UnitVector<-function(n){matrix(rep(1,n),n,1)}

sympower <- function(x,pow) {
edecomp <- eigen(x)
roots <- edecomp$val
v <- edecomp$vec
d <- roots^pow
if(length(roots)==1) d <- matrix(d,1,1) else d <- diag(d)
sympow <- v %*% d %*% t(v)
sympow
}

P <-function(x) {
y <- x %*% solve(t(x) %*% x) %*% t(x)
y
}

Q <- function(x) {
q <- diag(dim(x)[1]) - P(x)
q
}

CompleteSymmetricMatrix <- function(x) {L <- length(x)
p <- (sqrt(8*L + 1) -1)/2
y <- matrix(0,p,p)
count <- 0
for(i in 1:p ) {for (j in 1:i){count <- count+1
y[i,j] <- x[count]
y[j,i] <- x[count]
}
}
y
}

CompleteCorrelationMatrix <- function(x) {L <- length(x)
p <- (sqrt(8*L + 1) +1)/2
y <- matrix(1,p,p)
count <- 0
for(i in 2:p ) {for (j in 1:(i-1)){count <- count+1
y[i,j] <- x[count]
y[j,i] <- x[count]
}
}
y
}

MakeExactData <- function(mean,var,n,use.population=FALSE) {
mu<-mean
sigma <- var
if(length(mu) == 1) mu <- matrix(mu,1,1) else if(!is.matrix(mu))mu <- matrix(mu,ncol=1)
if(length(sigma)==1) sigma <- matrix(sigma,1,1) else if(!is.matrix(sigma))sigma <- diag(sigma)
p <- dim(sigma)[1]
x <- matrix(rnorm(n*p),n,p)
input.cov <- if(use.population)((n-1)/n) * cov(x) else cov(x)
x <-x %*% sympower(input.cov,-1/2) %*% sympower(sigma,1/2)
diff <- matrix(0,1,p)
for(i in 1:p){
diff[1,i] <- mu[i]-mean(x[,i])
}
for(i in 1:n) {
  for(j in 1:p) {
    x[i,j] <- x[i,j] + diff[1,j]}
}
x
}