public abstract class ComplexSingularValueDecomposition : ComplexDecomposition

Public MustInherit Class ComplexSingularValueDecomposition
	Inherits ComplexDecomposition

public ref class ComplexSingularValueDecomposition abstract : public ComplexDecomposition

[<AbstractClassAttribute>]
type ComplexSingularValueDecomposition =  
    class
        inherit ComplexDecomposition
    end

The ComplexSingularValueDecomposition type exposes the following members.

	Name	Description
	ComplexSingularValueDecomposition(ComplexDenseMatrix, Boolean)	Constructs a new ComplexSingularValueDecomposition object.
	ComplexSingularValueDecomposition(ComplexDenseMatrix, SingularValueDecompositionFactors, Boolean)	Constructs a new ComplexSingularValueDecomposition object.

	Name	Description
	BaseMatrix	Gets the underlying matrix of the decomposition. (Inherited from ComplexDecomposition.)
	ComplexSingularValueMatrix	Gets a matrix with the singular values on the diagonal.
	Done	Gets or sets whether the decomposition has been performed. (Inherited from ComplexDecomposition.)
	Factors	Gets a collection of the matrix factors that make up the decomposition. (Overrides ComplexDecompositionFactors.)
	LeftSingularVectors	Gets the left singular vectors of the decomposition.
	Overwrite	Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition. (Inherited from ComplexDecomposition.)
	RequestedFactors	Gets or sets which factors of the singular value decomposition should be calculated.
	RightSingularVectors	Gets the right singular vectors of the decomposition.
	SingularValueMatrix	Gets a matrix with the singular values on the diagonal.
	SingularValues	Gets a vector containing the singular values.

	Name	Description
	Decompose	Performs the actual decomposition. (Inherited from ComplexDecomposition.)
	Equals	Determines whether the specified Object is equal to the current Object. (Inherited from Object.)
	EstimateConditionNumber	Calculates an estimate for the condition number of the ComplexMatrix. (Overrides ComplexLinearOperatorEstimateConditionNumber.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetDeterminant	Calculates the determinant of the decomposed ComplexMatrix. (Overrides ComplexLinearOperatorGetDeterminant.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetInverse	Calculates the inverse matrix.. (Inherited from ComplexLinearOperator.)
	GetInverse(Boolean)	Calculates the inverse of the factorized ComplexMatrix. (Overrides ComplexLinearOperatorGetInverse(Boolean).)
	GetObjectData	Populates a SerializationInfo with the data needed to serialize the target object. (Inherited from ComplexLinearOperator.)
	GetPseudoInverse	Calculates the pseudo-inverse of the factorized ComplexMatrix.
	GetPseudoInverse(Double)	Calculates the pseudo-inverse of the factorized ComplexMatrix.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	IsSingular	Gets a value indicating whether the BaseMatrix of this decomposition is singular. (Inherited from ComplexDecomposition.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Multiply(ComplexMatrix)	Multiplies the decomposition to a matrix. (Inherited from ComplexDecomposition.)
	Multiply(ComplexVector)	Applies the base matrix of the decomposition to a vector. (Inherited from ComplexDecomposition.)
	MultiplyTranspose(ComplexMatrix)	Multiplies the transpose of the decomposition to a matrix. (Inherited from ComplexDecomposition.)
	MultiplyTranspose(ComplexVector)	Multiplies the transpose of the decomposition to a vector. (Inherited from ComplexDecomposition.)
	Rank	Returns the numerical rank of a matrix. (Inherited from ComplexLinearOperator.)
	Rank(Double)	Returns the numerical rank of a matrix using the specified tolerance. (Overrides ComplexLinearOperatorRank(Double).)
	SetSingular	Sets a flag that indicates the underlying matrix of this decomposition is singular. (Inherited from ComplexDecomposition.)
	Solve(ComplexMatrix)	Solves the system of linear equations for the specified right-hand side ComplexMatrix. (Inherited from ComplexLinearOperator.)
	Solve(ComplexVector)	Solves the system of linear equations for the specified right-hand side complex vector. (Inherited from ComplexLinearOperator.)
	Solve(ComplexDenseMatrix, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side ComplexDenseMatrix and overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolve(ComplexDenseMatrix, Boolean).)
	Solve(ComplexDenseVector, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side complex vector. (Overrides ComplexLinearOperatorSolve(ComplexDenseVector, Boolean).)
	SolveTranspose(ComplexMatrix)	Solves the transposed system of linear equations for the specified right-hand side ComplexMatrix. (Inherited from ComplexLinearOperator.)
	SolveTranspose(ComplexVector)	Solves the system of linear equations for the specified right-hand side complex vector. (Inherited from ComplexLinearOperator.)
	SolveTranspose(ComplexDenseMatrix, Boolean)	Solves the transposed system of linear equations for the specified right-hand side ComplexDenseMatrix and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolveTranspose(ComplexDenseMatrix, Boolean).)
	SolveTranspose(ComplexDenseVector, Boolean)	Solves the transposed system of linear equations for the specified right-hand side ComplexDenseVector and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolveTranspose(ComplexDenseVector, Boolean).)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

The singular value decomposition (SVD) of a matrix A rewrites the matrix in the form A= USV^T, where U and V are orthogonal matrices, and S is a diagonal matrix whose diagonal contains the singular values of the matrix.

ComplexQRDecomposition can operate in two modes. In overwrite mode, the original matrix is overwritten by the decomposition. In preserve mode, the original matrix is preserved, and a new matrix is created to hold the decomposition. You can set the mode through the Overwrite property.

ComplexSingularValueDecomposition inherits from LinearOperator. This means you can use it to solve systems of linear equations. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(ComplexDenseMatrix, Boolean) method. You can also calculate the determinant, the inverse, and an estimate for the EstimateConditionNumber.

In addition, the ComplexSingularValueDecomposition class provides some unique methods. The GetPseudoInverse method calculates the pseudo-inverse of the matrix. This is a matrix A⁺ such that AA⁺A = A.

The managed implementation of the singular value decomposition is based on the LINPACK routine DSVDC. The native version uses the LAPACK routine DGESDD.

Numerical Libraries

Reference