This class creates a point set based upon a linear feedback shift register sequence. More...

Inheritance diagram for umontreal.ssj.hups.F2wCycleBasedLFSR:

Public Member Functions
	F2wCycleBasedLFSR (int w, int r, int modQ, int step, int nbcoeff, int coeff[], int nocoeff[])
	Constructs a point set with \(2^{rw}\) points.
	F2wCycleBasedLFSR (String filename, int no)
	Constructs a point set after reading its parameters from file filename; the parameters are located at line numbered no of filename.
String	toString ()
	Formats a string that contains information about the point set.
Public Member Functions inherited from umontreal.ssj.hups.CycleBasedPointSetBase2
double	getCoordinate (int i, int j)
	Returns \(u_{i,j}\), the coordinate \(j\) of the point \(i\).
PointSetIterator	iterator ()
	Constructs and returns a point set iterator.
void	addRandomShift (int d1, int d2, RandomStream stream)
	Adds a random digital shift in base 2 to all the points of the point set, using stream stream to generate the random numbers, for coordinates d1 to d2 - 1.
void	clearRandomShift ()
	Erases the current digital random shift, if any.
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.
Public Member Functions inherited from umontreal.ssj.hups.CycleBasedPointSet
int	getDimension ()
	Returns the dimension (number of available coordinates) of the points.
Public Member Functions inherited from umontreal.ssj.hups.PointSet
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 (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 Member Functions inherited from umontreal.ssj.hups.CycleBasedPointSet
void	addCycle (AbstractList c)
	Adds the cycle c to the list of all cycles.
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

This class creates a point set based upon a linear feedback shift register sequence.

The recurrence used to produce the point set is

\[ m_n = \sum_{i=1}^r b_i m_{n-i} \]

where \(m_n\in\mathbb F_{2^w}\), \(n\geq0\) and \(b_i\in\mathbb F_{2^w}\). There is a polynomial in \(\mathbb F_{2^w}[z]\) associated with this recurrence called the characteristic polynomial. It is

\[ P(z) = z^r + \sum_{i=1}^r b_i z^{r-i}. \]

In the implementation, this polynomial is stored in an object F2wStructure.

Let \({\mathbf{x}} = (x^{(0)}, …, x^{(p-1)}) \in\mathbb F_2^p\) be a

\(p\)-bit vector. Let us define the function \(\phi(\mathbf{x}) = \sum_{i=1}^p 2^{-i} x^{(i-1)}\). The point set in \(t\) dimensions produced by this class is

\[ \left\{ (\phi(\mathbf{y}_0),\phi(\mathbf{y}_s),…,\phi(\mathbf{y}_{s(t-1)}): (\mathbf{v}_0,…,\mathbf{v}_{r-1})\in\mathbb F_2^{rw}\right\} \]

where \(\mathbf{y}_n = \mbox{trunc}_h(\mathbf{v}_n, \mathbf{v}_{n+1},…)\), \(\mathbf{v}_n\) is the representation of \(m_n\) under the polynomial basis of \(\mathbb F_{2^w}\) over \(\mathbb F_2\), and \(h=w\lfloor31/w\rfloor\). The parameter \(s\) is called the stepping parameter of the recurrence.

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Definition at line 57 of file F2wCycleBasedLFSR.java.

Constructor & Destructor Documentation

◆ F2wCycleBasedLFSR() [1/2]

umontreal.ssj.hups.F2wCycleBasedLFSR.F2wCycleBasedLFSR	(	int	w,
		int	r,
		int	modQ,
		int	step,
		int	nbcoeff,
		int	coeff[],
		int	nocoeff[] )

Constructs a point set with \(2^{rw}\) points.

See the description of the class umontreal.ssj.hups.F2wStructure for the meaning of the parameters. Constructs and stores the set of cycles for an LCG with modulus n and multiplier a. If pgcd(a, n) = 1, this constructs a full-period LCG which has two cycles, one containing 0 and one, the LCG period.

Parameters

n	required number of points and modulo of the LCG
a	generator a of the LCG

Definition at line 65 of file F2wCycleBasedLFSR.java.

◆ F2wCycleBasedLFSR() [2/2]

umontreal.ssj.hups.F2wCycleBasedLFSR.F2wCycleBasedLFSR	(	String	filename,
		int	no )

Constructs a point set after reading its parameters from file filename; the parameters are located at line numbered no of filename.

The available files are listed in the description of class umontreal.ssj.hups.F2wStructure.

Definition at line 90 of file F2wCycleBasedLFSR.java.

Member Function Documentation

◆ toString()

String umontreal.ssj.hups.F2wCycleBasedLFSR.toString ( )

Formats a string that contains information about the point set.

Returns: string representation of the point set information

Reimplemented from umontreal.ssj.hups.CycleBasedPointSet.

Definition at line 103 of file F2wCycleBasedLFSR.java.

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

src/main/java/umontreal/ssj/hups/F2wCycleBasedLFSR.java

SSJ API Documentation Stochastic Simulation in Java