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,
* The Sobol sequence,
* The Faure sequence,
* The Reverse Halton sequence of Vandewoestyne and Cools,
* The Niederreiter base 2 and arbitrary base sequence.
This component currently provides the following sequences:
* "slow" sequences based on macros : Halton, Sobol, Faure, Reverse
Halton, Niederreiter base 2,
* "fast" sequences based on C source code : Halton, Sobol, Faure,
Reverse Halton, Niederreiter in arbitrary base.
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.
* lowdisc_projections : An overview of bad 2D projections.
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.
Macro Generators:
* lowdisc_haltonnext : Returns the next element of the Halton sequence.
* lowdisc_sobolnext : Generates a new quasirandom Sobol vector.
* lowdisc_sobolskip : Skip elements in the Sobol sequence.
* lowdisc_sobolstart : Initialize the Sobol sequence.
* lowdisc_vandercorput : Returns the i-th term of the Van Der Corput sequence.
Static Functions:
* lowdisc_fauresuggest : Returns favorable parameters for Faure sequences.
* lowdisc_haltonsuggest : Returns favorable parameters for Halton sequence.
* lowdisc_methods : Returns available sequences.
* lowdisc_niederbase : Returns optimal base for Niederreiter sequence.
* lowdisc_niedersuggest : Returns favorable parameters for Niederreiter
sequence.
* lowdisc_primes100 : Returns a matrix containing the 100 first primes.
* lowdisc_primes1000 : Returns a matrix containing the 1000 first primes.
* lowdisc_primes10000 : Returns a matrix containing the 10000 first primes.
* lowdisc_sobolsuggest : Returns favorable parameters for Sobol sequences.
* lowdisc_soboltau : Returns favorable starting seeds for Sobol sequences.
* lowdisc_stopall : Stop all fast sequences.
Support Functions:
* lowdisc_bary : Returns the digits of a number given the basis.
* lowdisc_bitand : Bitwise AND.
* lowdisc_bithi1 : Returns the position of the high one bit base 2 in an
integer.
* lowdisc_bitlo0 : Returns the position of the low zero bit base 2 in an
integer.
* lowdisc_bitor : bitwise OR
* lowdisc_bitxor : Bitwise logical XOR operator.
* lowdisc_corrcoef : Correlation coefficients
* lowdisc_dec2bin : Convert a decimal floating point integer into binary.
* lowdisc_proj2d : Plots 2 dimensional projections.
Author
* 2009-2011 - DIGITEO - Michael Baudin
* 2008-2009 - INRIA - Michael Baudin
* 2003-2009 - John Burkardt
* 1994 - Paul Bratley, Bennett Fox, Harald Niederreiter
* 1986-1988 - Bennett Fox
Licence
This toolbox is distributed under the GNU LGPL license.
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.