Low WAFOM Niederreiter-Xing Sequence

R implementation of Low WAFOM Niederreiter-Xing Sequence, based on Shinsuke Mori, “Suuchi Sekibun no tameno QMC Ten Shuugou no Sekkei, Tansaku, oyobi sono Yuukousei”, Master’s Thesis, 2017, and Ryuichi Ohori, “Efficient Quasi Monte Carlo Integration by Adjusting the Derivation-sensitivity Parameter of Walsh Figure of Merit”, Master’s Thesis, 2015.

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

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

Reference

Sample

Get avairable dimension number of Low WAFOM Niederreiter-Xing Sequence.

library(LowWAFOMNX)
lowWAFOMNX.dimMinMax()
## [1]  4 32

Get avairable F2 dimension number of Low WAFOM Niederreiter-Xing Sequence.

lowWAFOMNX.dimF2MinMax(10)
## [1] 10 18

And get points. Each row of returned matrix contains an s-dimensional point.

s <- 4
m <- 10
c <- 2^m
mat <- lowWAFOMNX.points(dimR=s, dimF2=m, count=c)
mat[1,]
## [1] 5.421011e-20 5.421011e-20 5.421011e-20 5.421011e-20

Get digital shifted points.

s <- 4
m <- 10
c <- 2^m
mat <- lowWAFOMNX.points(dimR=s, dimF2=m, count=c, digitalShift=TRUE)
mat[1,]
## [1] 0.9851462 0.3864516 0.1844027 0.2333622