.. _DiscSobol: Discussion: Sobol sequence =========================== Description and background -------------------------- A Sobol sequence is a sequence of points in a design space which has the general property of being :ref:`space filling`. The procedure page :ref:`ProcSobolSequence` provides a detailed algorithm for constructing Sobol sequences based on Sobol's original description, and a worked example. Sobol's construction is based on bit-wise XOR operations between special generators called direction numbers. The first impression is that the construction of a Sobol sequence is a complex task. However, by constructiong a few Sobol numbers by hand, using the procedure in :ref:`ProcSobolSequence`, it is easy to understand the underlying structure. Discussion ---------- For users of the R programming language, we suggest the function ``runif.sobol(n,d)`` from the package fOptions in the `R repository `_. A well known concern about Sobol sequences is the correlation between points in high dimensional sequences. A solution to this is by scrambling the sequence. The R package above described allows for the sequence to be scrambled, if desired. In this case, either of the two functions described above can be called with the arguments :: (n,d,scrambling,seed,init) The argument scrambling takes an integer which is 0 if no scrambling is to be used, 1 for Owen type of scrambling, 2 for Faure-Tezuka scrambling and 3 for a combination of both. The argument seed is the integer seed to trigger the scrambling process and init is a logical flag which allows the Sobol sequence to restart if set to ``TRUE``.