SSJ  3.2.1
Stochastic Simulation in Java
Public Member Functions | List of all members
HaltonSequence Class Reference

This class implements the sequence of Halton [74] , which is essentially a modification of Hammersley nets for producing an infinite sequence of points having low discrepancy. More...

Inheritance diagram for HaltonSequence:
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Collaboration diagram for HaltonSequence:
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Public Member Functions

 HaltonSequence (int dim)
 Constructs a new Halton sequence in dim dimensions. More...
 
void setStart (double[] x0)
 Initializes the Halton sequence starting at point x0. More...
 
void init (double[] x0)
 Initializes the Halton sequence starting at point x0. More...
 
void addFaureLemieuxPermutations ()
 Permutes the digits using permutations from [55]  for all coordinates. More...
 
void addFaurePermutations ()
 Permutes the digits using Faure permutations for all coordinates. More...
 
void ErasePermutations ()
 Erases the permutations: from now on, the digits will not be permuted.
 
int getNumPoints ()
 
double getCoordinate (int i, int j)
 
- Public Member Functions inherited from PointSet
int getDimension ()
 Returns the dimension (number of available coordinates) of the point set. More...
 
int getNumPoints ()
 Returns the number of points. More...
 
abstract double getCoordinate (int i, int j)
 Returns \(u_{i,j}\), the coordinate \(j\) of the point \(i\). More...
 
PointSetIterator iterator ()
 Constructs and returns a point set iterator. More...
 
void setStream (RandomStream stream)
 Sets the random stream used to generate random shifts to stream. More...
 
RandomStream getStream ()
 Returns the random stream used to generate random shifts. More...
 
void randomize (PointSetRandomization rand)
 Randomizes the point set using the given rand. More...
 
void addRandomShift (int d1, int d2, RandomStream stream)
 This method does nothing for this generic class. More...
 
void addRandomShift (RandomStream stream)
 This method does nothing for this generic class. More...
 
void addRandomShift (int d1, int d2)
 Similar to addRandomShift(d1, d2, stream), with the current random stream.
 
void addRandomShift ()
 Similar to addRandomShift(0, d2, stream) with the current random stream and d2 the dimension of the current random shift.
 
void clearRandomShift ()
 Erases the current random shift, if any.
 
void randomize (int fromDim, int toDim, RandomStream stream)
 By default, this method simply calls addRandomShift (fromDim, toDim, stream), which does nothing.
 
void randomize (RandomStream stream)
 By default, this method simply calls randomize(0, dim, stream).
 
void randomize (int d1, int d2)
 By default, this method simply calls addRandomShift(d1, d2).
 
void randomize ()
 By default, this method simply calls addRandomShift().
 
void unrandomize ()
 By default, this method simply calls clearRandomShift().
 
String toString ()
 Formats a string that contains information about the point set. More...
 
String formatPoints ()
 Same as invoking formatPoints(n, d) with \(n\) and \(d\) equal to the number of points and the dimension of this object, respectively. More...
 
String formatPoints (int n, int d)
 Formats a string that displays the same information as returned by toString, together with the first \(d\) coordinates of the first \(n\) points. More...
 
String formatPoints (PointSetIterator iter)
 Same as invoking formatPoints(iter, n, d) with \(n\) and \(d\) equal to the number of points and the dimension, respectively. More...
 
String formatPoints (PointSetIterator iter, int n, int d)
 Same as invoking formatPoints(n, d), but prints the points by calling iter repeatedly. More...
 
String formatPointsBase (int b)
 Similar to formatPoints(), but the points coordinates are printed in base \(b\). More...
 
String formatPointsBase (int n, int d, int b)
 Similar to formatPoints(n, d), but the points coordinates are printed in base \(b\). More...
 
String formatPointsBase (PointSetIterator iter, int b)
 Similar to formatPoints(iter), but the points coordinates are printed in base \(b\). More...
 
String formatPointsBase (PointSetIterator iter, int n, int d, int b)
 Similar to formatPoints(iter, n, d), but the points coordinates are printed in base \(b\). More...
 
String formatPointsNumbered ()
 Same as invoking formatPointsNumbered(n, d) with \(n\) and \(d\) equal to the number of points and the dimension, respectively. More...
 
String formatPointsNumbered (int n, int d)
 Same as invoking formatPoints(n,d), except that the points are numbered. More...
 

Additional Inherited Members

- Protected Attributes inherited from PointSet
double EpsilonHalf = 1.0 / Num.TWOEXP[55]
 
int dim = 0
 
int numPoints = 0
 
int dimShift = 0
 
int capacityShift = 0
 
RandomStream shiftStream
 
- Static Protected Attributes inherited from PointSet
static final int MAXBITS = 31
 

Detailed Description

This class implements the sequence of Halton [74] , which is essentially a modification of Hammersley nets for producing an infinite sequence of points having low discrepancy.

The \(i\)th point in \(s\) dimensions is

\[ \mathbf{u}_i = (\psi_{b_1}(i),\psi_{b_2}(i),…, \psi_{b_s}(i)), \tag{Halton-point2} \]

for \(i=0,1,2,…\), where \(\psi_b\) is the radical inverse function in base \(b\), defined in class RadicalInverse, and where \(2 = b_1 < \cdots< b_s\) are the \(s\) smallest prime numbers in increasing order.

A fast method is implemented to generate randomized Halton sequences [216], [224] , starting from an arbitrary point \(x_0\).

The points can be "scrambled" by applying a permutation to the digits of \(i\) before computing each coordinate via ( Halton-point ), in the same way as for the class HammersleyPointSet, for all coordinates \(j\ge0\).

Constructor & Destructor Documentation

◆ HaltonSequence()

HaltonSequence ( int  dim)

Constructs a new Halton sequence in dim dimensions.

Parameters
dimdimension

Member Function Documentation

◆ addFaureLemieuxPermutations()

void addFaureLemieuxPermutations ( )

Permutes the digits using permutations from [55]  for all coordinates.

After the method is called, the coordinates \(u_{i,j}\) are generated via

\[ u_{i,j} = \sum_{r=0}^{k-1} \pi_j[a_r] b_j^{-r-1}, \]

for \(j=0,…,s-1\), where \(\pi_j\) is the Faure-Lemieux (2008) permutation of \(\{0,…,b_j-1\}\).

◆ addFaurePermutations()

void addFaurePermutations ( )

Permutes the digits using Faure permutations for all coordinates.

After the method is called, the coordinates \(u_{i,j}\) are generated via

\[ u_{i,j} = \sum_{r=0}^{k-1} \pi_j[a_r] b_j^{-r-1}, \]

for \(j=0,…,s-1\), where \(\pi_j\) is the Faure permutation of \(\{0,…,b_j-1\}\).

◆ init()

void init ( double []  x0)

Initializes the Halton sequence starting at point x0.

The dimension of x0 must be at least as large as the dimension of this object.

Parameters
x0starting point of the Halton sequence

◆ setStart()

void setStart ( double []  x0)

Initializes the Halton sequence starting at point x0.

For each coordinate \(j\), the sequence starts at index \(i_j\) such that x0[ \(j\)] is the radical inverse of \(i_j\). The dimension of x0 must be at least as large as the dimension of this object.

Parameters
x0starting point of the Halton sequence

The documentation for this class was generated from the following file: