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

This class implements Hammersley point sets, which are defined as follows. More...

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

 HammersleyPointSet (int n, int dim)
 Constructs a new Hammersley point set with n points in dim dimensions. More...
 
void addFaurePermutations ()
 Permutes the digits using Faure permutations for all coordinates. More...
 
void ErasePermutations ()
 Erases the Faure permutations: from now on, the digits will not be Faure permuted.
 
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 Hammersley point sets, which are defined as follows.

Let \(2 = b_1 < b_2 < \cdots\) denote the sequence of all prime numbers by increasing order. The Hammersley point set with \(n\) points in \(s\) dimensions contains the points

\[ \mathbf{u}_i = (i/n,\psi_{b_1}(i),\psi_{b_2}(i),…, \psi_{b_{s-1}}(i)), \tag{Hammersley-point2} \]

for \(i=0,…,n-1\), where \(\psi_b\) is the radical inverse function in base \(b\), defined in RadicalInverse. This class is not a subclass of DigitalNet, because the basis is not the same for all coordinates. We do obtain a net in a generalized sense if \(n = b_1^{k_1} = b_2^{k_2} = \cdots= b_{s-1}^{k_{s-1}}\) for some integers \(k_1,…,k_{s-1}\).

The points of a Hammersley point set can be "scrambled" by applying a permutation to the digits of \(i\) before computing each coordinate via ( Hammersley-point ). If

\[ i = a_0 + a_1 b_j + …+ a_{k_j-1} b_j^{k_j-1}, \]

and \(\pi_j\) is a permutation of the digits \(\{0,…,b_j-1\}\), then

\[ \psi_{b_j}(i) = \sum_{r=0}^{k_j-1} a_r b_j^{-r-1} \]

is replaced in ( Hammersley-point ) by

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

The permutations \(\pi_j\) can be deterministic or random. One (deterministic) possibility implemented here is to use the Faure permutation of \(\{0,…,b_j\}\) for \(\pi_j\), for each coordinate \(j > 0\).

Constructor & Destructor Documentation

◆ HammersleyPointSet()

HammersleyPointSet ( int  n,
int  dim 
)

Constructs a new Hammersley point set with n points in dim dimensions.

Parameters
nnumber of points
dimdimension of the point set

Member Function Documentation

◆ 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 \(j=1,…,s-1\) and \(u_{i,0}=i/n\), where \(\pi_j\) is the Faure permutation of \(\{0,…,b_j-1\}\).


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