This abstract class describes methods specific to digital sequences in base 2. More...
Inheritance diagram for DigitalSequenceBase2:
Collaboration diagram for DigitalSequenceBase2:
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... | |
 Public Member Functions inherited from DigitalNetBase2 | |
| 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... | |
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) |
| Protected Attributes inherited from DigitalNetBase2 | |
| 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... | |
| 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
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 \(n\).
Member Function Documentation
◆ extendSequence()
|
abstract |
Increases the number of points to \(n = 2^k\) from now on.
- Parameters
-
k there will be 2^k points
◆ iteratorShift()
| 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.
◆ iteratorShiftNoGray()
| 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.
◆ toNet()
| DigitalNetBase2 toNet | ( | ) |
Transforms this digital sequence into a digital net without changing the coordinates of the points.
Returns the digital net.
◆ toNetShiftCj()
| 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.
The documentation for this class was generated from the following file:
- DigitalSequenceBase2.java
