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

Inheritance diagram for umontreal.ssj.hups.HammersleyPointSet:

Public Member Functions
	HammersleyPointSet (int n, int dim)
	Constructs a new Hammersley point set with n points in dim dimensions.
void	addFaurePermutations ()
	Permutes the digits using Faure permutations for all coordinates.
void	ErasePermutations ()
	Erases the Faure permutations: from now on, the digits will not be Faure permuted.
double	getCoordinate (int i, int j)
	Returns \(u_{i,j}\), the coordinate \(j\) of the point \(i\).
Public Member Functions inherited from umontreal.ssj.hups.PointSet
int	getDimension ()
	Returns the dimension (number of available coordinates) of the points.
int	getNumPoints ()
	Returns the number of points.
PointSetIterator	iterator ()
	Constructs and returns a point set iterator.
void	randomize (PointSetRandomization rand)
	Randomizes this point set using the given rand.
void	addRandomShift (int d1, int d2, RandomStream stream)
	By default, this method generates a random shift in the protected double[] array shift, to be used eventually for a random shift modulo 1.
void	addRandomShift (RandomStream stream)
	Same as `addRandomShift(0, dim, stream)`, where dim is the dimension of the point set.
void	addRandomShift (int d1, int d2)
	Refreshes the random shift (generates new uniform values for the random shift coordinates) for coordinates d1 to d2-1, using the saved shiftStream.
void	addRandomShift ()
	Same as `addRandomShift(0, dim)`, where dim is the dimension of the point set.
void	clearRandomShift ()
	Erases the current random shift, if any.
String	toString ()
	Formats a string that contains information about the point set.
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.
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.
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.
String	formatPoints (PointSetIterator iter, int n, int d)
	Same as invoking `formatPoints(n, d)`, but prints the points by calling iter repeatedly.
String	formatPointsBase (int b)
	Similar to `formatPoints()`, but the points coordinates are printed in base \(b\).
String	formatPointsBase (int n, int d, int b)
	Similar to `formatPoints(n, d)`, but the points coordinates are printed in base \(b\).
String	formatPointsBase (PointSetIterator iter, int b)
	Similar to `formatPoints(iter)`, but the points coordinates are printed in base.
String	formatPointsBase (PointSetIterator iter, int n, int d, int b)
	Similar to `formatPoints(iter, n, d)`, but the points coordinates are printed in base \(b\).
String	formatPointsNumbered ()
	Same as invoking `formatPointsNumbered(n, d)` with \(n\) and \(d\) equal to the number of points and the dimension, respectively.
String	formatPointsNumbered (int n, int d)
	Same as invoking `formatPoints(n,d)`, except that the points are numbered.

Additional Inherited Members
Static Public Member Functions inherited from umontreal.ssj.hups.PointSet
static int	getMaxBits ()
	Returns the maximum number of usable bits.
Protected Attributes inherited from umontreal.ssj.hups.PointSet
double	EpsilonHalf = 1.0 / Num.TWOEXP[55]
	To avoid 0 for nextCoordinate when random shifting, we add this to each coordinate.
int	dim = 0
	Dimension of the points.
int	numPoints = 0
	Number of points.
int	dimShift = 0
	Current dimension of the shift.
int	capacityShift = 0
	Number of array elements in the shift vector, always >= dimShift.
double[]	shift
	This is the shift vector as a double[] array, which contains the current random shift in case we apply a random shift modulo 1.
RandomStream	shiftStream
	Stream used to generate the random shifts.
Static Protected Attributes inherited from umontreal.ssj.hups.PointSet
static final int	MAXBITS = 31
	Since Java has no unsigned type, the 32nd bit cannot be used efficiently, so we have only 31 bits.

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 @f$i@f$ before computing each coordinate via (
                   {@link REF_hups_overview_eq_Hammersley_point
                   Hammersley-point} ). If @f[ i = a_0 + a_1 b_j + …+
                   a_{k_j-1} b_j^{k_j-1}, @f] and @f$\pi_j@f$ is a
                   permutation of the digits @f$\{0,…,b_j-1\}@f$,
                   then @f[ \psi_{b_j}(i) = \sum_{r=0}^{k_j-1} a_r
                   b_j^{-r-1} @f] is replaced in (
                   {@link REF_hups_overview_eq_Hammersley_point
                   Hammersley-point} ) by @f[ u_{i,j}= \sum_{r=0}^{k_j-1}
                   \pi_j[a_r] b_j^{-r-1}. @f] The
                   permutations @f$\pi_j@f$ can be deterministic or
                   random. One (deterministic) possibility implemented
                   here is to use the Faure permutation
                   of @f$\{0,…,b_j\}@f$ for @f$\pi_j@f$, for each
                   coordinate

\(j > 0\).

 <div class="SSJ-bigskip"></div><div class="SSJ-bigskip"></div>

Definition at line 64 of file HammersleyPointSet.java.

Constructor & Destructor Documentation

◆ HammersleyPointSet()

umontreal.ssj.hups.HammersleyPointSet.HammersleyPointSet	(	int	n,
		int	dim )

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

Parameters

n	number of points
dim	dimension of the point set

Definition at line 75 of file HammersleyPointSet.java.

Member Function Documentation

◆ addFaurePermutations()

void umontreal.ssj.hups.HammersleyPointSet.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 \(\{0,…,b_j-1\}\).

Definition at line 91 of file HammersleyPointSet.java.

◆ ErasePermutations()

void umontreal.ssj.hups.HammersleyPointSet.ErasePermutations ( )

Erases the Faure permutations: from now on, the digits will not be Faure permuted.

Definition at line 106 of file HammersleyPointSet.java.

◆ getCoordinate()

double umontreal.ssj.hups.HammersleyPointSet.getCoordinate	(	int	i,
		int	j )

Returns \(u_{i,j}\), the coordinate \(j\) of the point \(i\).

When the points are randomized (e.g., a random shift is added), the values returned by this method should incorporate the randomizations. Richard: La méthode getCoordinate de certaines classes ne tient pas compte du random shift, contrairement à l’itérateur de la même classe. Faut-il que toutes les getCoordinate implémentent le random shift quand il existe? Oui.

Parameters

i	index of the point to look for
j	index of the coordinate to look for

Returns: the value of \(u_{i,j}\)

Reimplemented from umontreal.ssj.hups.PointSet.

Definition at line 111 of file HammersleyPointSet.java.

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

src/main/java/umontreal/ssj/hups/HammersleyPointSet.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions