SSJ
3.2.1
Stochastic Simulation in Java
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This class creates a point set based upon a linear congruential sequence in the finite field \(\mathbb F_{2^w}[z]/P(z)\). More...
Public Member Functions | |
F2wCycleBasedPolyLCG (int w, int r, int modQ, int step, int nbcoeff, int coeff[], int nocoeff[]) | |
Constructs a point set with \(2^{rw}\) points. More... | |
F2wCycleBasedPolyLCG (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 () |
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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 () |
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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 () |
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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 | |
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void | addCycle (AbstractList c) |
Adds the cycle c to the list of all cycles. More... | |
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int | numBits |
double | normFactor |
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int | numCycles = 0 |
ObjectArrayList | cycles = new ObjectArrayList() |
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double | EpsilonHalf = 1.0 / Num.TWOEXP[55] |
int | dim = 0 |
int | numPoints = 0 |
int | dimShift = 0 |
int | capacityShift = 0 |
RandomStream | shiftStream |
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static final int | MAXBITS = 31 |
This class creates a point set based upon a linear congruential sequence in the finite field \(\mathbb F_{2^w}[z]/P(z)\).
The recurrence is
\[ q_n(z) = z^s q_{n-1}(z) \mod P(z) \]
where \(P(z)\in\mathbb F_{2^w}[z]\) has degree \(r\) and \(q_n(z) = q_{n,1} z^{r-1} + \cdots+ q_{n,r} \in\mathbb F_{2^w}[z]/P(z)\). The parameter \(s\) is called the stepping parameter of the recurrence. The polynomial \(P(z)\) is not necessarily the characteristic polynomial of this recurrence, but it can still be used to store the parameters of the recurrence. In the implementation, it is stored in an object of the class umontreal.ssj.hups.F2wStructure. See the description of this class for more details on how the polynomial is stored.
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
\[ \{ (\phi(\mathbf{y}_0),\phi(\mathbf{y}_1),…,\phi(\mathbf{y}_{t-1}): (\mathbf{q}_{0,1},…,\mathbf{q}_{0,r-1})\in\mathbb F_2^{rw}\} \]
where \(\mathbf{y}_n = (\mathbf{q}_{n,1},…,\mathbf{q}_{n,r})\), \(\mathbf{q}_{n,i}\) is the representation of \(q_{n,i}\) under the polynomial basis of \(\mathbb F_{2^w}\) over \(\mathbb F_2\).
F2wCycleBasedPolyLCG | ( | 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.
n | required number of points and modulo of the LCG |
a | generator a of the LCG |
F2wCycleBasedPolyLCG | ( | 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.