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## 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 = bk and multiplier ã = a mod n. Its points have the form

ui = (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:

ui = ψb(i)(1, a, a2,…) mod 1.

where ψb(i) is the radical inverse function in base b, defined in `RadicalInverse`. The first n = bk 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
`toString`

Methods inherited from class umontreal.iro.lecuyer.hups.Rank1Lattice
`addRandomShift, clearRandomShift, iterator`

Methods inherited from class umontreal.iro.lecuyer.hups.PointSet
`addRandomShift, addRandomShift, addRandomShift, formatPoints, formatPoints, 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 ui, 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 ui, j

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To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.