umontreal.iro.lecuyer.hups
Class DigitalNetBase2

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

DigitalNetBase2()

Method Summary

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 ui, j, the coordinate j of the point i.
double	getCoordinateNoGray(int i, int j) Returns ui, 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 Mj 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 Cj on the left by a w×w nonsingular lower-triangular matrix Mj, 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 Mj are 0.
void	leftMatrixScrambleFaurePermut(RandomStream stream, int sb) Similar to leftMatrixScramble except that the diagonal elements of each matrix Mj 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 Cj 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 Mj are chosen as in leftMatrixScrambleFaurePermut.
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 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