This class implements a Korobov lattice, which represents the same point set as in class LCGPointSet, but implemented differently. More...
Public Member Functions | |
| KorobovLattice (int n, int a, int s) | |
| Instantiates a Korobov lattice point set with modulus \(n\) and multiplier \(a\) in dimension \(s\). | |
| KorobovLattice (int n, int a, int s, int t) | |
| Instantiates a shifted Korobov lattice point set with modulus \(n\) and multiplier \(a\) in dimension \(s\). More... | |
| void | setNumPoints (int n) |
| Resets the number of points of the lattice to \(n\). More... | |
| int | getA () |
| Returns the multiplier \(a\) of the lattice. More... | |
| String | toString () |
 Public Member Functions inherited from Rank1Lattice | |
| Rank1Lattice (int n, int[] a, int s) | |
| Instantiates a Rank1Lattice with \(n\) points and lattice vector \(a\) of dimension \(s\). More... | |
| void | setNumPoints (int n) |
| Resets the number of points of the lattice to \(n\). More... | |
| int [] | getAs () |
| Returns the generator \(a_j\) of the lattice. More... | |
| void | addRandomShift (int d1, int d2, RandomStream stream) |
Adds a random shift to all the points of the point set, using stream stream to generate the random numbers. More... | |
| void | clearRandomShift () |
| Clears the random shift. | |
| String | toString () |
| double | getCoordinate (int i, int j) |
| PointSetIterator | iterator () |
| 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 | genA |
| Protected Attributes inherited from Rank1Lattice | |
| int [] | genAs |
| double [] | v |
| double | normFactor |
| 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 Rank1Lattice | |
| long | modPower (long a, int e, int m) |
| double | radicalInverse (int base, int i) |
| 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 class implements a Korobov lattice, which represents the same point set as in class LCGPointSet, but implemented differently.
The parameters are the modulus \(n\) and the multiplier \(a\), for an arbitrary integer \(1 \le a < n\). When \(a\) is outside the interval \([1,n)\), then we replace \(a\) by ( \(a \bmod n\)) in all calculations. The number of points is \(n\), their dimension is \(s\), and they are defined by
\[ \mathbf{u}_i = (i/n)(1, a, a^2, …, a^{s-1}) \bmod1 \]
for \(i=0,…,n-1\).
It is also possible to build a "shifted" Korobov lattice for which the first \(t\) coordinates are skipped. The \(s\)-dimensionnal points are then defined as
\[ \mathbf{u}_i = (i/n)(a^t, a^{t+1}, a^{t+2}, …, a^{t+s-1}) \bmod1 \]
for \(i=0,…,n-1\) and fixed \(t\).
Constructor & Destructor Documentation
◆ KorobovLattice()
| KorobovLattice | ( | int | n, |
| int | a, | ||
| int | s, | ||
| int | t | ||
| ) |
Instantiates a shifted Korobov lattice point set with modulus \(n\) and multiplier \(a\) in dimension \(s\).
The first \(t\) coordinates of a standard Korobov lattice are dropped as described above. The case \(t=0\) corresponds to the standard Korobov lattice.
Member Function Documentation
◆ getA()
| int getA | ( | ) |
Returns the multiplier \(a\) of the lattice.
(The original one before it is reset to \(a \bmod n\)).
◆ setNumPoints()
| void setNumPoints | ( | int | n | ) |
Resets the number of points of the lattice to \(n\).
The values of \(s\), \(a\) and \(t\) are unchanged.
The documentation for this class was generated from the following file:
- KorobovLattice.java
