SSJ  3.2.1
Stochastic Simulation in Java
Public Member Functions | List of all members
F2wCycleBasedLFSR Class Reference

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

Inheritance diagram for F2wCycleBasedLFSR:
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Collaboration diagram for F2wCycleBasedLFSR:
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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. More...
 
 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. More...
 
String toString ()
 
- Public Member Functions inherited from CycleBasedPointSetBase2
double getCoordinate (int i, int j)
 
PointSetIterator 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. More...
 
void clearRandomShift ()
 Erases the current digital random shift, if any.
 
String formatPoints ()
 
- Public Member Functions inherited from CycleBasedPointSet
double getCoordinate (int i, int j)
 
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, for coordinates d1 to d2 - 1. More...
 
void clearRandomShift ()
 Erases the current random shift, if any.
 
int getDimension ()
 
PointSetIterator iterator ()
 
String toString ()
 
String formatPoints ()
 
- 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...
 

Additional Inherited Members

- Protected Member Functions inherited from CycleBasedPointSet
void addCycle (AbstractList c)
 Adds the cycle c to the list of all cycles. More...
 
- Protected Attributes inherited from CycleBasedPointSetBase2
int numBits
 
double normFactor
 
- Protected Attributes inherited from CycleBasedPointSet
int numCycles = 0
 
ObjectArrayList cycles = new ObjectArrayList()
 
- 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

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.

Constructor & Destructor Documentation

◆ F2wCycleBasedLFSR() [1/2]

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
nrequired number of points and modulo of the LCG
agenerator a of the LCG

◆ F2wCycleBasedLFSR() [2/2]

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.


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