C,E,S){
#indexI <- list[1]
#indexJ <- list[2]
Ai <- A == indexI
Aj <- A == indexJ;
Aij <- matrix(0,nrow(A),ncol(A))
Aij[Ai==T | A==T] <- 1
Si <- S == indexI;
Sj <- S == indexJ;
Sij <- matrix(0,nrow(S),ncol(S))
Sij[Si==T | Sj==T] <- 1
deriv15_I <- F %*% B %*% Ai %*% E %*% t(F) + F %*% B %*% Si %*% t(B) %*% t(F)
deriv15_J <- F %*% B %*% Aj %*% E %*% t(F) + F %*% B %*% Sj %*% t(B) %*% t(F)
deriv15_IJ <- F %*% B %*% Ai %*% B %*% Aj %*% E %*% t(F) +
F %*% B %*% Aj %*% B %*% Ai %*% E %*% t(F) +
F %*% B %*% Ai %*% B %*% Sj %*% t(B) %*% t(F) +
F %*% B %*% Ai %*% E %*% t(Aj) %*% t(B) %*% t(F) +
F %*% B %*% Aj %*% B %*% Si %*% t(B) %*% t(F)
# left out mean part
trace(solve(ImpCov) %*% deriv15_IJ %*% C - solve(ImpCov) %*%
deriv15_I %*% solve(ImpCov) %*% deriv15_J %*% C +
solve(ImpCov) %*% deriv15_J %*% solve(ImpCov %*% deriv15_I %*%
solve(ImpCov) %*% SampCov))
}
#lapply(li,hess_fun(indexI=li$i,indexJ=li$j,Areg,A,ImpCov,SampCov,B,C,E,S))
rett = matrix(unlist(snowfall::sfLapply(li,function(x) hess_fun(indexI=x["i"],indexJ=x["j"],Areg,A,ImpCov,SampCov,B,C,E,S))),length(par),length(par))
#as.numeric(rett)
rett
}
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