VarToChol <- function(param){
# this function computes a set of cholesky type parameters from a set of variance type parameters so that user
# can input variance parameters directly
B <- matrix(c(param[c(6,7,8)], 0, param[c(26,27,28)], 0,
param[c(7,9,10)], 0, param[c(29,30,31)], 0,
param[c(8,10,11)], 0, param[c(32,33,34)], 0,
rep(0,3), param[12], rep(0,3), param[25],
param[c(26,29,32)], 0, param[c(18,19,20)], 0,
param[c(27,30,33)], 0, param[c(19,21,22)], 0,
param[c(28,31,34)], 0, param[c(20,22,23)], 0,
rep(0,3), param[25], rep(0,3), param[24]), byrow = TRUE, nrow = 8)
U <- chol(B)
return(c(param[1:4], sqrt(param[5]), U[1,1], U[1,2], U[1,3], U[2,2], U[2,3], U[3,3], U[4,4],
param[13:16], sqrt(param[17]), U[5,5], U[5,6], U[5,7], U[6,6], U[6,7], U[7,7], U[8,8],
U[4,8], U[1,5], U[1,6], U[1,7], U[2,5], U[2,6], U[2,7], U[3,5], U[3,6], U[3,7]))
}
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