SLHD: Sliced Latin Hypercube Design (SLHD)
In LHD: Latin Hypercube Designs (LHDs)

Description Usage Arguments Value References Examples

SLHD returns a n by k LHD matrix generated by improved two-stage algorithm

SLHD(
  n,
  k,
  t = 1,
  N = 10,
  T0 = 10,
  rate = 0.1,
  Tmin = 1,
  Imax = 3,
  OC = "phi_p",
  p = 15,
  q = 1,
  stage2 = FALSE,
  maxtime = 5
)

`n`	A positive integer, which stands for the number of rows (or run size).
`k`	A positive integer, which stands for the number of columns (or factor size).
`t`	A positive integer, which stands for the number of slices. `n`/`t` must be a positive integer, that is, n is divisible by t. `t` must be smaller or equal to `k` when `n` is 9 or larger. `t` must be smaller than `k` when `n` is smaller than 9. Otherwise, the funtion will never stop. The default is set to be 1.
`N`	A positive integer, which stands for the number of iterations. The default is set to be 10. A large value of `N` will result a high CPU time, and it is recommended to be no greater than 500.
`T0`	A positive number, which stands for the user-defined initial temperature. The default is set to be 10.
`rate`	A positive percentage, which stands for temperature decrease rate, and it should be in (0,1). For example, rate=0.25 means the temperature decreases by 25% each time. The default is set to be 10%.
`Tmin`	A positive number, which stands for the minimium temperature allowed. When current temperature becomes smaller or equal to `Tmin`, the stopping criterion for current loop is met. The default is set to be 1.
`Imax`	A positive integer, which stands for the maximum perturbations the algorithm will try without improvements before temperature is reduced. The default is set to be 5. For the computation complexity consideration, `Imax` is recommended to be smaller or equal to 5.
`OC`	An optimality criterion. The default setting is "phi_p", and it could be one of the following: "phi_p", "AvgAbsCor", "MaxAbsCor", "MaxProCriterion".
`p`	A positive integer, which is the parameter in the phi_p formula, and `p` is prefered to be large. The default is set to be 15.
`q`	The default is set to be 1, and it could be either 1 or 2. If `q` is 1, `dij` is the Manhattan (rectangular) distance. If `q` is 2, `dij` is the Euclidean distance.
`stage2`	A logic input argument, and it could be either FALSE or TRUE. If `stage2` is FALSE (the default setting), `SLHD` will only implement the first stage of the algorithm. If `stage2` is TRUE, `SLHD` will implement the whole algorithm.
`maxtime`	A positive number, which indicates the expected maximum CPU time given by user, and it is measured by minutes. For example, maxtime=3.5 indicates the CPU time will be no greater than three and half minutes. The default is set to be 5.

If all inputs are logical, then the output will be a n by k LHD. As mentioned from the original paper, the first stage plays a much more important role since it optimizes the slice level. More resources should be given to the first stage if computational budgets are limited. Let m=n/t, where m is the number of rows for each slice, if (m)^k >> n, the second stage becomes optional. That is the reason why we add a stage2 parameter to let users decide if the second stage is needed.

Ba, S., Myers, W.R., and Brenneman, W.A. (2015) Optimal Sliced Latin Hypercube Designs. Technometrics, 57, 479-487.

#generate a 5 by 3 maximin distance LHD with the default setting
try=SLHD(n=5,k=3)
try
phi_p(try)   #calculate the phi_p of "try".

#generate a 5 by 3 maximin distance LHD with stage II
#let stage2=TRUE and other input are the same as above
try2=SLHD(n=5,k=3,stage2=TRUE)
try2
phi_p(try2)   #calculate the phi_p of "try2".

#Another example
#generate a 8 by 4 nearly orthogonal LHD
try3=SLHD(n=8,k=4,OC="AvgAbsCor",stage2=TRUE)
try3
AvgAbsCor(try3)  #calculate the average absolute correlation.