 | Niederreiter |
Class NiederreiterQuasiRandomGenerator is a quasi-random number generator which can be
used for generating sequences of quasi-random point in n-dimensional space.
Inheritance HierarchySystemObject
CenterSpace.NMath.CoreQuasiRandomNumberGenerator
CenterSpace.NMath.CoreNiederreiterQuasiRandomGenerator
CenterSpace.NMath.CoreQuasiRandomNumberGenerator
CenterSpace.NMath.CoreNiederreiterQuasiRandomGenerator
Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4
SyntaxThe NiederreiterQuasiRandomGenerator type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | NiederreiterQuasiRandomGenerator(Int32) | Constructs a NiederreiterQuasiRandomGenerator for generating quasi-random points in n-dimensioal space. |
| NiederreiterQuasiRandomGenerator(Int32, BitArray) | Constructs a NiederreiterQuasiRandomGenerator for generating quasi-random points in n-dimensioal space. Uses the given set of irreducible polynomials to initialize the generator. |
| NiederreiterQuasiRandomGenerator(Int32, Int32) | Constructs a NiederreiterQuasiRandomGenerator for generating quasi-random points in n-dimensioal space. The resulting generator is initialized with the given direction numbers. |
| NiederreiterQuasiRandomGenerator(Int32, BitArray, Int32) | Constructs a NiederreiterQuasiRandomGenerator for generating quasi-random points in n-dimensioal space. Uses the given set of irreducible polynomials and directionto initialize numbers to initialize the generator. |
Properties| Name | Description | |
|---|---|---|
 | Dimension |
Gets and sets the dimension.
(Inherited from QuasiRandomNumberGenerator) |
Methods| Name | Description | |
|---|---|---|
 | CheckDimensionAndDirectionNumbers |
Verifies that the direction numbers array has the correct number of rows and columns.
Rows must be equal to the number of dimensions, or the number of dimensions - 1. Number
of columns must equal 32.
(Overrides QuasiRandomNumberGeneratorCheckDimensionAndDirectionNumbers(Int32, Int32)) |
| CheckDimensionAndPolynomials |
Verifies that the number of dimensions and polynomials is correct. Number of
polynomials must be equal to the number of dimension or number of dimensions - 1.
(Overrides QuasiRandomNumberGeneratorCheckDimensionAndPolynomials(Int32, BitArray)) |
| Clone |
Creates a deep copy of self.
(Overrides QuasiRandomNumberGeneratorClone) |
| Fill(DoubleMatrix) |
Fills the given double precision matrix with M.Cols quasirandom points. The
points are the columns of the matrix, hence the number of rows in the
given matrix must be equal to the Dimension. The quasirandom numbers
will follow a uniform distribution in the hypercube [0,1]^n, where n is
equal to Dimension.
(Inherited from QuasiRandomNumberGenerator) |
| Fill(FloatMatrix) |
Fills the given single precision matrix with M.Cols quasirandom points. The
points are the columns of the matrix, hence the number of rows in the
given matrix must be equal to the Dimension. The quasirandom numbers
will follow a uniform distribution in the hypercube [0,1]^n, where n is
equal to Dimension.
(Inherited from QuasiRandomNumberGenerator) |
| Fill(IRandomNumberDistributionDouble, DoubleMatrix) |
Fills the given double precision matrix with M.Cols quasirandom points. The
points are the columns of the matrix, hence the number of rows in the
given matrix must be equal to the Dimension. The quasirandom numbers
will follow the given distribution.
(Inherited from QuasiRandomNumberGenerator) |
| Fill(IRandomNumberDistributionSingle, FloatMatrix) |
Fills the given single precision matrix with M.Cols quasirandom points. The
points are the columns of the matrix, hence the number of rows in the
given matrix must be equal to the Dimension. The quasirandom numbers
will follow the given distribution.
(Inherited from QuasiRandomNumberGenerator) |
| Fill(DoubleMatrix, Double, Double) |
Fills the given double precision matrix with M.Cols quasirandom points. The
points are the columns of the matrix, hence the number of rows in the
given matrix must be equal to the Dimension. The quasirandom numbers
will follow a uniform distribution in the hypercube [a,b]^n, where n is
equal to Dimension.
(Inherited from QuasiRandomNumberGenerator) |
| Fill(FloatMatrix, Single, Single) |
Fills the given single precision matrix with M.Cols quasirandom points. The
points are the columns of the matrix, hence the number of rows in the
given matrix must be equal to the Dimension. The quasirandom numbers
will follow a uniform distribution in the hypercube [a,b]^n, where n is
equal to Dimension.
(Inherited from QuasiRandomNumberGenerator) |
| FillT(IRandomNumberDistributionT, T) |
Fills an array with quasirandom numbers from the specified
distribution. The quasirandom numbers, which are tuples of length
Dimension are layed out linearly in the array r.
If Dimension = n, then the first n-dimensional quasirandom
point occupies r[0], r[1],...,r[n-1], the second occupies
r[n], r[n+1],...,r[2n-1], and so on.
(Inherited from QuasiRandomNumberGenerator) |
| Next(IRandomNumberDistributionDouble, Int32) |
Creates a double precision matrix filled with quasirandom points which follow the given
probability distribution. The columns of the matrix are the points, and
hence the matrix will contain Dimension rows and numSamples
columns.
(Inherited from QuasiRandomNumberGenerator) |
| Next(IRandomNumberDistributionSingle, Int32) |
Creates a single precision matrix filled with quasirandom points which follow the given
probability distribution. The columns of the matrix are the points, and
hence the matrix will contain Dimension rows and numSamples
columns.
(Inherited from QuasiRandomNumberGenerator) |
| NextT(IRandomNumberDistributionT, Int32) |
Creates an array filled with quasirandom numbers from the specified
distribution. The quasirandom numbers, which are tuples of length
Dimension are layed out linearly in the array r.
If Dimension = n, then the first n-dimensional quasirandom
point occupies r[0], r[1],...,r[n-1], the second occupies
r[n], r[n+1],...,r[2n-1], and so on.
(Inherited from QuasiRandomNumberGenerator) |
Fields| Name | Description | |
|---|---|---|
 | stream_ |
Basic random stream for uniform quasirandom numbers in n-dimensional
hypercube.
(Inherited from QuasiRandomNumberGenerator) |
Remarks
A quasi-random sequence is a sequence of n-tuples that fills n-dimensional space
more uniformly than uncorrelated random points.
Niederreiter is a 32-bit gray code-based quasirandom number generator defined by
Xn+1 = Xn @ Vc
Un = Xn/2^32
where @ represents an exclusive-or operation and the value of c is the rightmost bit in n - 1; Xn is an s-dimensional vector of 32-bit values. The s-dimensional vectors (calculated during random stream initialization) Vi, are called direction numbers. The vector Un is the generator output normalized to the unit s-dimensional hypercube (0,1)^s.
Xn+1 = Xn @ Vc
Un = Xn/2^32
where @ represents an exclusive-or operation and the value of c is the rightmost bit in n - 1; Xn is an s-dimensional vector of 32-bit values. The s-dimensional vectors (calculated during random stream initialization) Vi, are called direction numbers. The vector Un is the generator output normalized to the unit s-dimensional hypercube (0,1)^s.
See Also