Purpose
-------
The goal of this toolbox is to provide a collection of low discrepancy
sequences. These random numbers are designed to be used in a Monte-Carlo
simulation. For example, low discrepancy sequences provide a higher
convergence rate to the Monte-Carlo method when used in numerical
integration. The toolbox takes into account the dimension of the problem, i.e.
generate vectors with arbitrary size.
The current prototype has the following features :
* manage arbitrary number of dimensions,
* skips a given number of elements in the sequence,
* leaps (i.e. ignores) a given number of elements from call to call,
* fast sequences based on compiled source code,
* suggest optimal settings to use the best of the sequences,
* object oriented programming.
Overview of sequences
* The Halton sequence (classic, leaped, reverse or scrambled),
* The Sobol sequence (classic or scrambled),
* The Faure sequence,
* The Niederreiter arbitrary base sequence.
See the overview in the help provided with this toolbox.
Features
--------
The module provides the following help pages:
* lowdisc_overview : An overview of the Low Discrepancy toolbox.
Tutorials:
* lowdisc_plots ? A gallery of low discrepancy sequences.
* lowdisc_projections ? An overview of bad 2D projections.
* lowdisc_tmsnets ? (t,m,s)-nets and low discrepancy sequences.
* lowdisc_efficiency ? Efficiency of Monte-Carlo and QMC.
The flagship of this module is:
* lowdisc_ldgen : Returns uniform numbers from a low discrepancy sequence.
Sequences:
* lowdisc_cget : Returns the value associated with the given key.
* lowdisc_configure : Configure a field of the object and returns the modified
object.
* lowdisc_destroy : Destroy the current object.
* lowdisc_get : Quiery one not-configurable field.
* lowdisc_new : Create a new object.
* lowdisc_next : Returns the next term of the sequence
* lowdisc_startup : Startup the sequence.
Static Functions:
* lowdisc_methods : Returns available sequences.
* lowdisc_stopall : Stop all fast sequences.
Favorable Parameters:
* lowdisc_fauresuggest : Returns favorable parameters for Faure sequences.
* lowdisc_haltonsuggest : Returns favorable parameters for Halton sequence.
* lowdisc_niederbase : Returns optimal base for Niederreiter sequence.
* lowdisc_niedersuggest : Returns favorable parameters for Niederreiter
sequence.
* lowdisc_sobolsuggest : Returns favorable parameters for Sobol sequences.
Support Functions:
* lowdisc_getpath : Returns the path to the current module.
* lowdisc_plotbmbox : Plot all elementary boxes with volume b^m
* lowdisc_plotelembox : Plot elementary box
* lowdisc_proj2d : Plots 2 dimensional projections.
Acknowledgements
Michael Baudin thanks John Burkardt for his help during
the development of this library.
Thanks to Alan Cornet, Pierre Marechal for the technical help
for this project.
Thanks to Jean-Philippe Chancelier for finding bugs in the
source code of the gateway.
Thanks to Jeanne Demgne for her feedback on this module.
