Inheritance diagram for KorobovLatticeSequence:
Collaboration diagram for KorobovLatticeSequence:
Public Member Functions | |
| KorobovLatticeSequence (int b, int a) | |
Constructs a new lattice sequence with base b and generator \( = a\). More... | |
| double | getCoordinate (int i, int j) |
 Public Member Functions inherited from KorobovLattice | |
| 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... | |
Package Attributes | |
| int | base |
| int | inverse |
| int | n |
Additional Inherited Members | |
| Protected Member Functions inherited from Rank1Lattice | |
| long | modPower (long a, int e, int m) |
| double | radicalInverse (int base, int i) |
| Protected Attributes inherited from KorobovLattice | |
| 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... | |
| 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
- Remarks
- Pierre: This class is not yet fully implemented
This class implements Korobov lattice sequences, defined as follows. One selects a basis \(b\) and a (large) multiplier \(a\). For each integer \(k\ge0\), we may consider the \(n\)-point Korobov lattice with modulus \(n = b^k\) and multiplier \(\tilde{a} = a \bmod n\). Its points have the form
\[ \mathbf{u}_i = (a^i (1, a, a^2, …) \bmod n) / n = (\tilde{a}^i (1, \tilde{a}, \tilde{a}^2, …) \bmod n) / n \tag{Korobov-seq1} \]
for \(i=0,…,n-1\). For \(k = 0,1,…\), we have an increasing sequence of lattices contained in one another.
These embedded lattices contain an infinite sequence of points that can be enumerated as follows [80] :
\[ \mathbf{u}_i = \psi_b(i) \left(1, a, a^2, …\right) \bmod1. \tag{Korobov-seq2} \]
where \(\psi_b(i)\) is the radical inverse function in base \(b\), defined in RadicalInverse. The first \(n=b^k\) points in this sequence are exactly the same as the \(n\) points in ( Korobov-seq1 ), for each \(k\ge0\).
Constructor & Destructor Documentation
◆ KorobovLatticeSequence()
| KorobovLatticeSequence | ( | int | b, |
| int | a | ||
| ) |
Constructs a new lattice sequence with base b and generator \( = a\).
- Parameters
-
b number of points (modulus) is a power of b a multiplier \(a\) of this lattice sequence
The documentation for this class was generated from the following file:
- KorobovLatticeSequence.java
