SSJ
V. 2.6.

## 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 KorobovLatticeSequenceextends 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
`getA, setNumPoints, 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 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

SSJ
V. 2.6.

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