Low WAFOM Sobol Sequence

R implementation of Low WAFOM Sobol 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 return coordinate value zero, but returns value very near to zero, 2^-64.

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

Reference

Get available dimension number of Low WAFOM Sobol Sequence.

library(LowWAFOMSobol)
lowWAFOMSobol.dimMinMax()
## [1]  2 90

Get available F2 dimension number of Low WAFOM Sobol Sequence.

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

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

s <- 4
m <- 10
mat <- lowWAFOMSobol.points(dimR=s, dimF2=m)
mat[1,]
## [1] 5.421011e-20 5.421011e-20 5.421011e-20 5.421011e-20

Get digital shifted points.

s <- 4
m <- 10
mat <- lowWAFOMSobol.points(dimR=s, dimF2=m, digitalShift=TRUE)
mat[1,]
## [1] 0.37161665 0.09623796 0.58275929 0.23133454