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++

Copy

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

	Name	Description
	GeneralizedSingularValueDecompositionT	Constructs a new GeneralizedSingularValueDecompositionT object.

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Properties

	Name	Description
	BaseMatrix	Gets the primary underlying matrix of the decomposition. (Inherited from GeneralizedDecompositionT.)
	Done	Gets or sets a value that indicates whether the decomposition has been performed. (Inherited from GeneralizedDecompositionT.)
	GeneralizedSingularValues	Gets a vector containing the generalized singular values.
	Overwrite	Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition. (Inherited from GeneralizedDecompositionT.)
	PrimaryFactors	Gets a collection of the matrix factors that make up the decomposition of the first (primary) base matrix.
	PrimarySingularValueMatrix	Gets a matrix with the singular values on the diagonal.
	PrimarySingularValues	Gets a vector containing the singular values.
	PrimarySingularVectors	Gets the left singular vectors of the matrix A in the decomposition.
	Rank	Returns the numerical rank of a matrix using the specified tolerance.
	RequestedFactors	Gets or sets which factors of the singular value decomposition should be calculated.
	SecondaryBaseMatrix	Gets the secondary underlying matrix of the decomposition. (Inherited from GeneralizedDecompositionT.)
	SecondaryFactors	Gets a collection of the matrix factors that make up the decomposition of the secondary base matrix.
	SecondarySingularValueMatrix	Gets a matrix with the singular values on the diagonal.
	SecondarySingularValues	Gets a vector containing the secondary singular values.
	SecondarySingularVectors	Gets the left singular vectors of the matrix B in the decomposition.
	SharedFactor	Gets the shared factor in the decomposition.
	SharedOrthogonalFactor	Gets the shared orthogonal matrix of the decomposition.
	SharedTriangularFactor	Gets the full shared triangular factor of the decomposition.
	TrimmedSharedTriangularFactor	Gets the non-zero portion of the shared triangular matrix of the decomposition.

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Methods

	Name	Description
	Decompose	Performs the actual decomposition. (Inherited from GeneralizedDecompositionT.)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	SetSingular	Sets a flag that indicates the underlying matrix of this decomposition is singular. (Inherited from GeneralizedDecompositionT.)
	ToString	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.

Reference

Extreme.Mathematics.LinearAlgebra Namespace

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Type Parameters

Reference

GeneralizedSingularValueDecompositionT Class