umontreal.iro.lecuyer.hups

Class Rank1Lattice

java.lang.Object

umontreal.iro.lecuyer.hups.PointSet

umontreal.iro.lecuyer.hups.Rank1Lattice

Direct Known Subclasses:

KorobovLattice

public class Rank1Lattice
extends PointSet

This class implements point sets defined by integration lattices of rank 1, defined as follows. One selects an arbitrary positive integer n and a s-dimensional integer vector (a₀,..., a_s-1), where 0 <= a_j < n for each j. Usually, a₀ = 1. The points are defined by

u_i = (i/n)(a₀, a₁,…, a_s-1) mod 1

for i = 0,..., n - 1. These n points are distinct provided that n and the a_j's have no common factor.

Constructor Summary

Constructors

Constructor and Description
Rank1Lattice(int n, int[] a, int s) Instantiates a Rank1Lattice with n points and lattice vector a of dimension s.

Method Summary

Modifier and Type	Method and Description
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.
int[]	getAs() Returns the generator aj of the lattice.
double	getCoordinate(int i, int j) Returns ui, j, the coordinate j of the point i.
PointSetIterator	iterator() Constructs and returns a point set iterator.
java.lang.String	toString() Formats a string that contains information about the point set.

Methods inherited from class umontreal.iro.lecuyer.hups.PointSet

addRandomShift, addRandomShift, addRandomShift, formatPoints, formatPoints, formatPoints, formatPoints, formatPointsBase, formatPointsBase, formatPointsBase, formatPointsBase, formatPointsNumbered, formatPointsNumbered, getDimension, getNumPoints, getStream, randomize, randomize, randomize, randomize, randomize, setStream, unrandomize

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Rank1Lattice

public 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

Method Detail

getAs

public int[] getAs()

Returns the generator a_j of the lattice. Its components are returned as a[j], for j = 0, 1,…,(s - 1).

addRandomShift

public 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. 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.

Overrides:

addRandomShift in class PointSet

Parameters:

d1 - lower dimension of shift

d2 - upper dimension of shift is d2 - 1

stream - random number stream used to generate uniforms

clearRandomShift

public void clearRandomShift()

Clears the random shift.

Overrides:

clearRandomShift in class PointSet

toString

public java.lang.String toString()

Description copied from class: PointSet

Formats a string that contains information about the point set.

Overrides:

toString in class PointSet

Returns:

string representation of the point set information

getCoordinate

public double getCoordinate(int i,
                            int j)

Description copied from class: PointSet

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

Specified by:

getCoordinate in class PointSet

Parameters:

i - index of the point to look for

j - index of the coordinate to look for

Returns:

the value of u_{i, j}

iterator

public PointSetIterator iterator()

Description copied from class: PointSet

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.

Overrides:

iterator in class PointSet

Returns:

point set iterator for the point set