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

Description Usage Arguments Details Value Author(s) References Examples

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

1	runif.faure(n, dimension)

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

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.

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

design

the design of experiments

J. Franco

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

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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))

       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