Latin Hypercube Sampling

Generates a Latin Hypercube Sampling (LHS) design matrix over the hypercube.

Usage

hypcube_lhs(n, d, lbound = NA_real_, ubound = NA_real_)

Arguments

n

Integer. The number of samples points of the hypercube.

d

Integer. The the dimension of the hypercube.

lbound

Numeric vector of length d specifying the lower bounds for each dimension of the d-dimensional hypercube.

ubound

Numeric vector of length d specifying the ubound bounds for each dimension of the d-dimensional hypercube.

Value

A n x d matrix containing the LHS design. Each element is scaled to the range defined by lbound and ubound.

References

McKay, M.D., Beckman, R.J., Conover, W.J. (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics. 21(2), 239–-245 (reprinted in 2000: Technometrics 42(1), 55–61).

Owen, A. B. (1992b) A central limit theorem for Latin hypercube sampling. JRSS Series B 54, 541-551.

Stein, M. (1987) Large sample properties of simulations using Latin hypercube sampling. Technometrics 29, 143-151.

Examples

x = hypcube_lhs(100, 2)
plot(x, xlim = c(0,1), ylim = c(0,1))
rug(x[,1]); rug(x[,2], side = 2)

x = hypcube_lhs(100, 2, lbound = c(-5,1), ubound = c(10,3))
plot(x, xlim = c(-5,10), ylim = c(1,3))
rug(x[,1]); rug(x[,2], side = 2)