SSJ
3.2.1
Stochastic Simulation in Java
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A special case of DigitalNet for the base \(b=2\). More...
Classes | |
class | DigitalNetBase2Iterator |
class | DigitalNetBase2IteratorNoGray |
Public Member Functions | |
void | printGeneratorMatrices (int s) |
Prints the generator matrices as bit matrices in standard form for dimensions 1 to \(s\). | |
void | printGeneratorMatricesTrans (int s) |
Prints the generator matrices transposed in the form of integers for dimensions 1 to \(s\). More... | |
double | getCoordinate (int i, int j) |
double | getCoordinateNoGray (int i, int j) |
PointSetIterator | iterator () |
PointSetIterator | iteratorNoGray () |
This iterator does not use the Gray code. More... | |
String | toString () |
void | clearRandomShift () |
void | addRandomShift (RandomStream stream) |
void | addRandomShift (int d1, int d2, RandomStream stream) |
void | leftMatrixScramble (RandomStream stream) |
void | iBinomialMatrixScramble (RandomStream stream) |
void | stripedMatrixScramble (RandomStream stream) |
void | rightMatrixScramble (RandomStream stream) |
void | nestedUniformScramble (RandomStream stream, double[][] output) |
Same as nestedUniformScramble(stream, output, 0) . | |
void | nestedUniformScramble (RandomStream stream, double[][] output, int numBits) |
Apply Owen's nested uniform scrambling. More... | |
void | leftMatrixScrambleDiag (RandomStream stream) |
void | leftMatrixScrambleFaurePermut (RandomStream stream, int sb) |
void | leftMatrixScrambleFaurePermutDiag (RandomStream stream, int sb) |
void | leftMatrixScrambleFaurePermutAll (RandomStream stream, int sb) |
void | iBinomialMatrixScrambleFaurePermut (RandomStream stream, int sb) |
void | iBinomialMatrixScrambleFaurePermutDiag (RandomStream stream, int sb) |
void | iBinomialMatrixScrambleFaurePermutAll (RandomStream stream, int sb) |
void | stripedMatrixScrambleFaurePermutAll (RandomStream stream, int sb) |
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double | getCoordinate (int i, int j) |
PointSetIterator | iterator () |
DigitalNet () | |
Empty constructor. | |
double | getCoordinateNoGray (int i, int j) |
Returns \(u_{i,j}\), the coordinate \(j\) of point \(i\), the points being enumerated in the standard order (no Gray code). More... | |
PointSetIterator | iteratorNoGray () |
This iterator does not use the Gray code. More... | |
void | addRandomShift (int d1, int d2, RandomStream stream) |
Adds a random digital shift to all the points of the point set, using stream stream to generate the random numbers. More... | |
void | addRandomShift (RandomStream stream) |
Same as addRandomShift(0, dim, stream), where dim is the dimension of the digital net. More... | |
void | clearRandomShift () |
Erases the current digital random shift, if any. | |
String | toString () |
void | leftMatrixScramble (RandomStream stream) |
Applies a linear scramble by multiplying each \(\mathbf{C}_j\) on the left by a \(w\times w\) nonsingular lower-triangular matrix \(\mathbf{M}_j\), as suggested by Matoušek [169] and implemented by Hong and Hickernell [86] . More... | |
void | leftMatrixScrambleDiag (RandomStream stream) |
Similar to leftMatrixScramble except that all the off-diagonal elements of the \(\mathbf{M}_j\) are 0. More... | |
void | leftMatrixScrambleFaurePermut (RandomStream stream, int sb) |
Similar to leftMatrixScramble except that the diagonal elements of each matrix \(\mathbf{M}_j\) are chosen from a restricted set of the best integers as calculated by Faure [56] . More... | |
void | leftMatrixScrambleFaurePermutDiag (RandomStream stream, int sb) |
Similar to leftMatrixScrambleFaurePermut except that all off-diagonal elements are 0. More... | |
void | leftMatrixScrambleFaurePermutAll (RandomStream stream, int sb) |
Similar to leftMatrixScrambleFaurePermut except that the elements under the diagonal are also chosen from the same restricted set as the diagonal elements. More... | |
void | iBinomialMatrixScramble (RandomStream stream) |
Applies the \(i\)-binomial matrix scramble proposed by Tezuka [217] (see also [184] ). More... | |
void | iBinomialMatrixScrambleFaurePermut (RandomStream stream, int sb) |
Similar to iBinomialMatrixScramble except that the diagonal elements of each matrix \(\mathbf{M}_j\) are chosen as in leftMatrixScrambleFaurePermut. More... | |
void | iBinomialMatrixScrambleFaurePermutDiag (RandomStream stream, int sb) |
Similar to iBinomialMatrixScrambleFaurePermut except that all the off-diagonal elements are 0. More... | |
void | iBinomialMatrixScrambleFaurePermutAll (RandomStream stream, int sb) |
Similar to iBinomialMatrixScrambleFaurePermut except that the elements under the diagonal are also chosen from the same restricted set as the diagonal elements. More... | |
void | stripedMatrixScramble (RandomStream stream) |
Applies the striped matrix scramble proposed by Owen [184] . More... | |
void | stripedMatrixScrambleFaurePermutAll (RandomStream stream, int sb) |
Similar to stripedMatrixScramble except that the elements on and under the diagonal of each matrix \(\mathbf{M}_j\) are chosen as in leftMatrixScrambleFaurePermut. More... | |
void | rightMatrixScramble (RandomStream stream) |
Applies a linear scramble by multiplying each \(\mathbf{C}_j\) on the right by a single \(k\times k\) nonsingular upper-triangular matrix \(\mathbf{M}\), as suggested by Faure and Tezuka [56] (see also [86] ). More... | |
void | unrandomize () |
Restores the original generator matrices and removes the random shift. | |
void | resetGeneratorMatrices () |
Restores the original generator matrices. More... | |
void | eraseOriginalGeneratorMatrices () |
Erases the original generator matrices and replaces them by the current ones. More... | |
void | printGeneratorMatrices (int s) |
Prints the generator matrices in standard form for dimensions 1 to \(s\). | |
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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... | |
Protected Attributes | |
int [] | genMat |
int [] | digitalShift |
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int | b = 0 |
int | numCols = 0 |
int | numRows = 0 |
int | outDigits = 0 |
int [][] | genMat |
int [][] | digitalShift |
double | normFactor |
double [] | factor |
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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 |
Additional Inherited Members | |
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int | intToDigitsGray (int b, int i, int numDigits, int[] bary, int[] gray) |
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static final int | MAXBITS = 31 |
A special case of DigitalNet for the base \(b=2\).
The implementation exploit the binary nature of computers and is much more efficient than for the general case. Binary expansions are easy to obtain because the computer already uses them internally. The generator matrices \(\mathbf{C}_j\) are stored in a large array of size \(sk\). The \(c\)-th column of \(\mathbf{C}_j\), for \(c=0,…,k-1\), is stored at position \(jk + c\) of that array, as a 32-bit integer. For all derived classes, the above 32-bit integer must be of the form \( [0 0 \cdots C_0 C_1 \cdots C_{r-1}]\). The value of \(k\) cannot exceed 31 (32 is not allowed because Java does not have 32-bit unsigned integers). The value of \(w\) is always 31.
The random digital shift in base 2 corresponds to a random XOR. It can be applied via the method #addRandomShift.
PointSetIterator iteratorNoGray | ( | ) |
This iterator does not use the Gray code.
Thus the points are enumerated in the order of their first coordinate before randomization.
void nestedUniformScramble | ( | RandomStream | stream, |
double | output[][], | ||
int | numBits | ||
) |
Apply Owen's nested uniform scrambling.
This type of scrambling does not modify the DigitalNetBase2 object. In particular, it does not randomize the generator matrices stored in the object. Rather, it computes the randomized points all at once and stores them in the two-dimensional array output
. All points are randomized at once to avoid storing all the permutations.
The implementation is an adaptation of that found in SAMPLE PACKage by Thomas Kollig and Alexander Keller.
stream | Random stream used to randomize the bits. |
output | Output array that will store the randomized points. The size of its first dimension must be getNumPoints() and the size of its second dimension must be getDimension(). |
numBits | Number of ouput bits to scramble. If it is zero, the number of ouput bits of the DigitalNetBase2 instance is used. It can be smaller than, equal to or larger than DigitalNet.outDigits. |
void printGeneratorMatricesTrans | ( | int | s | ) |
Prints the generator matrices transposed in the form of integers for dimensions 1 to \(s\).
Each integer corresponds to a column of bits.