org.jquantlib.math.randomnumbers

Class SobolRsg

java.lang.Object

org.jquantlib.math.randomnumbers.SobolRsg

All Implemented Interfaces:

UniformRandomSequenceGenerator

public class SobolRsg
extends java.lang.Object
implements UniformRandomSequenceGenerator

Sobol low-discrepancy sequence generator

A Gray code counter and bitwise operations are used for very fast sequence generation.

The implementation relies on primitive polynomials modulo two from the book "Monte Carlo Methods in Finance" by Peter Jaeckel.

21 200 primitive polynomials modulo two are provided in QuantLib. Jaeckel has calculated 8 129 334 polynomials: if you need that many dimensions you can replace the primitivepolynomials.c file included in QuantLib with the one provided in the CD of the "Monte Carlo Methods in Finance" book.

The choice of initialization numbers (also know as free direction integers) is crucial for the homogeneity properties of the sequence. Sobol defines two homogeneity properties: Property A and Property A'.

The unit initialization numbers suggested in "Numerical Recipes in C", 2nd edition, by Press, Teukolsky, Vetterling, and Flannery (section 7.7) fail the test for Property A even for low dimensions.

Bratley and Fox published coefficients of the free direction integers up to dimension 40, crediting unpublished work of Sobol' and Levitan. See Bratley, P., Fox, B.L. (1988) "Algorithm 659: Implementing Sobol's quasirandom sequence generator," ACM Transactions on Mathematical Software 14:88-100. These values satisfy Property A for d<=20 and d = 23, 31, 33, 34, 37; Property A' holds for d<=6.

Jaeckel provides in his book (section 8.3) initialization numbers up to dimension 32. Coefficients for d<=8 are the same as in Bradley-Fox, so Property A' holds for d<=6 but Property A holds for d<=32.

The implementation of Lemieux, Cieslak, and Luttmer includes coefficients of the free direction integers up to dimension 360. Coefficients for d<=40 are the same as in Bradley-Fox. For dimension 40 For more info on Sobol' sequences see also "Monte Carlo Methods in Financial Engineering," by P. Glasserman, 2004, Springer, section 5.2.3

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	SobolRsg.DirectionIntegers

Constructor Summary

Constructors

Constructor and Description
SobolRsg(int dimensionality) dimensionality must be <= PPMT_MAX_DIM
SobolRsg(int dimensionality, long seed)
SobolRsg(int dimensionality, long seed, SobolRsg.DirectionIntegers direction)

Method Summary

Modifier and Type	Method and Description
int	dimension()
Sample<double[]>	lastSequence()
long[]	nextInt32Sequence() Once JVM does not support unsigned fixed arithmetic, we use 64bit variables as containers for 32bit values in order to reduce the complexity and performance overhead of certain fixed arithmetic operations.
Sample<double[]>	nextSequence()

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SobolRsg

public SobolRsg(int dimensionality)

dimensionality must be <= PPMT_MAX_DIM

SobolRsg

public SobolRsg(int dimensionality,
                long seed)

SobolRsg

public SobolRsg(int dimensionality,
                long seed,
                SobolRsg.DirectionIntegers direction)

Method Detail

dimension

public int dimension()

Specified by:

dimension in interface UniformRandomSequenceGenerator

nextInt32Sequence

public final long[] nextInt32Sequence()

Description copied from interface: UniformRandomSequenceGenerator

Once JVM does not support unsigned fixed arithmetic, we use 64bit variables as containers for 32bit values in order to reduce the complexity and performance overhead of certain fixed arithmetic operations.

From the user's perspective, it's easier to understand that a certain long variable contains values from 0 to 2^32 than understand that a certain int variable contains negative values that should be converted to it's two's complement and extended to a long variable before use.

Specified by:

nextInt32Sequence in interface UniformRandomSequenceGenerator

Returns:

an array of unsigned 32bit wide numbers encapsulated in a 64bit containers

See Also:

Bug 4504839, Java and Unsigned Types, Two's complement

nextSequence

public final Sample<double[]> nextSequence()

Specified by:

nextSequence in interface UniformRandomSequenceGenerator

lastSequence

public final Sample<double[]> lastSequence()

Specified by:

lastSequence in interface UniformRandomSequenceGenerator