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  • Extreme.Mathematics.LinearAlgebra
    • BandMatrix(T) Class
    • BlockVector(T) Class
    • CholeskyDecomposition(T) Class
    • CloningMethod Enumeration
    • ColumnCollection(T) Structure
    • ComplexSingularValueDecomposition(T) Class
    • ComponentReadOnlyException Class
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    • ComposedComplexVector(T) Class
    • ConstantMatrix(T) Class
    • ConstantVector(T) Class
    • Decomposition(T) Class
    • DenseMatrix(T) Class
    • DenseVector(T) Class
    • DiagonalMatrix(T) Class
    • EigenvalueDecomposition(T) Class
    • EigenvalueRange Enumeration
    • GeneralizedDecomposition(T) Class
    • GeneralizedEigenvalueDecomposition(T) Class
    • GeneralizedSingularValueDecomposition(T) Class
    • GeneralizedSingularValueDecompositionFactors Enumeration
    • HermitianMatrix(T) Class
    • IndexedVector(T) Class
    • IndexValuePair(T) Structure
    • IResizableMatrix(T) Interface
    • LeastSquaresSolutionMethod Enumeration
    • LeastSquaresSolver(T) Class
    • LinearAlgebraOperations Class
    • LinearOperator(T) Class
    • LQDecomposition(T) Class
    • LUDecomposition(T) Class
    • MatrixNotPositiveDefiniteException Class
    • MatrixSingularException Class
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    • NonNegativeMatrixFactorization(T) Class
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    • PivotVector Structure
    • QLDecomposition(T) Class
    • QRDecomposition(T) Class
    • RealEigenvalueDecomposition(T) Class
    • RowCollection(T) Structure
    • RowColumnValueTriplet(T) Structure
    • RQDecomposition(T) Class
    • SingularValueDecomposition(T) Class
    • SingularValueDecompositionFactors Enumeration
    • SparseCompressedColumnMatrix(T) Class
    • SparseMatrix(T) Class
    • SparseVector(T) Class
    • SymmetricIndefiniteDecomposition(T) Class
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  • GeneralizedSingularValueDecomposition(T) Class
    • GeneralizedSingularValueDecomposition(T) Constructor
    • Properties
    • GeneralizedSingularValueDecomposition(T) Methods

GeneralizedSingularValueDecompositionT Class

Extreme Optimization Numerical Libraries for .NET Professional
Represents the generalized singular value decomposition of two matrices.
Inheritance Hierarchy

SystemObject
  Extreme.Mathematics.LinearAlgebraGeneralizedDecompositionT
    Extreme.Mathematics.LinearAlgebraGeneralizedSingularValueDecompositionT

Namespace:  Extreme.Mathematics.LinearAlgebra
Assembly:  Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1
Syntax

C#
VB
C++
F#
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public abstract class GeneralizedSingularValueDecomposition<T> : GeneralizedDecomposition<T>
Public MustInherit Class GeneralizedSingularValueDecomposition(Of T)
	Inherits GeneralizedDecomposition(Of T)
generic<typename T>
public ref class GeneralizedSingularValueDecomposition abstract : public GeneralizedDecomposition<T>
[<AbstractClassAttribute>]
type GeneralizedSingularValueDecomposition<'T> =  
    class
        inherit GeneralizedDecomposition<'T>
    end

Type Parameters

T

The GeneralizedSingularValueDecompositionT type exposes the following members.

Constructors

  NameDescription
Protected methodGeneralizedSingularValueDecompositionT
Constructs a new GeneralizedSingularValueDecompositionT object.
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Properties

  NameDescription
Public propertyBaseMatrix
Gets the primary underlying matrix of the decomposition.
(Inherited from GeneralizedDecompositionT.)
Protected propertyDone
Gets or sets a value that indicates whether the decomposition has been performed.
(Inherited from GeneralizedDecompositionT.)
Public propertyGeneralizedSingularValues
Gets a vector containing the generalized singular values.
Public propertyOverwrite
Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition.
(Inherited from GeneralizedDecompositionT.)
Public propertyPrimaryFactors
Gets a collection of the matrix factors that make up the decomposition of the first (primary) base matrix.
Public propertyPrimarySingularValueMatrix
Gets a matrix with the singular values on the diagonal.
Public propertyPrimarySingularValues
Gets a vector containing the singular values.
Public propertyPrimarySingularVectors
Gets the left singular vectors of the matrix A in the decomposition.
Public propertyRank
Returns the numerical rank of a matrix using the specified tolerance.
Public propertyRequestedFactors
Gets or sets which factors of the singular value decomposition should be calculated.
Public propertySecondaryBaseMatrix
Gets the secondary underlying matrix of the decomposition.
(Inherited from GeneralizedDecompositionT.)
Public propertySecondaryFactors
Gets a collection of the matrix factors that make up the decomposition of the secondary base matrix.
Public propertySecondarySingularValueMatrix
Gets a matrix with the singular values on the diagonal.
Public propertySecondarySingularValues
Gets a vector containing the secondary singular values.
Public propertySecondarySingularVectors
Gets the left singular vectors of the matrix B in the decomposition.
Public propertySharedFactor
Gets the shared factor in the decomposition.
Public propertySharedOrthogonalFactor
Gets the shared orthogonal matrix of the decomposition.
Public propertySharedTriangularFactor
Gets the full shared triangular factor of the decomposition.
Public propertyTrimmedSharedTriangularFactor
Gets the non-zero portion of the shared triangular matrix of the decomposition.
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Methods

  NameDescription
Public methodDecompose
Performs the actual decomposition.
(Inherited from GeneralizedDecompositionT.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Protected methodSetSingular
Sets a flag that indicates the underlying matrix of this decomposition is singular.
(Inherited from GeneralizedDecompositionT.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

The generalized singular value decomposition (GSVD) of two matrices, A and B rewrites the matrices as

A = U Σ1 [0 R] QT
B = V Σ2 [0 R] QT

where U, V, and Q are orthogonal matrices (unitary if T is complex), Σ1 and Σ2 are real diagonal matrices, and R is an upper triangular matrix.

See Also

Reference

Extreme.Mathematics.LinearAlgebra Namespace

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