This class creates a point set based upon a linear feedback shift register sequence. More...
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
-
n required number of points and modulo of the LCG a generator 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:
- F2wCycleBasedLFSR.java
