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f_surGRT_beta <- function(beta,Tm,G,N,Y,X,Sigma){
chol_Sigma <- chol(Sigma)
ldet_Sigma <- sum(2*log(diag(chol_Sigma)))
Sigma_inv <- try(chol2inv(chol_Sigma))
IT <- diag(Tm) # as.matrix(Matrix::Diagonal(Tm))
IR <- diag(N) # as.matrix(Matrix::Diagonal(N))
#momegap1 <- Matrix::Matrix(kronecker(IT,S0_inv))
# k0 <- kronecker(Sigma_inv,IR)
Res <- (Y - X%*%beta)
#IOME <- kronecker(IT,kronecker(Sigma_inv,IR))
#IOMER<- IOME%*%Res
RES=matrix(as.matrix(Res),nrow = N)
IOMER<-matrix(RES%*%kronecker(IT,Sigma_inv),ncol = 1)
# llike <- as.numeric( -(Tm*G*N/2)*log(2*pi) - (N*Tm/2)*ldet_Sigma - (1/2)*(t(Res) %*% IOME %*% Res))
llike <- as.numeric( -(Tm*G*N/2)*log(2*pi) - (N*Tm/2)*ldet_Sigma - (1/2)*Matrix::crossprod(Res,IOMER))
return((-1)*llike)
}
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