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SSJ V. 2.6. |
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java.lang.Object umontreal.iro.lecuyer.hups.PointSet umontreal.iro.lecuyer.hups.DigitalNet umontreal.iro.lecuyer.hups.DigitalNetBase2
public class DigitalNetBase2
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
Cj are stored in a large array of size sk.
The c-th column of
Cj, 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 ... Cr-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 | |
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DigitalNetBase2()
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Method Summary | |
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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 |
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eraseOriginalGeneratorMatrices, resetGeneratorMatrices, unrandomize |
Methods inherited from class umontreal.iro.lecuyer.hups.PointSet |
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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 |
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equals, getClass, hashCode, notify, notifyAll, wait, wait, wait |
Constructor Detail |
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public DigitalNetBase2()
Method Detail |
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public void printGeneratorMatrices(int s)
printGeneratorMatrices
in class DigitalNet
public void printGeneratorMatricesTrans(int s)
public double getCoordinate(int i, int j)
PointSet
getCoordinate
in class DigitalNet
i
- index of the point to look forj
- index of the coordinate to look for
public double getCoordinateNoGray(int i, int j)
DigitalNet
getCoordinateNoGray
in class DigitalNet
i
- point indexj
- coordinate index
public PointSetIterator iterator()
PointSet
getCoordinate
(i,j) to iterate over the
points and coordinates, but subclasses can reimplement it
for better efficiency.
iterator
in class DigitalNet
public PointSetIterator iteratorNoGray()
iteratorNoGray
in class DigitalNet
public String toString()
PointSet
toString
in class DigitalNet
public void clearRandomShift()
PointSet
clearRandomShift
in class DigitalNet
public void addRandomShift(RandomStream stream)
DigitalNet
addRandomShift
(0, dim, stream),
where dim is the dimension of the digital net.
addRandomShift
in class DigitalNet
stream
- random number stream used to generate uniformspublic void addRandomShift(int d1, int d2, RandomStream stream)
DigitalNet
addRandomShift
in class DigitalNet
stream
- random number stream used to generate uniformspublic void leftMatrixScramble(RandomStream stream)
DigitalNet
leftMatrixScramble
in class DigitalNet
stream
- random number stream used to generate the randomnesspublic void iBinomialMatrixScramble(RandomStream stream)
DigitalNet
leftMatrixScramble
, but with the additional constraint that
all entries on any given diagonal or subdiagonal of
Mj are identical.
iBinomialMatrixScramble
in class DigitalNet
stream
- random number stream used as generator of the randomnesspublic void stripedMatrixScramble(RandomStream stream)
DigitalNet
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
Mj become deterministic, with
all entries on and below the diagonal equal to 1.
stripedMatrixScramble
in class DigitalNet
stream
- random number stream used as generator of the randomnesspublic void rightMatrixScramble(RandomStream stream)
DigitalNet
rightMatrixScramble
in class DigitalNet
stream
- random number stream used as generator of the randomnesspublic void leftMatrixScrambleDiag(RandomStream stream)
DigitalNet
leftMatrixScramble
except that all the
off-diagonal elements of the
Mj are 0.
leftMatrixScrambleDiag
in class DigitalNet
stream
- random number stream used to generate the randomnesspublic void leftMatrixScrambleFaurePermut(RandomStream stream, int sb)
DigitalNet
leftMatrixScramble
except that the diagonal elements
of each matrix
Mj 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.
leftMatrixScrambleFaurePermut
in class DigitalNet
stream
- random number stream used to generate the randomnesssb
- Only the first sb elements of F are usedpublic void leftMatrixScrambleFaurePermutDiag(RandomStream stream, int sb)
DigitalNet
leftMatrixScrambleFaurePermut
except that all
off-diagonal elements are 0.
leftMatrixScrambleFaurePermutDiag
in class DigitalNet
stream
- random number stream used to generate the randomnesssb
- Only the first sb elements of F are usedpublic void leftMatrixScrambleFaurePermutAll(RandomStream stream, int sb)
DigitalNet
leftMatrixScrambleFaurePermut
except that the
elements under the diagonal are also
chosen from the same restricted set as the diagonal elements.
leftMatrixScrambleFaurePermutAll
in class DigitalNet
stream
- random number stream used to generate the randomnesssb
- Only the first sb elements of F are usedpublic void iBinomialMatrixScrambleFaurePermut(RandomStream stream, int sb)
DigitalNet
iBinomialMatrixScramble
except that the diagonal
elements of each matrix
Mj are chosen as in
leftMatrixScrambleFaurePermut
.
iBinomialMatrixScrambleFaurePermut
in class DigitalNet
stream
- random number stream used to generate the randomnesssb
- Only the first sb elements of F are usedpublic void iBinomialMatrixScrambleFaurePermutDiag(RandomStream stream, int sb)
DigitalNet
iBinomialMatrixScrambleFaurePermut
except that all the
off-diagonal elements are 0.
iBinomialMatrixScrambleFaurePermutDiag
in class DigitalNet
stream
- random number stream used to generate the randomnesssb
- Only the first sb elements of F are usedpublic void iBinomialMatrixScrambleFaurePermutAll(RandomStream stream, int sb)
DigitalNet
iBinomialMatrixScrambleFaurePermut
except that the
elements under the diagonal are also
chosen from the same restricted set as the diagonal elements.
iBinomialMatrixScrambleFaurePermutAll
in class DigitalNet
stream
- random number stream used to generate the randomnesssb
- Only the first sb elements of F are usedpublic void stripedMatrixScrambleFaurePermutAll(RandomStream stream, int sb)
DigitalNet
stripedMatrixScramble
except that the
elements on and under the diagonal of each matrix
Mj are
chosen as in leftMatrixScrambleFaurePermut
.
stripedMatrixScrambleFaurePermutAll
in class DigitalNet
stream
- random number stream used as generator of the randomnesssb
- Only the first sb elements of F are used
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SSJ V. 2.6. |
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SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |