# Example: How to use od.REX.D for a quadratic model on [-1,1]x[-1,1]

# First, we will use the function F.cube of the package OptimalDesign
# to easily generate the matrix of all permissible regressors:
library(OptimalDesign)
Fq <- F.cube(~x1+x2+I(x1^2)+I(x2^2)+I(x1*x2), c(-1,-1), c(1,1), c(101, 101))

# Let n be the size of the design space and m the number of parameters:
n <- dim(Fq)[1]; m <- dim(Fq)[2]

# Compute the D-optimal approximate design using od.REX.D:
resR <- od.REX.D(Fq, sample(1:n, m), gam=4, eff=1-1e-10, t.max=Inf)

# Extract the indices of the support of the design:
supp <- (1:n)[resR$w.best > 1e-12]

# Print a compact table of the D-optimal design:
cbind(Fq[supp, 2:3], weight=resR$w.best[supp])

# Print the time-profile of the computation:
print(cbind(format(round(resR$prof[,1], 2), nsmall = 2),
      format(round(resR$prof[,2], 12), nsmall = 12)), quote=FALSE)