SSJ
3.2.1
Stochastic Simulation in Java
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This abstract class describes methods specific to digital sequences in base 2. More...
Classes | |
class | DigitalNetBase2IteratorShiftGenerators |
class | DigitalNetBase2IteratorShiftNoGray |
Public Member Functions | |
abstract void | extendSequence (int k) |
Increases the number of points to \(n = 2^k\) from now on. More... | |
DigitalNetBase2 | toNet () |
Transforms this digital sequence into a digital net without changing the coordinates of the points. More... | |
DigitalNetBase2 | toNetShiftCj () |
Transforms this digital sequence into a digital net by adding one dimension and shifting all coordinates by one position. More... | |
PointSetIterator | iteratorShift () |
Similar to #iterator, except that the first coordinate of the points is \(i/n\), the second coordinate is obtained via the generating matrix \(\mathbf{C}_0\), the next one via \(\mathbf{C}_1\), and so on. More... | |
PointSetIterator | iteratorShiftNoGray () |
This iterator shifts all coordinates of each point one position to the right and sets the first coordinate of point \(i\) to \(i/n\), so that the points enumerated with this iterator have one more dimension. More... | |
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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... | |
Additional Inherited Members | |
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int | intToDigitsGray (int b, int i, int numDigits, int[] bary, int[] gray) |
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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 |
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static final int | MAXBITS = 31 |
This abstract class describes methods specific to digital sequences in base 2.
Concrete classes must implement the extendSequence method that increases the number of points of the digital sequence. Calling the methods toNet or toNetShiftCj will transform the digital sequence into a digital net, which has a fixed number of points \(n\).
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abstract |
Increases the number of points to \(n = 2^k\) from now on.
k | there will be 2^k points |
PointSetIterator iteratorShift | ( | ) |
Similar to #iterator, except that the first coordinate of the points is \(i/n\), the second coordinate is obtained via the generating matrix \(\mathbf{C}_0\), the next one via \(\mathbf{C}_1\), and so on.
Thus, this iterator shifts all coordinates of each point one position to the right and sets the first coordinate of point \(i\) to \(i/n\), so that the points enumerated with this iterator have one more dimension. A digital shift, if present, will have one more dimension also. This iterator uses the Gray code.
PointSetIterator iteratorShiftNoGray | ( | ) |
This iterator shifts all coordinates of each point one position to the right and sets the first coordinate of point \(i\) to \(i/n\), so that the points enumerated with this iterator have one more dimension.
This iterator does not use the Gray code: the points are enumerated in the order of their first coordinate before randomization. A digital shift, if present, will have one more dimension also.
DigitalNetBase2 toNet | ( | ) |
Transforms this digital sequence into a digital net without changing the coordinates of the points.
Returns the digital net.
DigitalNetBase2 toNetShiftCj | ( | ) |
Transforms this digital sequence into a digital net by adding one dimension and shifting all coordinates by one position.
The first coordinate of point \(i\) is \(i/n\), where \(n\) is the total number of points. Thus if the coordinates of a point of the digital sequence were \((x_0, x_1, x_2, …, x_{s-1})\), then the coordinates of the point of the digital net will be \((i/n, x_0, x_1, …, x_{s-1})\). In other words, for the digital net, \(\mathbf{C}_0\) is the reflected identity and for \(j\ge1\), the \(\mathbf{C}_j\) used is the \(\mathbf{C}_{j-1}\) of the digital sequence. If the digital sequence uses a digital shift, then the digital net will include the digital shift with one more dimension also. Returns the digital net.