Implement Quasi Monte Carlo Methods

FriesischScott commented 2 years ago

Currently we have Sobol and Halton from two different packages. It might be a good idea to switch to QuasiMonteCarlo.jl and implement everything it offers.

QMC.jl includes:

GridSample(dx) where the grid is given by lb:dx[i]:ub in the ith direction.
UniformSample for uniformly distributed random numbers.
SobolSample for the Sobol sequence.
LatinHypercubeSample for a Latin Hypercube.
LatticeRuleSample for a randomly-shifted rank-1 lattice rule.
LowDiscrepancySample(base) where base[i] is the base in the ith direction.

I vaguely remember an issue with creating high dimensional LH samples in this but I am not sure.

FriesischScott commented 2 years ago

33e33556ff397885e04a8812e39f1de84a8f824c added LHS and dropped the dependency on Sobol. QMC.jl uses Sobol internally, so the end result is the same.

FriesischScott commented 2 years ago

Depends on #55

FriesischScott commented 2 years ago

Depends on #58

FriesischScott commented 2 years ago

Since I don't care about grid sampling, these are all done now.

FriesischScott / UncertaintyQuantification.jl

Implement Quasi Monte Carlo Methods #45