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QuasiMonteCarlo.jl: Quasi-Monte Carlo (QMC) Samples Made Easy

QuasiMonteCarlo.jl is a lightweight package for generating Quasi-Monte Carlo (QMC) samples using various different methods.

Installation

To install QuasiMonteCarlo.jl, use the Julia package manager:

using Pkg
Pkg.add("QuasiMonteCarlo")

Example

using QuasiMonteCarlo, Distributions
lb = [0.1,-0.5]
ub = [1.0,20.0]
n = 5
d = 2

s = QuasiMonteCarlo.sample(n,lb,ub,GridSample([0.1,0.5]))
s = QuasiMonteCarlo.sample(n,lb,ub,UniformSample())
s = QuasiMonteCarlo.sample(n,lb,ub,SobolSample())
s = QuasiMonteCarlo.sample(n,lb,ub,LatinHypercubeSample())
s = QuasiMonteCarlo.sample(n,lb,ub,LatticeRuleSample())
s = QuasiMonteCarlo.sample(n,lb,ub,LowDiscrepancySample([10,3]))

The output s is a matrix, so one can use things like @uview from UnsafeArrays.jl for a stack-allocated view of the ith point:

using UnsafeArrays
@uview s[:,i]

Adding a new sampling method

Adding a new sampling method is a two-step process:

  1. Add a new SamplingAlgorithm type.
  2. Overload the sample function with the new type.

All sampling methods are expected to return a matrix with dimension d by n, where d is the dimension of the sample space and n is the number of samples.

Example

struct NewAmazingSamplingAlgorithm{OPTIONAL} <: SamplingAlgorithm end

function sample(n,lb,ub,::NewAmazingSamplingAlgorithm)
    if lb isa Number
        ...
        return x
    else
        ...
        return reduce(hcat, x)
    end
end

Contributing