SSJ  3.3.1
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)
 Same as the same method in PointSet. 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 points. 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 randomize (PointSetRandomization rand)
 Randomizes this point set using the given rand. More...
 
void addRandomShift (int d1, int d2, RandomStream stream)
 By default, this method generates a random shift in the protected double[] array shift, to be used eventually for a random shift modulo 1. More...
 
void addRandomShift (RandomStream stream)
 Same as addRandomShift(0, dim, stream), where dim is the dimension of the point set. More...
 
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.
 
void clearRandomShift ()
 Erases the current random shift, if any.
 
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]
 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. More...
 
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. More...
 
RandomStream shiftStream
 Stream used to generate the random shifts. More...
 
- Static Protected Attributes inherited from 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. More...
 

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: