SSJ API Documentation
Stochastic Simulation in Java
Loading...
Searching...
No Matches
umontreal.ssj.hups.DigitalSequenceBase2 Class Referenceabstract

This abstract class describes methods specific to digital sequences in base. More...

Inheritance diagram for umontreal.ssj.hups.DigitalSequenceBase2:
umontreal.ssj.hups.DigitalNetBase2 umontreal.ssj.hups.DigitalNet umontreal.ssj.hups.PointSet umontreal.ssj.hups.NiedSequenceBase2 umontreal.ssj.hups.NiedXingSequenceBase2 umontreal.ssj.hups.SobolSequence

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.
DigitalNetBase2 toNet ()
 Transforms this digital sequence into a digital net without changing the coordinates of the points.
DigitalNetBase2 toNetShiftCj ()
 Transforms this digital sequence into a digital net by adding one dimension and shifting all coordinates by one position.
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.
PointSetIterator iteratorShiftNoGray ()
 This iterator shifts all coordinates of each point one position to the right and sets the first coordinate of point \(i\) to.
Public Member Functions inherited from umontreal.ssj.hups.DigitalNetBase2
double getCoordinate (int i, int j)
 Returns \(u_{i',j}\), the coordinate \(j\) of point \(i'\), where \(i'\) is the Gray code for \(i\).
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).
PointSetIterator iterator ()
 Returns a DigitalNetBase2Iterator which enumerates the points using a Gray code.
PointSetIterator iteratorNoGray ()
 This iterator does not use the Gray code.
String toString ()
 Formats a string that contains information on this digital net.
void addRandomShift (int d1, int d2, RandomStream stream)
 Generates a random digital shift for coordinates \(j\) from d1 to d2-1, using stream to generate the random numbers.
void addRandomShift (RandomStream stream)
 Same as addRandomShift(0, dim, stream), where dim is the dimension of the digital net.
void clearRandomShift ()
 Erases the current digital random shift, if any.
void leftMatrixScramble (int r, RandomStream stream)
 This is a version of LMS in which each column of the lower-triangular scrambling matrix is represented as an integer less than 2^w, just like for Cj.
void leftMatrixScramble (RandomStream stream)
 By default, the matrices L_j have r = w rows.
void iBinomialMatrixScramble (RandomStream stream)
 Similar to leftMatrixScramble, except that all entries on any given diagonal or subdiagonal of any given \(\mathbf{M}_j\) are identical.
void stripedMatrixScramble (RandomStream stream)
 Applies the striped matrix scramble proposed by Owen.
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.
void nestedUniformScramble (RandomStream stream, double[][] output)
 Same as nestedUniformScramble(stream, output, 0) .
void nestedUniformScramble (RandomStream stream, double[][] output, int numBits)
 Applies Owen's nested uniform scrambling to the digital net and returns the scrambled points in the two-dimensional array output.
void nestedUniformScramble (RandomStream stream, int[][] output, int numBits)
 Same as nestedUniformScramble(RandomStream,double[][],int), but it returns the points as integers from 0 to 2^outDigits - 1, instead of doubles.
void leftMatrixScrambleDiag (RandomStream stream)
 Similar to leftMatrixScramble except that all the off-diagonal elements of the \(\mathbf{M}_j\) are 0.
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 [58] .
void leftMatrixScrambleFaurePermutDiag (RandomStream stream, int sb)
 Similar to leftMatrixScrambleFaurePermut except that all off-diagonal elements are 0.
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.
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.
void iBinomialMatrixScrambleFaurePermutDiag (RandomStream stream, int sb)
 Similar to iBinomialMatrixScrambleFaurePermut except that all the off-diagonal elements are 0.
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.
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.
void unrandomize ()
 Restores the original generator matrices and removes the random shift.
void resetGenMatrices ()
 Restores genMat to the original generator matrices.
void eraseOriginalGenMatrices ()
 Erases the original generator matrices and replaces them by the current ones.
int[][][] genMatricesToBitByBitFormat ()
 Returns the generator matrices as a 3-dimensional array of shape dim x numRows x numCols integers, one integer for each bit.
void genMatricesFromBitByBitFormat (int[][][] matrices)
 Reverse of the previous function.
void printGeneratorMatrices (int s)
 Prints the generating matrices bit by bit for dimensions 1 to \(s\).
void printGenMatrices (int s)
 Prints the generating matrices in the standard format, one integer per column, for dimensions 1 to \(s\).
void printOriginalMatrices (int s)
 Prints the generating matrices in the standard format, one integer per column, for dimensions 1 to \(s\).
int[] getGenMatrices ()
 Returns a copy of the generator matrices for dimensions 1 to \(s\).
void outputInterlace (int[][] points, double[][] interlacedPoints)
 Interlaces the points from a digital net.
DigitalNetBase2 matrixInterlace ()
 Interlaces the matrices from a digital net.
Public Member Functions inherited from umontreal.ssj.hups.DigitalNet
 DigitalNet ()
 Empty constructor.
int getInterlacing ()
 Returns the interlacing factor.
void setInterlacing (int interlacing)
 Sets the interlacing factor.
void resetGeneratorMatrices ()
 Restores the original generator matrices.
void eraseOriginalGeneratorMatrices ()
 Erases the original generator matrices and replaces them by the current ones.
Public Member Functions inherited from umontreal.ssj.hups.PointSet
int getDimension ()
 Returns the dimension (number of available coordinates) of the points.
int getNumPoints ()
 Returns the number of points.
void randomize (PointSetRandomization rand)
 Randomizes this point set using the given rand.
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.
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.
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.
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.
String formatPoints (PointSetIterator iter, int n, int d)
 Same as invoking formatPoints(n, d), but prints the points by calling iter repeatedly.
String formatPointsBase (int b)
 Similar to formatPoints(), but the points coordinates are printed in base \(b\).
String formatPointsBase (int n, int d, int b)
 Similar to formatPoints(n, d), but the points coordinates are printed in base \(b\).
String formatPointsBase (PointSetIterator iter, int b)
 Similar to formatPoints(iter), but the points coordinates are printed in base.
String formatPointsBase (PointSetIterator iter, int n, int d, int b)
 Similar to formatPoints(iter, n, d), but the points coordinates are printed in base \(b\).
String formatPointsNumbered ()
 Same as invoking formatPointsNumbered(n, d) with \(n\) and \(d\) equal to the number of points and the dimension, respectively.
String formatPointsNumbered (int n, int d)
 Same as invoking formatPoints(n,d), except that the points are numbered.

Additional Inherited Members

Static Public Member Functions inherited from umontreal.ssj.hups.PointSet
static int getMaxBits ()
 Returns the maximum number of usable bits.
Protected Attributes inherited from umontreal.ssj.hups.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.
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.
RandomStream shiftStream
 Stream used to generate the random shifts.
Static Protected Attributes inherited from umontreal.ssj.hups.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.

Detailed Description

This abstract class describes methods specific to digital sequences in base.

  1. 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 \(n\).

Definition at line 37 of file DigitalSequenceBase2.java.

Member Function Documentation

◆ extendSequence()

abstract void umontreal.ssj.hups.DigitalSequenceBase2.extendSequence ( int k)
abstract

Increases the number of points to \(n = 2^k\) from now on.

Parameters
kthere will be 2^k points

Reimplemented in umontreal.ssj.hups.NiedSequenceBase2, umontreal.ssj.hups.NiedXingSequenceBase2, and umontreal.ssj.hups.SobolSequence.

◆ iteratorShift()

PointSetIterator umontreal.ssj.hups.DigitalSequenceBase2.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.

Definition at line 132 of file DigitalSequenceBase2.java.

◆ iteratorShiftNoGray()

PointSetIterator umontreal.ssj.hups.DigitalSequenceBase2.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.

Definition at line 146 of file DigitalSequenceBase2.java.

◆ toNet()

DigitalNetBase2 umontreal.ssj.hups.DigitalSequenceBase2.toNet ( )

Transforms this digital sequence into a digital net without changing the coordinates of the points.

Returns the digital net. Note that since this class is already a subclass of DigitalNetBase2, this transformation is not really needed!

Definition at line 86 of file DigitalSequenceBase2.java.

◆ toNetShiftCj()

DigitalNetBase2 umontreal.ssj.hups.DigitalSequenceBase2.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.

Definition at line 108 of file DigitalSequenceBase2.java.

The documentation for this class was generated from the following file: