umontreal.ssj.hups.KorobovLatticeSequence Class Reference

Inheritance diagram for umontreal.ssj.hups.KorobovLatticeSequence:

Public Member Functions
	KorobovLatticeSequence (int b, int a)
	Constructs a new lattice sequence with base b and generator \( = a\).
double	getCoordinate (int i, int j)
	Returns \(u_{i,j}\), the coordinate \(j\) of the point \(i\).
Public Member Functions inherited from umontreal.ssj.hups.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.
void	setNumPoints (int n)
	Resets the number of points of the lattice to \(n\).
int	getA ()
	Returns the multiplier \(a\) of the lattice.
String	toString ()
	Formats a string that contains information about the point set.
Public Member Functions inherited from umontreal.ssj.hups.Rank1Lattice
	Rank1Lattice (int n, int[] a, int s)
	Instantiates a Rank1Lattice with \(n\) points and lattice vector \(a\) of dimension \(s\).
int[]	getAs ()
	Returns the generator \(a_j\) of the lattice.
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.
PointSetIterator	iterator ()
	Constructs and returns a point set iterator.
Public Member Functions inherited from umontreal.ssj.hups.PointSet
int	getDimension ()
	Returns the dimension (number of available coordinates) of the points.
int	getNumPoints ()
	Returns the number of points.
void	randomize (PointSetRandomization rand)
	Randomizes this point set using the given rand.
void	addRandomShift (RandomStream stream)
	Same as addRandomShift(0, dim, stream), where dim is the dimension of the point set.
void	addRandomShift (int d1, int d2)
	Refreshes the random shift (generates new uniform values for the random shift coordinates) for coordinates d1 to d2-1, using the saved shiftStream.
void	addRandomShift ()
	Same as addRandomShift(0, dim), where dim is the dimension of the point set.
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.
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.
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.
String	formatPoints (PointSetIterator iter, int n, int d)
	Same as invoking formatPoints(n, d), but prints the points by calling iter repeatedly.
String	formatPointsBase (int b)
	Similar to formatPoints(), but the points coordinates are printed in base \(b\).
String	formatPointsBase (int n, int d, int b)
	Similar to formatPoints(n, d), but the points coordinates are printed in base \(b\).
String	formatPointsBase (PointSetIterator iter, int b)
	Similar to formatPoints(iter), but the points coordinates are printed in base.
String	formatPointsBase (PointSetIterator iter, int n, int d, int b)
	Similar to formatPoints(iter, n, d), but the points coordinates are printed in base \(b\).
String	formatPointsNumbered ()
	Same as invoking formatPointsNumbered(n, d) with \(n\) and \(d\) equal to the number of points and the dimension, respectively.
String	formatPointsNumbered (int n, int d)
	Same as invoking formatPoints(n,d), except that the points are numbered.

Additional Inherited Members
Static Public Member Functions inherited from umontreal.ssj.hups.PointSet
static int	getMaxBits ()
	Returns the maximum number of usable bits.
Protected Attributes inherited from umontreal.ssj.hups.PointSet
double	EpsilonHalf = 1.0 / Num.TWOEXP[55]
	To avoid 0 for nextCoordinate when random shifting, we add this to each coordinate.
int	dim = 0
	Dimension of the points.
int	numPoints = 0
	Number of points.
int	dimShift = 0
	Current dimension of the shift.
int	capacityShift = 0
	Number of array elements in the shift vector, always >= dimShift.
double[]	shift
	This is the shift vector as a double[] array, which contains the current random shift in case we apply a random shift modulo 1.
RandomStream	shiftStream
	Stream used to generate the random shifts.
Static Protected Attributes inherited from umontreal.ssj.hups.PointSet
static final int	MAXBITS = 31
	Since Java has no unsigned type, the 32nd bit cannot be used efficiently, so we have only 31 bits.

Detailed Description

Remarks

Pierre: This class is not yet fully implemented

    This class implements Korobov lattice sequences, defined as follows.
    One selects a *basis* @f$b@f$ and a (large) multiplier @f$a@f$. For
    each integer @f$k\ge0@f$, we may consider the @f$n@f$-point Korobov
    lattice with modulus @f$n = b^k@f$ and multiplier @f$\tilde{a} = a
    \bmod n@f$. 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 [77] :

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

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 \(k\ge0\).

Definition at line 53 of file KorobovLatticeSequence.java.

Constructor & Destructor Documentation

KorobovLatticeSequence()

umontreal.ssj.hups.KorobovLatticeSequence.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

Definition at line 66 of file KorobovLatticeSequence.java.

Member Function Documentation

getCoordinate()

double umontreal.ssj.hups.KorobovLatticeSequence.getCoordinate	(	int	i,
		int	j )

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

When the points are randomized (e.g., a random shift is added), the values returned by this method should incorporate the randomizations. Richard: La méthode getCoordinate de certaines classes ne tient pas compte du random shift, contrairement à l’itérateur de la même classe. Faut-il que toutes les getCoordinate implémentent le random shift quand il existe? Oui.

Parameters

i	index of the point to look for
j	index of the coordinate to look for

Returns

the value of \(u_{i,j}\)

Reimplemented from umontreal.ssj.hups.Rank1Lattice.

Definition at line 78 of file KorobovLatticeSequence.java.

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

• src/main/java/umontreal/ssj/hups/KorobovLatticeSequence.java