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
Package: stk