umontreal.iro.lecuyer.hups
Class KorobovLatticeSequence

java.lang.Object
  umontreal.iro.lecuyer.hups.PointSet
      umontreal.iro.lecuyer.hups.Rank1Lattice
          umontreal.iro.lecuyer.hups.KorobovLattice
              umontreal.iro.lecuyer.hups.KorobovLatticeSequence

public class KorobovLatticeSequence
extends KorobovLattice

This class implements Korobov lattice sequences, defined as follows. One selects a basis b and a (large) multiplier a. For each integer k >= 0, we may consider the n-point Korobov lattice with modulus n = b^k and multiplier ã = a mod n. Its points have the form

u_i = (aⁱ(1, a, a²,…) modn)/n = (ãⁱ(1,ã,ã²,…) modn)/n

for i = 0,..., n - 1. For k = 0, 1,..., we have an increasing sequence of lattices contained in one another.

These embedded lattices contain an infinite sequence of points that can be enumerated as follows:

u_i = ψ_b(i)(1, a, a²,…) mod 1.

where ψ_b(i) is the radical inverse function in base b, defined in RadicalInverse. The first n = b^k points in this sequence are exactly the same as the n points in, for each k >= 0.

Constructor Summary

KorobovLatticeSequence(int b, int a)
Constructs a new lattice sequence with base b and generator = a.

Method Summary

double

getCoordinate(int i, int j) Returns ui, j, the coordinate j of the point i.

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

getA, toString

Methods inherited from class umontreal.iro.lecuyer.hups.Rank1Lattice

addRandomShift, clearRandomShift, getAs, iterator

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

KorobovLatticeSequence

public KorobovLatticeSequence(int b,
                              int a)

Constructs a new lattice sequence with base b and generator = a.

Parameters:

b - number of points (modulus) is a power of b

a - multiplier a of this lattice sequence

Method Detail

getCoordinate

public double getCoordinate(int i,
                            int j)

Description copied from class: PointSet

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

Overrides:

getCoordinate in class Rank1Lattice

Parameters:

i - index of the point to look for

j - index of the coordinate to look for

Returns:

the value of u_{i, j}