# runif.faure: Low discrepancy sequence : Faure In DiceDesign: Designs of Computer Experiments

## Description

Generate a Faure sequence with n experiments in [0,1]^d.

## Usage

 1 runif.faure(n, dimension)

## Arguments

 n the number of experiments dimension the number of variables (<100)

## Details

A quasirandom or low discrepancy sequence, such as the Faure, Halton, Hammersley, Niederreiter or Sobol sequences, is "less random" than a pseudorandom number sequence, but more useful for such tasks as approximation of integrals in higher dimensions, and in global optimization. This is because low discrepancy sequences tend to sample space "more uniformly" than random numbers.

see randtoolbox or fOptions packages for other low discrepancy sequences.

## Value

runif.halton returns a list containing all the input arguments detailed before, plus the following component:

 design the design of experiments

J. Franco

## References

Faure H. (1982), Discrepance de suites associees a un systeme de numeration (en dimension s), Acta Arith., 41, 337-351

## Examples

 1 2 3 f <- runif.faure(20,2) plot(f\$design, xlim=c(0,1), ylim=c(0,1)) xDRDN(f, letter="T", dgts=2, range=c(-10, 10))

### Example output

T1     T2
1    0.34   0.34
2   -5.17   5.86
3    5.86  -5.17
4   -7.93   3.10
5    3.10  -7.93
6   -2.41  -2.41
7    8.62   8.62
8   -9.31  10.00
9    1.72  -1.03
10  -3.79  -6.55
11   7.24   4.48
12  -6.55  -3.79
13   4.48   7.24
14  -1.03   1.72
15  10.00  -9.31
16 -10.00   1.03
17   1.03 -10.00
18  -4.48  -4.48
19   6.55   6.55
20  -7.24  -7.24

DiceDesign documentation built on Feb. 13, 2021, 1:06 a.m.