Apache Commons Math 3.6.1 · org.apache.commons.math3.random.HaltonSequenceGenerator

Implementation of a Halton sequence.

A Halton sequence is a low-discrepancy sequence generating points in the interval [0, 1] according to

  H(n) = d_0 / b + d_1 / b^2 .... d_j / b^j+1

  with

  n = d_j * b^j-1 + ... d_1 * b + d_0 * b^0

For higher dimensions, subsequent prime numbers are used as base, e.g. { 2, 3, 5 } for a Halton sequence in R^3.

Halton sequences are known to suffer from linear correlation for larger prime numbers, thus the individual digits are usually scrambled. This implementation already comes with support for up to 40 dimensions with optimal weight numbers from H. Chi: Scrambled quasirandom sequences and their applications.

The generator supports two modes:

sequential generation of points: nextVector()
random access to the i-th point in the sequence: skipTo(int)

Field Summary

Modifier and Type	Field and Description
private final int[]	base The base numbers for each component.
private int	count The current index in the sequence.
private final int	dimension Space dimension.
private static final int[]	PRIMES The first 40 primes.
private final int[]	weight The scrambling weights for each component.
private static final int[]	WEIGHTS The optimal weights used for scrambling of the first 40 dimension.

Constructor Summary

Access	Constructor and Description
public	HaltonSequenceGenerator(final int the space dimension dimension) Construct a new Halton sequence generator for the given space dimension.
public	HaltonSequenceGenerator(final int the space dimension dimension, final int[] the base number for each dimension, entries should be (pairwise) prime, may not be null bases, final int[] the weights used during scrambling, may be null in which case no scrambling will be performed weights) Construct a new Halton sequence generator with the given base numbers and weights for each dimension.

Method Summary

Modifier and Type	Method and Description
public int	Returns: the index of the next point getNextIndex() Returns the index i of the next point in the Halton sequence that will be returned by calling `nextVector()`.
public double[]	nextVector() Implements org.apache.commons.math3.random.RandomVectorGenerator.nextVector. Generate a random vector.
protected int	Returns: the scrambled digit scramble(final int the dimension index i, final int the digit index j, final int the base for this dimension b, final int the j-th digit digit) Performs scrambling of digit `d_j` according to the formula: ( weight_i * d_j ) mod base
public double[]	Returns: the i-th point in the Halton sequence skipTo(final int the index in the sequence to skip to index) Skip to the i-th point in the Halton sequence.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

base	back to summary
private final int[] base The base numbers for each component.

count	back to summary
private int count The current index in the sequence.

dimension	back to summary
private final int dimension Space dimension.

PRIMES	back to summary
private static final int[] PRIMES The first 40 primes.

weight	back to summary
private final int[] weight The scrambling weights for each component.

WEIGHTS	back to summary
private static final int[] WEIGHTS The optimal weights used for scrambling of the first 40 dimension.

Constructor Detail

HaltonSequenceGenerator	back to summary
public HaltonSequenceGenerator(final int dimension) throws OutOfRangeException Construct a new Halton sequence generator for the given space dimension. Parameters dimension:int the space dimension Exceptions OutOfRangeException: if the space dimension is outside the allowed range of [1, 40]

HaltonSequenceGenerator

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public HaltonSequenceGenerator(final int dimension) throws OutOfRangeException

Construct a new Halton sequence generator for the given space dimension.

Parameters

dimension:int: the space dimension

Exceptions

OutOfRangeException:: if the space dimension is outside the allowed range of [1, 40]

HaltonSequenceGenerator	back to summary
public HaltonSequenceGenerator(final int dimension, final int[] bases, final int[] weights) throws NullArgumentException, OutOfRangeException, DimensionMismatchException Construct a new Halton sequence generator with the given base numbers and weights for each dimension. The length of the bases array defines the space dimension and is required to be > 0. Parameters dimension:int the space dimension bases:int[] the base number for each dimension, entries should be (pairwise) prime, may not be null weights:int[] the weights used during scrambling, may be null in which case no scrambling will be performed Exceptions NullArgumentException: if base is null OutOfRangeException: if the space dimension is outside the range [1, len], where len refers to the length of the bases array DimensionMismatchException: if weights is non-null and the length of the input arrays differ

HaltonSequenceGenerator

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public HaltonSequenceGenerator(final int dimension, final int[] bases, final int[] weights) throws NullArgumentException, OutOfRangeException, DimensionMismatchException

Construct a new Halton sequence generator with the given base numbers and weights for each dimension. The length of the bases array defines the space dimension and is required to be > 0.

Parameters

dimension:int: the space dimension
bases:int[]: the base number for each dimension, entries should be (pairwise) prime, may not be null
weights:int[]: the weights used during scrambling, may be null in which case no scrambling will be performed

Exceptions

NullArgumentException:: if base is null
OutOfRangeException:: if the space dimension is outside the range [1, len], where len refers to the length of the bases array
DimensionMismatchException:: if weights is non-null and the length of the input arrays differ

Method Detail

getNextIndex back to summary

getNextIndex	back to summary
public int getNextIndex() Returns the index i of the next point in the Halton sequence that will be returned by calling `nextVector()`. Returns:int the index of the next point

public int getNextIndex()

Returns the index i of the next point in the Halton sequence that will be returned by calling nextVector().

Returns:int: the index of the next point

nextVector	back to summary
public double[] nextVector() Implements org.apache.commons.math3.random.RandomVectorGenerator.nextVector. Doc from org.apache.commons.math3.random.RandomVectorGenerator.nextVector. Generate a random vector. Returns:double[] a random vector as an array of double.

nextVector

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public double[] nextVector()

Implements org.apache.commons.math3.random.RandomVectorGenerator.nextVector.

Doc from org.apache.commons.math3.random.RandomVectorGenerator.nextVector.

Generate a random vector.

Returns:double[]: a random vector as an array of double.

scramble back to summary

scramble	back to summary
protected int scramble(final int i, final int j, final int b, final int digit) Performs scrambling of digit `d_j` according to the formula: ( weight_i * d_j ) mod base Implementations can override this method to do a different scrambling. Parameters i:int the dimension index j:int the digit index b:int the base for this dimension digit:int the j-th digit Returns:int the scrambled digit

protected int scramble(final int i, final int j, final int b, final int digit)

Performs scrambling of digit d_j according to the formula:

  ( weight_i * d_j ) mod base

Implementations can override this method to do a different scrambling.

Parameters

i:int: the dimension index
j:int: the digit index
b:int: the base for this dimension
digit:int: the j-th digit

Returns:int

the scrambled digit

skipTo	back to summary
public double[] skipTo(final int index) throws NotPositiveException Skip to the i-th point in the Halton sequence. This operation can be performed in O(1). Parameters index:int the index in the sequence to skip to Returns:double[] the i-th point in the Halton sequence Exceptions NotPositiveException: if index < 0

skipTo

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public double[] skipTo(final int index) throws NotPositiveException

Skip to the i-th point in the Halton sequence.

This operation can be performed in O(1).

Parameters

index:int: the index in the sequence to skip to

Returns:double[]

the i-th point in the Halton sequence

Exceptions

NotPositiveException:: if index < 0

public Class HaltonSequenceGenerator

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail