# Construct a D-optimal design for SLR on [0,1]

k0 = 5
k.end = 1000
par(mfrow = c(2,1))
x0 = seq(from = 0, to = 1, length = k0) # Five-point intial design
hist(x0, breaks = 100, freq = F)
x = x0
for (k in k0:(k.end-1)) {
M = cbind(c(1, mean(x)), c(mean(x), mean(x^2))) # Form M(xi_k)
Minv = solve(M)  # and its inverse
q = function(t) -sum(c(1,t)*(Minv%*%c(1,t))) # The minimizer of q(t) is the next design point
newx= nlminb(start = .5, objective = q, lower = 0,upper = 1)$par
cat("k = ", k, "newx = ", newx, "\n")
x = c(x,newx)
}
x
hist(x, breaks = 100, freq = F)