A special case of DigitalNet for the base \(b=2\). More...

Inheritance diagram for umontreal.ssj.hups.DigitalNetBase2:

Classes
class	DigitalNetBase2Iterator
class	DigitalNetBase2IteratorNoGray

Public Member Functions
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

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 case of a general \(b=2\). Binary expansions are easy to obtain because the computer already uses them internally. The generator matrices \(\mathbf{C}_j\) are stored in a single large array of size \(sk\). The \(c\)-th column of \(\mathbf{C}_j\), for \(c=0,\dots,k-1\), is stored at position \(jk + c\) of this array, as a 32-bit integer. For all derived classes, this 32-bit integer must have a binary representation of the form \(c_0\, c_1 \cdots \, c_{w-1}\) where the most significant bit is for the first row of the matrix. By default, \(w=31\). It can be changed to a smaller value in subclasses, usually in the constructor, but this is not recommended. To represent matrices with \(r < w\) rows, one can also set the last \(w-r\) bits of each integer to 0. We take \(w=31\) by default to make the implementation simpler and faster. The value of \(k\) cannot exceed 31 (32 is not allowed because Java does not have 32-bit unsigned integers). In this class, the random digital shift in base 2 generated by addRandomShift corresponds to a XOR with a random \(w\)-bit integer.

Definition at line 55 of file DigitalNetBase2.java.

Member Function Documentation

◆ addRandomShift() [1/2]

void umontreal.ssj.hups.DigitalNetBase2.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.

The dimension of the current shift is reset to d2 and the current streamShift is set to stream. This shift vector \((d_{j,0},…,d_{j,k-1})\) is generated uniformly over \(\{0,\dots,b-1\}^k\) for each coordinate. This shift vector will be added modulo \(b\) to the digits of all the points by any iterator on this point set. After adding a digital shift, all iterators must be reconstructed or reset to zero.

Parameters

stream random number stream used to generate the uniforms

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 130 of file DigitalNetBase2.java.

◆ addRandomShift() [2/2]

void umontreal.ssj.hups.DigitalNetBase2.addRandomShift ( RandomStream stream )

Same as addRandomShift(0, dim, stream), where dim is the dimension of the digital net.

Parameters

stream random number stream used to generate the uniforms

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 160 of file DigitalNetBase2.java.

◆ clearRandomShift()

void umontreal.ssj.hups.DigitalNetBase2.clearRandomShift ( )

Erases the current digital random shift, if any.

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 164 of file DigitalNetBase2.java.

◆ eraseOriginalGenMatrices()

void umontreal.ssj.hups.DigitalNetBase2.eraseOriginalGenMatrices ( )

Erases the original generator matrices and replaces them by the current ones.

The current linear matrix scrambles thus become permanent. This is useful if we want to apply several scrambles in succession to a given digital net.

Definition at line 612 of file DigitalNetBase2.java.

◆ genMatricesFromBitByBitFormat()

void umontreal.ssj.hups.DigitalNetBase2.genMatricesFromBitByBitFormat ( int matrices[][][] )

Reverse of the previous function.

Sets the generator matrices from matrices in bit by bit format.

Definition at line 642 of file DigitalNetBase2.java.

◆ genMatricesToBitByBitFormat()

int[][][] umontreal.ssj.hups.DigitalNetBase2.genMatricesToBitByBitFormat ( )

Returns the generator matrices as a 3-dimensional array of shape dim x numRows x numCols integers, one integer for each bit.

This is slow and takes much memory!

Definition at line 622 of file DigitalNetBase2.java.

◆ getCoordinate()

double umontreal.ssj.hups.DigitalNetBase2.getCoordinate	(	int	i,
		int	j )

Returns \(u_{i',j}\), the coordinate \(j\) of point \(i'\), where \(i'\) is the Gray code for \(i\).

Parameters

i	point index, to be transformed to a Gray code
j	coordinate index

Returns: the value of \(u_{i,j}\)

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 64 of file DigitalNetBase2.java.

◆ getCoordinateNoGray()

double umontreal.ssj.hups.DigitalNetBase2.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).

Parameters

i	point index
j	coordinate index

Returns: the value of \(u_{i,j}\)

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 83 of file DigitalNetBase2.java.

◆ getGenMatrices()

int[] umontreal.ssj.hups.DigitalNetBase2.getGenMatrices ( )

Returns a copy of the generator matrices for dimensions 1 to \(s\).

Each integer corresponds to one column of bits.

Definition at line 712 of file DigitalNetBase2.java.

◆ iBinomialMatrixScramble()

void umontreal.ssj.hups.DigitalNetBase2.iBinomialMatrixScramble ( RandomStream stream )

Similar to leftMatrixScramble, except that all entries on any given diagonal or subdiagonal of any given \(\mathbf{M}_j\) are identical.

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 360 of file DigitalNetBase2.java.

◆ iBinomialMatrixScrambleFaurePermut()

void umontreal.ssj.hups.DigitalNetBase2.iBinomialMatrixScrambleFaurePermut	(	RandomStream	stream,
		int	sb )

Similar to iBinomialMatrixScramble except that the diagonal elements of each matrix \(\mathbf{M}_j\) are chosen as in leftMatrixScrambleFaurePermut.

Parameters

stream	random number stream used to generate the randomness
sb	Only the first \(sb\) elements of \(F\) are used

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 571 of file DigitalNetBase2.java.

◆ iBinomialMatrixScrambleFaurePermutAll()

void umontreal.ssj.hups.DigitalNetBase2.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.

Parameters

stream	random number stream used to generate the randomness
sb	Only the first \(sb\) elements of \(F\) are used

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 579 of file DigitalNetBase2.java.

◆ iBinomialMatrixScrambleFaurePermutDiag()

void umontreal.ssj.hups.DigitalNetBase2.iBinomialMatrixScrambleFaurePermutDiag	(	RandomStream	stream,
		int	sb )

Similar to iBinomialMatrixScrambleFaurePermut except that all the off-diagonal elements are 0.

Parameters

stream	random number stream used to generate the randomness
sb	Only the first \(sb\) elements of \(F\) are used

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 575 of file DigitalNetBase2.java.

◆ iterator()

PointSetIterator umontreal.ssj.hups.DigitalNetBase2.iterator ( )

Returns a DigitalNetBase2Iterator which enumerates the points using a Gray code.

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 111 of file DigitalNetBase2.java.

◆ iteratorNoGray()

PointSetIterator umontreal.ssj.hups.DigitalNetBase2.iteratorNoGray ( )

This iterator does not use the Gray code.

Thus the points are enumerated in the order of their first coordinate before randomization.

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 119 of file DigitalNetBase2.java.

◆ leftMatrixScramble() [1/2]

void umontreal.ssj.hups.DigitalNetBase2.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.

The nonzero part of L_j will be r x numRows, i.e., the scrambled generating matrices will have r nonzero rows only. They are put in genMat. The algo is described in the document "latnetbuider notes".

Definition at line 222 of file DigitalNetBase2.java.

◆ leftMatrixScramble() [2/2]

void umontreal.ssj.hups.DigitalNetBase2.leftMatrixScramble ( RandomStream stream )

By default, the matrices L_j have r = w rows.

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 276 of file DigitalNetBase2.java.

◆ leftMatrixScrambleDiag()

void umontreal.ssj.hups.DigitalNetBase2.leftMatrixScrambleDiag ( RandomStream stream )

Similar to leftMatrixScramble except that all the off-diagonal elements of the \(\mathbf{M}_j\) are 0.

In base b=2, M_j must be the identity, so this scramble does nothing!

Parameters

stream random number stream used to generate the randomness

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 555 of file DigitalNetBase2.java.

◆ leftMatrixScrambleFaurePermut()

void umontreal.ssj.hups.DigitalNetBase2.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] .

They are generated uniformly over the first sb elements of array \(F\), where \(F\) is made up of a permutation of the integers \([1..(b-1)]\). These integers are sorted by increasing order of the upper bounds of the extreme discrepancy for the given integer.

Parameters

stream	random number stream used to generate the randomness
sb	Only the first \(sb\) elements of \(F\) are used

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 559 of file DigitalNetBase2.java.

◆ leftMatrixScrambleFaurePermutAll()

void umontreal.ssj.hups.DigitalNetBase2.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.

Parameters

stream	random number stream used to generate the randomness
sb	Only the first \(sb\) elements of \(F\) are used

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 567 of file DigitalNetBase2.java.

◆ leftMatrixScrambleFaurePermutDiag()

void umontreal.ssj.hups.DigitalNetBase2.leftMatrixScrambleFaurePermutDiag	(	RandomStream	stream,
		int	sb )

Similar to leftMatrixScrambleFaurePermut except that all off-diagonal elements are 0.

Parameters

stream	random number stream used to generate the randomness
sb	Only the first \(sb\) elements of \(F\) are used

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 563 of file DigitalNetBase2.java.

◆ matrixInterlace()

DigitalNetBase2 umontreal.ssj.hups.DigitalNetBase2.matrixInterlace ( )

Interlaces the matrices from a digital net.

This function returns a new digital net, whose dimension equals getDimension() / getInterlacing(), and whose generating matrices are interlaced. **** Pierre: This seems to be very inefficient!

Definition at line 773 of file DigitalNetBase2.java.

◆ nestedUniformScramble() [1/3]

void umontreal.ssj.hups.DigitalNetBase2.nestedUniformScramble	(	RandomStream	stream,
		double	output[][] )

Same as nestedUniformScramble(stream, output, 0) .

Definition at line 448 of file DigitalNetBase2.java.

◆ nestedUniformScramble() [2/3]

void umontreal.ssj.hups.DigitalNetBase2.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.

The points are computed by using the generating matrices, and scrambled right away. Only the first numBits bits are scrambled. This function does not modify the DigitalNetBase2 object. In particular, it does not change the generating matrices stored in the object. All points are randomized at once to avoid storing the permutations.

The implementation is an adaptation of that found in SAMPLE PACKage by Thomas Kollig and Alexander Keller.

Parameters

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 output bits to scramble. It can be smaller than, equal to or larger than DigitalNet.outDigits. If this parameter is zero, outDigits bits will be scrambled.

Definition at line 473 of file DigitalNetBase2.java.

◆ nestedUniformScramble() [3/3]

void umontreal.ssj.hups.DigitalNetBase2.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.

Definition at line 491 of file DigitalNetBase2.java.

◆ outputInterlace()

void umontreal.ssj.hups.DigitalNetBase2.outputInterlace	(	int	points[][],
		double	interlacedPoints[][] )

Interlaces the points from a digital net.

This is useful for interlacing after NUS, since NUS returns the points. For other use cases, matrixInterlace() should be preferred.

Parameters

points	Array that stores the non-interlaced points as integers. The size of its first dimension must be getNumPoints() and the size of its second dimension must be getDimension().
interlacedPoints	Output array that will store the interlaced points. The size of its first dimension must be getNumPoints() and the size of its second dimension must be getDimension() / getInterlacing().

Definition at line 733 of file DigitalNetBase2.java.

◆ printGeneratorMatrices()

void umontreal.ssj.hups.DigitalNetBase2.printGeneratorMatrices ( int s )

Prints the generating matrices bit by bit for dimensions 1 to \(s\).

Each matrix has \(r\) rows and \(k\) columns.

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 664 of file DigitalNetBase2.java.

◆ printGenMatrices()

void umontreal.ssj.hups.DigitalNetBase2.printGenMatrices ( int s )

Prints the generating matrices in the standard format, one integer per column, for dimensions 1 to \(s\).

Definition at line 684 of file DigitalNetBase2.java.

◆ printOriginalMatrices()

void umontreal.ssj.hups.DigitalNetBase2.printOriginalMatrices ( int s )

Prints the generating matrices in the standard format, one integer per column, for dimensions 1 to \(s\).

Definition at line 698 of file DigitalNetBase2.java.

◆ resetGenMatrices()

void umontreal.ssj.hups.DigitalNetBase2.resetGenMatrices ( )

Restores genMat to the original generator matrices.

This removes the current linear matrix scrambles. A new genMat object will be created next time we scramble.

Definition at line 600 of file DigitalNetBase2.java.

◆ rightMatrixScramble()

void umontreal.ssj.hups.DigitalNetBase2.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.

[58] (see also [84] ). The diagonal entries of the matrix \(\mathbf{M}\) are generated uniformly over \(\{1,…,b-1\}\), the entries above the diagonal are generated uniformly over \(\{0,…,b-1\}\), and all the entries are generated independently. The effect of this scramble is only to change the order in which the points are generated. If one computes the average value of a function over all the points of a given digital net, or over a number of points that is a power of the basis, then this scramble makes no difference.

Parameters

stream random number stream used as generator of the randomness

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 408 of file DigitalNetBase2.java.

◆ stripedMatrixScramble()

void umontreal.ssj.hups.DigitalNetBase2.stripedMatrixScramble ( RandomStream stream )

Applies the striped matrix scramble proposed by Owen.

[189] . It multiplies each \(\mathbf{C}_j\) on the left by a \(w\times w\) nonsingular lower-triangular matrix \(\mathbf{M}_j\) as in leftMatrixScramble, but with the additional constraint that in any column, all entries below the diagonal are equal to the diagonal entry, which is generated randomly over \(\{1,…,b-1\}\). Note that for \(b=2\), the matrices \(\mathbf{M}_j\) become deterministic, with all entries on and below the diagonal equal to 1.

Parameters

stream random number stream used as generator of the randomness

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 389 of file DigitalNetBase2.java.

◆ stripedMatrixScrambleFaurePermutAll()

void umontreal.ssj.hups.DigitalNetBase2.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.

Parameters

stream	random number stream used as generator of the randomness
sb	Only the first \(sb\) elements of \(F\) are used

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 583 of file DigitalNetBase2.java.

◆ toString()

String umontreal.ssj.hups.DigitalNetBase2.toString ( )

Formats a string that contains information on this digital net.

Returns: string representation of basic information on this digital net

Reimplemented from umontreal.ssj.hups.DigitalNet.

Reimplemented in umontreal.ssj.hups.DigitalNetBase2FromFile, umontreal.ssj.hups.F2wNetLFSR, umontreal.ssj.hups.F2wNetPolyLCG, umontreal.ssj.hups.NiedSequenceBase2, umontreal.ssj.hups.NiedXingSequenceBase2, and umontreal.ssj.hups.SobolSequence.

Definition at line 123 of file DigitalNetBase2.java.

◆ unrandomize()

void umontreal.ssj.hups.DigitalNetBase2.unrandomize ( )

Restores the original generator matrices and removes the random shift.

Reimplemented from umontreal.ssj.hups.DigitalNet.

Definition at line 591 of file DigitalNetBase2.java.

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

src/main/java/umontreal/ssj/hups/DigitalNetBase2.java

SSJ API Documentation Stochastic Simulation in Java

Classes

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ addRandomShift() [1/2]

◆ addRandomShift() [2/2]

◆ clearRandomShift()

◆ eraseOriginalGenMatrices()

◆ genMatricesFromBitByBitFormat()

◆ genMatricesToBitByBitFormat()

◆ getCoordinate()

◆ getCoordinateNoGray()

◆ getGenMatrices()

◆ iBinomialMatrixScramble()

◆ iBinomialMatrixScrambleFaurePermut()

◆ iBinomialMatrixScrambleFaurePermutAll()

◆ iBinomialMatrixScrambleFaurePermutDiag()

◆ iterator()

◆ iteratorNoGray()

◆ leftMatrixScramble() [1/2]

◆ leftMatrixScramble() [2/2]

◆ leftMatrixScrambleDiag()

◆ leftMatrixScrambleFaurePermut()

◆ leftMatrixScrambleFaurePermutAll()

◆ leftMatrixScrambleFaurePermutDiag()

◆ matrixInterlace()

◆ nestedUniformScramble() [1/3]

◆ nestedUniformScramble() [2/3]

◆ nestedUniformScramble() [3/3]

◆ outputInterlace()

◆ printGeneratorMatrices()

◆ printGenMatrices()

◆ printOriginalMatrices()

◆ resetGenMatrices()

◆ rightMatrixScramble()

◆ stripedMatrixScramble()

◆ stripedMatrixScrambleFaurePermutAll()

◆ toString()

◆ unrandomize()