| Title: | Low WAFOM Niederreiter-Xing Sequence |
|---|---|
| Description: | Implementation of Low Walsh Figure of Merit (WAFOM) sequence based on Niederreiter-Xing sequence <DOI:10.1007/978-3-642-56046-0_30>. |
| Authors: | Shinsuke Mori [aut], Ryuichi Ohori [aut], Makoto Matsumoto [aut], Mutsuo Saito [cre] |
| Maintainer: | Mutsuo Saito <[email protected]> |
| License: | BSD_3_clause + file LICENSE |
| Version: | 1.1.1 |
| Built: | 2024-11-19 05:56:49 UTC |
| Source: | https://github.com/mersennetwister-lab/lowwafomnx |
Description: R implementation of Low Walsh Figure of Merit Sequence based on Niederreiter-Xing Sequence.
Porting to R by Mutsuo Saito. The R version does not return coordinate value zero, but returns value very near to zero, 2^-64.
The development of this code is partially supported by JST CREST.
* 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.
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)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)
get minimum and maximum F2 dimension number.
lowWAFOMNX.dimF2MinMax(dimR)lowWAFOMNX.dimF2MinMax(dimR)
dimR |
dimention. |
supported minimum and maximum F2 dimension number
get minimum and maximum dimension number of Low WAFOM Niederreiter-Xing Sequence
lowWAFOMNX.dimMinMax()lowWAFOMNX.dimMinMax()
supported minimum and maximum dimension number.
This R version does not returns coordinate value zero, but returns value very near to zero, 2^-64.
lowWAFOMNX.points(dimR, dimF2 = 10, digitalShift = FALSE)lowWAFOMNX.points(dimR, dimF2 = 10, digitalShift = FALSE)
dimR |
dimension. |
dimF2 |
F2-dimension of each element. |
digitalShift |
use digital shift or not. |
matrix of points where every row contains dimR dimensional point.