This class implements point sets specified by integration lattices of rank 1. More...

Inheritance diagram for umontreal.ssj.hups.Rank1Lattice:

Classes
class	Rank1LatticeIterator

Public Member Functions
	Rank1Lattice (int n, int[] a, int s)
	Instantiates a Rank1Lattice with \(n\) points and lattice vector \(a\) of dimension \(s\).
void	setNumPoints (int n)
	Resets the number of points of the lattice to \(n\).
int[]	getAs ()
	Returns the generator \(a_j\) of the lattice.
void	addRandomShift (int d1, int d2, RandomStream stream)
	Adds a random shift to all the points of the point set, using stream stream to generate the random numbers.
void	clearRandomShift ()
	Clears the random shift.
String	toString ()
	Formats a string that contains information about the point set.
double	getCoordinate (int i, int j)
	Returns \(u_{i,j}\), the coordinate \(j\) of the point \(i\).
PointSetIterator	iterator ()
	Constructs and returns a point set iterator.
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.
void	randomize (PointSetRandomization rand)
	Randomizes this point set using the given rand.
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.
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 point sets specified by integration lattices of rank 1.

They are defined as follows [212] . One selects an arbitrary positive integer \(n\) and a \(s\)-dimensional integer vector \((a_0,…,a_{s-1})\). [Usually, \(a_0=1\) and \(0 \le a_j < n\) for each \(j\); when the \(a_j\) are outside the interval

\([0,n)\), then we replace \(a_j\) by ( \(a_j \bmod n\)) in all calculations.] The points are defined by

\[ \mathbf{u}_i = (i/n)(a_0, a_1, …, a_{s-1}) \bmod1 \]

for \(i=0,…,n-1\). These \(n\) points are distinct provided that \(n\) and the \(a_j\)’s have no common factor.

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Definition at line 45 of file Rank1Lattice.java.

Constructor & Destructor Documentation

◆ Rank1Lattice()

umontreal.ssj.hups.Rank1Lattice.Rank1Lattice	(	int	n,
		int[]	a,
		int	s )

Instantiates a Rank1Lattice with \(n\) points and lattice vector \(a\) of dimension \(s\).

Parameters

n	there are n points
a	the lattice vector
s	dimension of the lattice vector a

Definition at line 68 of file Rank1Lattice.java.

Member Function Documentation

◆ addRandomShift()

void umontreal.ssj.hups.Rank1Lattice.addRandomShift	(	int	d1,
		int	d2,
		RandomStream	stream )

Adds a random shift to all the points of the point set, using stream stream to generate the random numbers.

For each coordinate \(j\) from d1 to d2-1, the shift \(d_j\) is generated uniformly over \([0, 1)\) and added modulo \(1\) to all the coordinates of all the points.

Parameters

d1	lower dimension of shift
d2	upper dimension of shift is d2 - 1
stream	random number stream used to generate uniforms

Reimplemented from umontreal.ssj.hups.PointSet.

Definition at line 106 of file Rank1Lattice.java.

◆ clearRandomShift()

void umontreal.ssj.hups.Rank1Lattice.clearRandomShift ( )

Clears the random shift.

Reimplemented from umontreal.ssj.hups.PointSet.

Definition at line 133 of file Rank1Lattice.java.

◆ getAs()

int[] umontreal.ssj.hups.Rank1Lattice.getAs ( )

Returns the generator \(a_j\) of the lattice.

(The original ones before they are reset to \(a_j \bmod n\)). Its components are returned as a[ \(j\)], for \(j = 0, 1, …, (s-1)\).

Definition at line 92 of file Rank1Lattice.java.

◆ getCoordinate()

double umontreal.ssj.hups.Rank1Lattice.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.

Reimplemented in umontreal.ssj.hups.KorobovLatticeSequence.

Definition at line 144 of file Rank1Lattice.java.

◆ iterator()

PointSetIterator umontreal.ssj.hups.Rank1Lattice.iterator ( )

Constructs and returns a point set iterator.

The default implementation returns an iterator that uses the method getCoordinate(i,j) to iterate over the points and coordinates, but subclasses can reimplement it for better efficiency.

Returns: point set iterator for the point set

Reimplemented from umontreal.ssj.hups.PointSet.

Definition at line 186 of file Rank1Lattice.java.

◆ setNumPoints()

void umontreal.ssj.hups.Rank1Lattice.setNumPoints ( int n )

Resets the number of points of the lattice to \(n\).

The dimension

\(s\) and the \(a_j\) are unchanged.

Reimplemented in umontreal.ssj.hups.KorobovLattice.

Definition at line 83 of file Rank1Lattice.java.

◆ toString()

String umontreal.ssj.hups.Rank1Lattice.toString ( )

Formats a string that contains information about the point set.

Returns: string representation of the point set information

Reimplemented from umontreal.ssj.hups.PointSet.

Reimplemented in umontreal.ssj.hups.KorobovLattice.

Definition at line 138 of file Rank1Lattice.java.

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

src/main/java/umontreal/ssj/hups/Rank1Lattice.java

SSJ API Documentation Stochastic Simulation in Java

Classes

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Rank1Lattice()

Member Function Documentation

◆ addRandomShift()

◆ clearRandomShift()

◆ getAs()

◆ getCoordinate()

◆ iterator()

◆ setNumPoints()

◆ toString()