STK_SAMPLING_SOBOL generates points from a Sobol sequence
CALL: X = stk_sampling_sobol (N, D)
computes the first N terms of a D-dimensional Sobol sequence (with
N < 2^32 and D <= 1111). The sequence is generated using the algorithm
of Bratley and Fox [1], as modified by Joe and Kuo [3].
CALL: X = stk_sampling_sobol (N, DIM, BOX)
does the same thing in the DIM-dimensional hyperrectangle specified by the
argument BOX, which is a 2 x DIM matrix where BOX(1, j) and BOX(2, j) are
the lower- and upper-bound of the interval on the j^th coordinate.
CALL: X = stk_sampling_sobol (N, D, BOX, DO_SKIP)
skips an initial segment of the Sobol sequence if DO_SKIP is true. More
precisely, according to the recommendation of [2] and [3], a number of
points equal to the largest power of 2 smaller than n is skipped. If
DO_SKIP is false, the beginning of the sequence is returns, as in the
previous cases (in other words, DO_SKIP = false is the default).
NOTE: Implementation
The C implementation under the hood is due to Steven G. Johnson, and
was borrowed from the NLopt toolbox [4] (version 2.4.2).
REFERENCE
[1] Paul Bratley and Bennett L. Fox, "Algorithm 659: Implementing Sobol's
quasirandom sequence generator", ACM Transactions on Mathematical
Software, 14(1):88-100, 1988.
[2] Peter Acworth, Mark Broadie and Paul Glasserman, "A Comparison of Some
Monte Carlo and Quasi Monte Carlo Techniques for Option Pricing", in
Monte Carlo and Quasi-Monte Carlo Methods 1996, Lecture Notes in
Statistics 27:1-18, Springer, 1998.
[3] Stephen Joe and Frances Y. Kuo, "Remark on Algorithm 659: Implementing
Sobol's Quasirandom Sequence Generator', ACM Transactions on
Mathematical Software, 29(1):49-57, 2003.
[4] Steven G. Johnson, The NLopt nonlinear-optimization package,
http://ab-initio.mit.edu/nlopt.
SEE ALSO: stk_sampling_halton_rr2