SSJ  3.2.1
Stochastic Simulation in Java
Public Member Functions | Package Attributes | List of all members
KorobovLatticeSequence Class Reference
Inheritance diagram for KorobovLatticeSequence:
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Collaboration diagram for KorobovLatticeSequence:
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Public Member Functions

 KorobovLatticeSequence (int b, int a)
 Constructs a new lattice sequence with base b and generator \( = a\). More...
 
double getCoordinate (int i, int j)
 
- Public Member Functions inherited from KorobovLattice
 KorobovLattice (int n, int a, int s)
 Instantiates a Korobov lattice point set with modulus \(n\) and multiplier \(a\) in dimension \(s\).
 
 KorobovLattice (int n, int a, int s, int t)
 Instantiates a shifted Korobov lattice point set with modulus \(n\) and multiplier \(a\) in dimension \(s\). More...
 
void setNumPoints (int n)
 Resets the number of points of the lattice to \(n\). More...
 
int getA ()
 Returns the multiplier \(a\) of the lattice. More...
 
String toString ()
 
- Public Member Functions inherited from Rank1Lattice
 Rank1Lattice (int n, int[] a, int s)
 Instantiates a Rank1Lattice with \(n\) points and lattice vector \(a\) of dimension \(s\). More...
 
void setNumPoints (int n)
 Resets the number of points of the lattice to \(n\). More...
 
int [] getAs ()
 Returns the generator \(a_j\) of the lattice. More...
 
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. More...
 
void clearRandomShift ()
 Clears the random shift.
 
String toString ()
 
double getCoordinate (int i, int j)
 
PointSetIterator iterator ()
 
- Public Member Functions inherited from PointSet
int getDimension ()
 Returns the dimension (number of available coordinates) of the point set. More...
 
int getNumPoints ()
 Returns the number of points. More...
 
abstract double getCoordinate (int i, int j)
 Returns \(u_{i,j}\), the coordinate \(j\) of the point \(i\). More...
 
PointSetIterator iterator ()
 Constructs and returns a point set iterator. More...
 
void setStream (RandomStream stream)
 Sets the random stream used to generate random shifts to stream. More...
 
RandomStream getStream ()
 Returns the random stream used to generate random shifts. More...
 
void randomize (PointSetRandomization rand)
 Randomizes the point set using the given rand. More...
 
void addRandomShift (int d1, int d2, RandomStream stream)
 This method does nothing for this generic class. More...
 
void addRandomShift (RandomStream stream)
 This method does nothing for this generic class. More...
 
void addRandomShift (int d1, int d2)
 Similar to addRandomShift(d1, d2, stream), with the current random stream.
 
void addRandomShift ()
 Similar to addRandomShift(0, d2, stream) with the current random stream and d2 the dimension of the current random shift.
 
void clearRandomShift ()
 Erases the current random shift, if any.
 
void randomize (int fromDim, int toDim, RandomStream stream)
 By default, this method simply calls addRandomShift (fromDim, toDim, stream), which does nothing.
 
void randomize (RandomStream stream)
 By default, this method simply calls randomize(0, dim, stream).
 
void randomize (int d1, int d2)
 By default, this method simply calls addRandomShift(d1, d2).
 
void randomize ()
 By default, this method simply calls addRandomShift().
 
void unrandomize ()
 By default, this method simply calls clearRandomShift().
 
String toString ()
 Formats a string that contains information about the point set. More...
 
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. More...
 
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 \(n\) points. More...
 
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. More...
 
String formatPoints (PointSetIterator iter, int n, int d)
 Same as invoking formatPoints(n, d), but prints the points by calling iter repeatedly. More...
 
String formatPointsBase (int b)
 Similar to formatPoints(), but the points coordinates are printed in base \(b\). More...
 
String formatPointsBase (int n, int d, int b)
 Similar to formatPoints(n, d), but the points coordinates are printed in base \(b\). More...
 
String formatPointsBase (PointSetIterator iter, int b)
 Similar to formatPoints(iter), but the points coordinates are printed in base \(b\). More...
 
String formatPointsBase (PointSetIterator iter, int n, int d, int b)
 Similar to formatPoints(iter, n, d), but the points coordinates are printed in base \(b\). More...
 
String formatPointsNumbered ()
 Same as invoking formatPointsNumbered(n, d) with \(n\) and \(d\) equal to the number of points and the dimension, respectively. More...
 
String formatPointsNumbered (int n, int d)
 Same as invoking formatPoints(n,d), except that the points are numbered. More...
 

Package Attributes

int base
 
int inverse
 
int n
 

Additional Inherited Members

- Protected Member Functions inherited from Rank1Lattice
long modPower (long a, int e, int m)
 
double radicalInverse (int base, int i)
 
- Protected Attributes inherited from KorobovLattice
int genA
 
- Protected Attributes inherited from Rank1Lattice
int [] genAs
 
double [] v
 
double normFactor
 
double [] shift
 
- Protected Attributes inherited from PointSet
double EpsilonHalf = 1.0 / Num.TWOEXP[55]
 
int dim = 0
 
int numPoints = 0
 
int dimShift = 0
 
int capacityShift = 0
 
RandomStream shiftStream
 
- Static Protected Attributes inherited from PointSet
static final int MAXBITS = 31
 

Detailed Description

Remarks
Pierre: This class is not yet fully implemented

This class implements Korobov lattice sequences, defined as follows. One selects a basis \(b\) and a (large) multiplier \(a\). For each integer \(k\ge0\), we may consider the \(n\)-point Korobov lattice with modulus \(n = b^k\) and multiplier \(\tilde{a} = a \bmod n\). Its points have the form

\[ \mathbf{u}_i = (a^i (1, a, a^2, …) \bmod n) / n = (\tilde{a}^i (1, \tilde{a}, \tilde{a}^2, …) \bmod n) / n \tag{Korobov-seq1} \]

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 [78] :

\[ \mathbf{u}_i = \psi_b(i) \left(1, a, a^2, …\right) \bmod1. \tag{Korobov-seq2} \]

where \(\psi_b(i)\) 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 ( Korobov-seq1 ), for each \(k\ge0\).

Constructor & Destructor Documentation

◆ KorobovLatticeSequence()

KorobovLatticeSequence ( int  b,
int  a 
)

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

Parameters
bnumber of points (modulus) is a power of b
amultiplier \(a\) of this lattice sequence

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