Sobol' Sequence Missing First 4 Points

[alegresor]

Running the following code

using QuasiMonteCarlo
QuasiMonteCarlo.sample(4,0,1,SobolSample())

yields

4-element Vector{Float64}:
 0.375
 0.875
 0.625
 0.125

However, the first 4 points in a 1 dimensional Sobol' sample should be [0, .5, .25, .75]. The output are points at index 5 to 8.
I am looping in my collaborator @fjhickernell, an expert in QMC methods who will be valuable to this discussion.

[dmetivie]

I believe this is caused by the “famous” debate about starting the Sobol sequence at zero (-> theory) or not (-> practical implementation).
QuasiMonteCarlo.jl uses Sobol.jl which use the latter convention (drop zero), see related issue and refs therein (Owen' paper).
This debate was started way back I believed and amplified with Pytorch using the drop zero solution. @fjhickernell probably knows better.

Meanwhile, a while ago, I ported the R Owen (@dcarrera you suggested that at some point) code to do scrambling in a package RandomizedQuasiMonteCarlo.jl.
There, you can find the implementation starting at zero.

Note: I don't maintain the package anymore since all its features have been moved in QuasiMonteCarlo.jl (excepted the following function, in fact).

using RandomizedQuasiMonteCarlo
m = 2
N = 2^m # Number of points
d = 1 # dimension
b = 2 # always 2 for Sobol
M = 32 # number of bits to encode points
unrandomized_bits = sobol_pts2bits(m, d, M) 
u_sobol = dropdims(mapslices(bits2unif, unrandomized_bits, dims=3), dims=3)

yields

4×1 Matrix{Rational{Int64}}:
 0//1
 1//2
 1//4
 3//4

I believe this convention should be specified somewhere in bold in Readme.md and docs.

[alegresor]

Thank you for the quick response. I'll close this issue and monitor the other one you linked.