A special case of DigitalNet for the base \(b=2\). More...
Inheritance diagram for DigitalNetBase2:
Collaboration diagram for DigitalNetBase2:
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 \(s\). More... | |
| 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 () |
Returns a DigitalNetBase2Iterator which enumerates the points using a Gray code. | |
| PointSetIterator | iteratorNoGray () |
| This iterator does not use the Gray code. More... | |
| String | toString () |
| void | clearRandomShift () |
| void | addRandomShift (int d1, int d2, RandomStream stream) |
| void | addRandomShift (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) |
 Public Member Functions inherited from DigitalNet | |
| DigitalNet () | |
| Empty constructor. | |
| double | getCoordinate (int i, int j) |
| Returns \(u_{i',j}\), the coordinate \(j\) of point \(i'\), where \(i'\) is the Gray code for \(i\). More... | |
| PointSetIterator | iterator () |
| 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 () |
| Returns an iterator that does not use the Gray code. More... | |
| 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. 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 () |
| Formats a string that contains information on this digital net. More... | |
| 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. 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 [59] . 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. 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. 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. 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 \(s\). | |
| Public Member Functions inherited from PointSet | |
| int | getDimension () |
| Returns the dimension (number of available coordinates) of the points. 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 | randomize (PointSetRandomization rand) |
Randomizes this point set using the given rand. More... | |
| void | addRandomShift (int d1, int d2, RandomStream stream) |
By default, this method generates a random shift in the protected double[] array shift, to be used eventually for a random shift modulo 1. More... | |
| void | addRandomShift (RandomStream stream) |
Same as addRandomShift(0, dim, stream), where dim is the dimension of the point set. More... | |
| 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. | |
| void | clearRandomShift () |
| Erases the current random shift, if any. | |
| 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 |
| Protected Attributes inherited from DigitalNet | |
| int | b = 0 |
| int | numCols = 0 |
| int | numRows = 0 |
| int | outDigits = 0 |
| int [][] | genMat |
| int [][] | digitalShift |
| double | normFactor |
| double [] | factor |
| Protected Attributes inherited from 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. More... | |
| 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. More... | |
| RandomStream | shiftStream |
| Stream used to generate the random shifts. More... | |
Additional Inherited Members | |
| Protected Member Functions inherited from DigitalNet | |
| void | printMat (int N, int[][][] A, String name) |
| void | printMat0 (int[][] A, String name) |
| int | intToDigitsGray (int b, int i, int numDigits, int[] bary, int[] gray) |
| Static Protected Attributes inherited from 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. More... | |
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 \( [0\, 0\, \cdots\, c_0\, c_1 \cdots \, c_{r-1}]\), i.e., should be less than \(2^r\). 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
- In this class, the random digital shift in base 2 generated by
addRandomShiftcorresponds to a random XOR.
Member Function Documentation
◆ iteratorNoGray()
| PointSetIterator iteratorNoGray | ( | ) |
This iterator does not use the Gray code.
Thus the points are enumerated in the order of their first coordinate before randomization.
◆ nestedUniformScramble()
| 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.
- 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 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.
◆ printGeneratorMatrices()
| void printGeneratorMatrices | ( | int | s | ) |
Prints the generator matrices as bit matrices in standard form for dimensions 1 to \(s\).
Each matrix has \(r\) rows and \(k\) columns.
◆ printGeneratorMatricesTrans()
| void printGeneratorMatricesTrans | ( | int | s | ) |
Prints the generator matrices transposed in the form of integers for dimensions 1 to \(s\).
Each integer corresponds to one column of bits.
The documentation for this class was generated from the following file:
- DigitalNetBase2.java
