Similar to CycleBasedPointSet, except that the successive values in the cycles are stored as integers in the range \(\{0,\dots,2^k-1\}\), where \(1\le k \le31\). More...
Inheritance diagram for CycleBasedPointSetBase2:
Collaboration diagram for CycleBasedPointSetBase2:
Classes | |
| class | CycleBasedPointSetBase2Iterator |
Public Member Functions | |
| double | getCoordinate (int i, int j) |
| PointSetIterator | iterator () |
| void | addRandomShift (int d1, int d2, RandomStream stream) |
Adds a random digital shift in base 2 to all the points of the point set, using stream stream to generate the random numbers, for coordinates d1 to d2 - 1. More... | |
| void | clearRandomShift () |
| Erases the current digital random shift, if any. | |
| String | formatPoints () |
 Public Member Functions inherited from CycleBasedPointSet | |
| double | getCoordinate (int i, int j) |
| void | addRandomShift (int d1, int d2, RandomStream stream) |
Same as the same method in PointSet. More... | |
| void | clearRandomShift () |
| Erases the current random shift, if any. | |
| int | getDimension () |
| PointSetIterator | iterator () |
| String | toString () |
| String | formatPoints () |
| 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 | numBits |
| double | normFactor |
| Protected Attributes inherited from CycleBasedPointSet | |
| int | numCycles = 0 |
| ObjectArrayList | cycles = new ObjectArrayList() |
| 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 CycleBasedPointSet | |
| void | addCycle (AbstractList c) |
Adds the cycle c to the list of all cycles. 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
Similar to CycleBasedPointSet, except that the successive values in the cycles are stored as integers in the range \(\{0,\dots,2^k-1\}\), where \(1\le k \le31\).
The output values \(u_{i,j}\) are obtained by dividing these integer values by \(2^k\). Point sets where the successive coordinates of each point are obtained via linear recurrences modulo 2 (e.g., linear feedback shift registers or Korobov-type polynomial lattice rules) are naturally expressed in this form. Storing the integers \(2^k u_{i,j}\) instead of the \(u_{i,j}\) themselves makes it easier to apply randomizations such as digital random shifts in base 2, which are applied to the bits before transforming the value to a real number \(u_{i,j}\). When a random digital shift is performed, it applies a bitwise exclusive-or of all the points with a single random point.
Member Function Documentation
◆ addRandomShift()
| void addRandomShift | ( | int | d1, |
| int | d2, | ||
| RandomStream | stream | ||
| ) |
Adds a random digital shift in base 2 to all the points of the point set, using stream stream to generate the random numbers, for coordinates d1 to d2 - 1.
This applies a bitwise exclusive-or of all the points with a single random point.
The documentation for this class was generated from the following file:
- CycleBasedPointSetBase2.java
