Package description: QuasiRandom
The Quasi Monte Carlo (QMC) package. Contains implementations of the
Halton, Sobol and Niederreiter-Xing generator in various dimensions:
- Halton: unlimited (but useless in high dimensions)
- Sobol: up to dimension 300 but easily extended if more primitive
polynomials modulo two are obtained (see Peter Jaeckels book Monte Carlo
Methods in Finance which comes with a disk containing millions of
primitive polynomials, only one is needed for each dimension).
- Niederrreiter-Xing: up to dimension 20. Lowest L2-discrepancy in each
dimension but there is no easy way to extend this to higher dimensions.
Each low discrepancy sequence has 2 methods to compute its L2-discrepancy,
straightforward (non optimized) algorithms are used. This means that this is
very slow if the number of low discrepancy points is large.
There are also some nasty test integrals (very narrow and tall spikes
all integrating to one in several dimensions) and a class to plot projections
of low discrepancy points onto two dimensional coordinate parallel subspaces
of the space in which the sequence lives.