LowWAFOMNX (version 1.1.1)

LowWAFOMNX-package: Low WAFOM Niederreiter-Xing Sequence

Description

Description: R implementation of Low Walsh Figure of Merit Sequence based on Niederreiter-Xing Sequence.

Acknowledgment

The development of this code is partially supported by JST CREST.

Reference

* Shinsuke Mori, "Suuchi Sekibun no tameno QMC Ten Shuugou no Sekkei, Tansaku, oyobi sono Yuukousei", Master's Thesis, 2017, * Ryuichi Ohori, "Efficient Quasi Monte Carlo Integration by Adjusting the Derivation-sensitivity Parameter of Walsh Figure of Merit", Master's Thesis, 2015. * S. Harase and R. Ohori, "A search for extensible low-WAFOM point sets", arXiv preprint, arXiv:1309.7828, (2013), https://arxiv.org/abs/1309.7828. * Harase, S. (2016). "A search for extensible low-WAFOM point sets", Monte Carlo Methods and Applications, 22(4), pp. 349-357, 2017. * M. Matsumoto and R. Ohori, "Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC", Springer International Publishing, Cham, 2016, pp. 143-160. * M. Matsumoto, M. Saito, and K. Matoba, "A computable figure of merit for quasi-Monte Carlo point sets", Mathematics of Computation, 83 (2014), pp. 1233-1250. * G. Pirsic, "A software implementation of Niederreiter-Xing sequences", in Monte Carlo and Quasi-Monte Carlo Methods 2000, Springer, 2002, pp. 434-445. https://sites.google.com/site/isabelpirsic/nxlegacy. * C. P. Xing and H. Niederreiter, "A construction of low-discrepancy sequences using global function fields", ACTA ARITHMETICA, 73 (1995), pp. 87-102.

Details

Porting to R by Mutsuo Saito. The R version does not return coordinate value zero, but returns value very near to zero, 2^-64.

Examples

# NOT RUN {
srange <- lowWAFOMNX.dimMinMax()
mrange <- lowWAFOMNX.dimF2MinMax(srange[1])
points <- lowWAFOMNX.points(dimR=srange[1], dimF2=mrange[1])
points <- lowWAFOMNX.points(dimR=srange[1], dimF2=mrange[1], digitalShift=TRUE)
# }