HaltonSequenceGenerator (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.random.HaltonSequenceGenerator

All Implemented Interfaces:

RandomVectorGenerator
```
public class HaltonSequenceGenerator
extends Object
implements RandomVectorGenerator
```
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)
Since:

3.3

See Also:
Halton sequence (Wikipedia), On the Halton sequence and its scramblings

Constructor Summary

Constructors
Constructor and Description
`HaltonSequenceGenerator(int dimension)` Construct a new Halton sequence generator for the given space dimension.
`HaltonSequenceGenerator(int dimension, int[] bases, int[] weights)` Construct a new Halton sequence generator with the given base numbers and weights for each dimension.

Method Summary

Methods
Modifier and Type	Method and Description
`int`	`getNextIndex()` Returns the index i of the next point in the Halton sequence that will be returned by calling `nextVector()`.
`double[]`	`nextVector()` Generate a random vector.
`protected int`	`scramble(int i, int j, int b, int digit)` Performs scrambling of digit `d_j` according to the formula:
`double[]`	`skipTo(int index)` Skip to the i-th point in the Halton sequence.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - HaltonSequenceGenerator
```
public HaltonSequenceGenerator(int dimension)
                        throws OutOfRangeException
```
    Construct a new Halton sequence generator for the given space dimension.
    
    Parameters:
    dimension - the space dimension
    
    Throws:
    
    OutOfRangeException - if the space dimension is outside the allowed range of [1, 40]
  - HaltonSequenceGenerator
```
public HaltonSequenceGenerator(int dimension,
                       int[] bases,
                       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 - the space dimension
    bases - the base number for each dimension, entries should be (pairwise) prime, may not be null
    weights - the weights used during scrambling, may be null in which case no scrambling will be performed
    
    Throws:
    
    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
  - nextVector
```
public double[] nextVector()
```
    Generate a random vector.
    
    Specified by:
    
    nextVector in interface RandomVectorGenerator
    
    Returns:
    a random vector as an array of double.
  - scramble
```
protected int scramble(int i,
           int j,
           int b,
           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 - the dimension index
    j - the digit index
    b - the base for this dimension
    digit - the j-th digit
    
    Returns:
    the scrambled digit
  - skipTo
```
public double[] skipTo(int index)
                throws NotPositiveException
```
    Skip to the i-th point in the Halton sequence.
    This operation can be performed in O(1).
    
    Parameters:
    index - the index in the sequence to skip to
    
    Returns:
    the i-th point in the Halton sequence
    
    Throws:
    
    NotPositiveException - if index < 0
  - getNextIndex
```
public int getNextIndex()
```
    Returns the index i of the next point in the Halton sequence that will be returned by calling nextVector().
    
    Returns:
    the index of the next point

Class HaltonSequenceGenerator

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

HaltonSequenceGenerator

HaltonSequenceGenerator

Method Detail

nextVector

scramble

skipTo

getNextIndex