DigitalNetBase2 (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.hups.PointSet
- - umontreal.iro.lecuyer.hups.DigitalNet
  - - umontreal.iro.lecuyer.hups.DigitalNetBase2

Direct Known Subclasses:

DigitalNetBase2FromFile, DigitalSequenceBase2, F2wNetLFSR, F2wNetPolyLCG
```
public class DigitalNetBase2
extends DigitalNet
```
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 general case. Binary expansions are easy to obtain because the computer already uses them internally. The generator matrices C_j are stored in a large array of size sk. The c-th column of C_j, for c = 0,..., k - 1, is stored at position jk + c of that array, as a 32-bit integer. For all derived classes, the above 32-bit integer must be of the form [00^...C₀C₁^...C_r-1]. 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 31.
The random digital shift in base 2 corresponds to a random XOR. It can be applied via the method addRandomShift.

Constructor Summary

Constructors
Constructor and Description

DigitalNetBase2()

Constructors
Constructor and Description
`DigitalNetBase2()`

Method Summary

Methods
Modifier and Type	Method and Description
`void`	`addRandomShift(int d1, int d2, RandomStream stream)` Adds a random digital shift to all the points of the point set, using stream `stream` to generate the random numbers.
`void`	`addRandomShift(RandomStream stream)` Same as `addRandomShift(0, dim, stream)`, where `dim` is the dimension of the digital net.
`void`	`clearRandomShift()` Erases the current random shift, if any.
`double`	`getCoordinate(int i, int j)` Returns u_{i, j}, the coordinate j of the point i.
`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).
`void`	`iBinomialMatrixScramble(RandomStream stream)` Applies the i-binomial matrix scramble proposed by Tezuka .
`void`	`iBinomialMatrixScrambleFaurePermut(RandomStream stream, int sb)` Similar to `iBinomialMatrixScramble` except that the diagonal elements of each matrix M_j are chosen as in `leftMatrixScrambleFaurePermut`.
`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.
`void`	`iBinomialMatrixScrambleFaurePermutDiag(RandomStream stream, int sb)` Similar to `iBinomialMatrixScrambleFaurePermut` except that all the off-diagonal elements are 0.
`PointSetIterator`	`iterator()` Constructs and returns a point set iterator.
`PointSetIterator`	`iteratorNoGray()` This iterator does not use the Gray code.
`void`	`leftMatrixScramble(RandomStream stream)` Applies a linear scramble by multiplying each C_j on the left by a w×w nonsingular lower-triangular matrix M_j, as suggested by Matoušek and implemented by Hong and Hickernell.
`void`	`leftMatrixScrambleDiag(RandomStream stream)` Similar to `leftMatrixScramble` except that all the off-diagonal elements of the M_j are 0.
`void`	`leftMatrixScrambleFaurePermut(RandomStream stream, int sb)` Similar to `leftMatrixScramble` except that the diagonal elements of each matrix M_j are chosen from a restricted set of the best integers as calculated by Faure.
`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.
`void`	`leftMatrixScrambleFaurePermutDiag(RandomStream stream, int sb)` Similar to `leftMatrixScrambleFaurePermut` except that all off-diagonal elements are 0.
`void`	`printGeneratorMatrices(int s)` Prints the generator matrices as bit matrices in standard form for dimensions 1 to s.
`void`	`printGeneratorMatricesTrans(int s)` Prints the generator matrices transposed in the form of integers for dimensions 1 to s.
`void`	`rightMatrixScramble(RandomStream stream)` Applies a linear scramble by multiplying each C_j on the right by a single k×k nonsingular upper-triangular matrix M, as suggested by Faure and Tezuka.
`void`	`stripedMatrixScramble(RandomStream stream)` Applies the striped matrix scramble proposed by Owen.
`void`	`stripedMatrixScrambleFaurePermutAll(RandomStream stream, int sb)` Similar to `stripedMatrixScramble` except that the elements on and under the diagonal of each matrix M_j are chosen as in `leftMatrixScrambleFaurePermut`.
`java.lang.String`	`toString()` Formats a string that contains information about the point set.

Methods inherited from class umontreal.iro.lecuyer.hups.DigitalNet
eraseOriginalGeneratorMatrices, resetGeneratorMatrices, unrandomize

Methods inherited from class umontreal.iro.lecuyer.hups.PointSet
addRandomShift, addRandomShift, formatPoints, formatPoints, formatPoints, formatPoints, formatPointsBase, formatPointsBase, formatPointsBase, formatPointsBase, formatPointsNumbered, formatPointsNumbered, getDimension, getNumPoints, getStream, randomize, randomize, randomize, randomize, randomize, setStream

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - DigitalNetBase2
```
public DigitalNetBase2()
```
- Method Detail
  - printGeneratorMatrices
```
public void printGeneratorMatrices(int s)
```
    Prints the generator matrices as bit matrices in standard form for dimensions 1 to s.
    
    Overrides:
    
    printGeneratorMatrices in class DigitalNet
  - printGeneratorMatricesTrans
```
public void printGeneratorMatricesTrans(int s)
```
    Prints the generator matrices transposed in the form of integers for dimensions 1 to s. Each integer corresponds to a column of bits.
  - getCoordinate
```
public double getCoordinate(int i,
                   int j)
```
    Description copied from class: PointSet
    
    Returns u_{i, j}, the coordinate j of the point i.
    
    Overrides:
    
    getCoordinate in class DigitalNet
    
    Parameters:
    i - index of the point to look for
    j - index of the coordinate to look for
    
    Returns:
    the value of u_{i, j}
  - getCoordinateNoGray
```
public double getCoordinateNoGray(int i,
                         int j)
```
    Description copied from class: DigitalNet
    
    Returns u_{i, j}, the coordinate j of point i, the points being enumerated in the standard order (no Gray code).
    
    Overrides:
    
    getCoordinateNoGray in class DigitalNet
    
    Parameters:
    i - point index
    j - coordinate index
    
    Returns:
    the value of u_{i, j}
  - iterator
```
public PointSetIterator iterator()
```
    Description copied from class: PointSet
    
    Constructs and returns a point set iterator. The default implementation returns an iterator that uses the method getCoordinate (i,j) to iterate over the points and coordinates, but subclasses can reimplement it for better efficiency.
    
    Overrides:
    
    iterator in class DigitalNet
    
    Returns:
    point set iterator for the point set
  - iteratorNoGray
```
public PointSetIterator iteratorNoGray()
```
    This iterator does not use the Gray code. Thus the points are enumerated in the order of their first coordinate before randomization.
    
    Overrides:
    
    iteratorNoGray in class DigitalNet
  - toString
```
public java.lang.String toString()
```
    Description copied from class: PointSet
    
    Formats a string that contains information about the point set.
    
    Overrides:
    
    toString in class DigitalNet
    
    Returns:
    string representation of the point set information
  - clearRandomShift
```
public void clearRandomShift()
```
    Description copied from class: PointSet
    
    Erases the current random shift, if any.
    
    Overrides:
    
    clearRandomShift in class DigitalNet
  - addRandomShift
```
public void addRandomShift(RandomStream stream)
```
    Description copied from class: DigitalNet
    
    Same as addRandomShift(0, dim, stream), where dim is the dimension of the digital net.
    
    Overrides:
    
    addRandomShift in class DigitalNet
    
    Parameters:
    stream - random number stream used to generate uniforms
  - addRandomShift
```
public void addRandomShift(int d1,
                  int d2,
                  RandomStream stream)
```
    Description copied from class: DigitalNet
    
    Adds a random digital shift to all the points of the point set, using stream stream to generate the random numbers. For each coordinate j from d1 to d2-1, the shift vector (d_{j, 0},..., d_{j, k-1}) is generated uniformly over {0,..., b - 1}^k and added modulo b to the digits of all the points. After adding a digital shift, all iterators must be reconstructed or reset to zero.
    
    Overrides:
    
    addRandomShift in class DigitalNet
    
    stream - random number stream used to generate uniforms
  - leftMatrixScramble
```
public void leftMatrixScramble(RandomStream stream)
```
    Description copied from class: DigitalNet
    
    Applies a linear scramble by multiplying each C_j on the left by a w×w nonsingular lower-triangular matrix M_j, as suggested by Matoušek and implemented by Hong and Hickernell. The diagonal entries of each matrix M_j are generated uniformly over {1,..., b - 1}, the entries below the diagonal are generated uniformly over {0,..., b - 1}, and all these entries are generated independently. This means that in base b = 2, all diagonal elements are equal to 1.
    
    Overrides:
    
    leftMatrixScramble in class DigitalNet
    
    Parameters:
    stream - random number stream used to generate the randomness
  - iBinomialMatrixScramble
```
public void iBinomialMatrixScramble(RandomStream stream)
```
    Description copied from class: DigitalNet
    
    Applies the i-binomial matrix scramble proposed by Tezuka . This multiplies each C_j on the left by a w×w nonsingular lower-triangular matrix M_j as in leftMatrixScramble, but with the additional constraint that all entries on any given diagonal or subdiagonal of M_j are identical.
    
    Overrides:
    
    iBinomialMatrixScramble in class DigitalNet
    
    Parameters:
    stream - random number stream used as generator of the randomness
  - stripedMatrixScramble
```
public void stripedMatrixScramble(RandomStream stream)
```
    Description copied from class: DigitalNet
    
    Applies the striped matrix scramble proposed by Owen. It multiplies each C_j on the left by a w×w nonsingular lower-triangular matrix M_j as in leftMatrixScramble, but with the additional constraint that in any column, all entries below the diagonal are equal to the diagonal entry, which is generated randomly over {1,..., b - 1}. Note that for b = 2, the matrices M_j become deterministic, with all entries on and below the diagonal equal to 1.
    
    Overrides:
    
    stripedMatrixScramble in class DigitalNet
    
    Parameters:
    stream - random number stream used as generator of the randomness
  - rightMatrixScramble
```
public void rightMatrixScramble(RandomStream stream)
```
    Description copied from class: DigitalNet
    
    Applies a linear scramble by multiplying each C_j on the right by a single k×k nonsingular upper-triangular matrix M, as suggested by Faure and Tezuka. The diagonal entries of the matrix M are generated uniformly over {1,..., b - 1}, the entries above the diagonal are generated uniformly over {0,..., b - 1}, and all the entries are generated independently. The effect of this scramble is only to change the order in which the points are generated. If one computes the average value of a function over all the points of a given digital net, or over a number of points that is a power of the basis, then this scramble makes no difference.
    
    Overrides:
    
    rightMatrixScramble in class DigitalNet
    
    Parameters:
    stream - random number stream used as generator of the randomness
  - leftMatrixScrambleDiag
```
public void leftMatrixScrambleDiag(RandomStream stream)
```
    Description copied from class: DigitalNet
    
    Similar to leftMatrixScramble except that all the off-diagonal elements of the M_j are 0.
    
    Overrides:
    
    leftMatrixScrambleDiag in class DigitalNet
    
    Parameters:
    stream - random number stream used to generate the randomness
  - leftMatrixScrambleFaurePermut
```
public void leftMatrixScrambleFaurePermut(RandomStream stream,
                                 int sb)
```
    Description copied from class: DigitalNet
    
    Similar to leftMatrixScramble except that the diagonal elements of each matrix M_j are chosen from a restricted set of the best integers as calculated by Faure. They are generated uniformly over the first sb elements of array F, where F is made up of a permutation of the integers [1..(b - 1)]. These integers are sorted by increasing order of the upper bounds of the extreme discrepancy for the given integer.
    
    Overrides:
    
    leftMatrixScrambleFaurePermut in class DigitalNet
    
    Parameters:
    stream - random number stream used to generate the randomness
    sb - Only the first sb elements of F are used
  - leftMatrixScrambleFaurePermutDiag
```
public void leftMatrixScrambleFaurePermutDiag(RandomStream stream,
                                     int sb)
```
    Description copied from class: DigitalNet
    
    Similar to leftMatrixScrambleFaurePermut except that all off-diagonal elements are 0.
    
    Overrides:
    
    leftMatrixScrambleFaurePermutDiag in class DigitalNet
    
    Parameters:
    stream - random number stream used to generate the randomness
    sb - Only the first sb elements of F are used
  - leftMatrixScrambleFaurePermutAll
```
public void leftMatrixScrambleFaurePermutAll(RandomStream stream,
                                    int sb)
```
    Description copied from class: DigitalNet
    
    Similar to leftMatrixScrambleFaurePermut except that the elements under the diagonal are also chosen from the same restricted set as the diagonal elements.
    
    Overrides:
    
    leftMatrixScrambleFaurePermutAll in class DigitalNet
    
    Parameters:
    stream - random number stream used to generate the randomness
    sb - Only the first sb elements of F are used
  - iBinomialMatrixScrambleFaurePermut
```
public void iBinomialMatrixScrambleFaurePermut(RandomStream stream,
                                      int sb)
```
    Description copied from class: DigitalNet
    
    Similar to iBinomialMatrixScramble except that the diagonal elements of each matrix M_j are chosen as in leftMatrixScrambleFaurePermut.
    
    Overrides:
    
    iBinomialMatrixScrambleFaurePermut in class DigitalNet
    
    Parameters:
    stream - random number stream used to generate the randomness
    sb - Only the first sb elements of F are used
  - iBinomialMatrixScrambleFaurePermutDiag
```
public void iBinomialMatrixScrambleFaurePermutDiag(RandomStream stream,
                                          int sb)
```
    Description copied from class: DigitalNet
    
    Similar to iBinomialMatrixScrambleFaurePermut except that all the off-diagonal elements are 0.
    
    Overrides:
    
    iBinomialMatrixScrambleFaurePermutDiag in class DigitalNet
    
    Parameters:
    stream - random number stream used to generate the randomness
    sb - Only the first sb elements of F are used
  - iBinomialMatrixScrambleFaurePermutAll
```
public void iBinomialMatrixScrambleFaurePermutAll(RandomStream stream,
                                         int sb)
```
    Description copied from class: DigitalNet
    
    Similar to iBinomialMatrixScrambleFaurePermut except that the elements under the diagonal are also chosen from the same restricted set as the diagonal elements.
    
    Overrides:
    
    iBinomialMatrixScrambleFaurePermutAll in class DigitalNet
    
    Parameters:
    stream - random number stream used to generate the randomness
    sb - Only the first sb elements of F are used
  - stripedMatrixScrambleFaurePermutAll
```
public void stripedMatrixScrambleFaurePermutAll(RandomStream stream,
                                       int sb)
```
    Description copied from class: DigitalNet
    
    Similar to stripedMatrixScramble except that the elements on and under the diagonal of each matrix M_j are chosen as in leftMatrixScrambleFaurePermut.
    
    Overrides:
    
    stripedMatrixScrambleFaurePermutAll in class DigitalNet
    
    Parameters:
    stream - random number stream used as generator of the randomness
    sb - Only the first sb elements of F are used

Class DigitalNetBase2

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.hups.DigitalNet

Methods inherited from class umontreal.iro.lecuyer.hups.PointSet

Methods inherited from class java.lang.Object

Constructor Detail

DigitalNetBase2

Method Detail

printGeneratorMatrices

printGeneratorMatricesTrans

getCoordinate

getCoordinateNoGray

iterator

iteratorNoGray

toString

clearRandomShift

addRandomShift

addRandomShift

leftMatrixScramble

iBinomialMatrixScramble

stripedMatrixScramble

rightMatrixScramble

leftMatrixScrambleDiag

leftMatrixScrambleFaurePermut

leftMatrixScrambleFaurePermutDiag

leftMatrixScrambleFaurePermutAll

iBinomialMatrixScrambleFaurePermut

iBinomialMatrixScrambleFaurePermutDiag

iBinomialMatrixScrambleFaurePermutAll

stripedMatrixScrambleFaurePermutAll