SingularValueDecompositionT Class

public abstract class SingularValueDecomposition<T> : Decomposition<T>

Public MustInherit Class SingularValueDecomposition(Of T)
	Inherits Decomposition(Of T)

generic<typename T>
public ref class SingularValueDecomposition abstract : public Decomposition<T>

[<AbstractClassAttribute>]
type SingularValueDecomposition<'T> =  
    class
        inherit Decomposition<'T>
    end

Type Parameters

T

The SingularValueDecompositionT type exposes the following members.

	Name	Description
	SingularValueDecompositionT	Constructs a new SingularValueDecompositionT object.

	Name	Description
	BaseMatrix	Gets the underlying matrix of the decomposition. (Inherited from DecompositionT.)
	ColumnCount	Gets the number of columns in the matrix. (Inherited from LinearOperatorT.)
	ColumnIndex	Gets or sets the index of labels for the columns of the matrix. (Inherited from LinearOperatorT.)
	Done	Gets or sets a value that indicates whether the decomposition has been performed. (Inherited from DecompositionT.)
	ElementType	Gets the element type of the matrix. (Inherited from LinearOperatorT.)
	Factors	Gets a collection of the matrix factors that make up the decomposition. (Overrides DecompositionTFactors.)
	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 DecompositionT.)
	RequestedFactors	Gets or sets which factors of the singular value decomposition should be calculated.
	RightSingularVectors	Gets the right singular vectors of the decomposition.
	RowCount	Gets the number of rows in the matrix. (Inherited from LinearOperatorT.)
	RowIndex	Gets or sets the index of labels for the rows of the matrix. (Inherited from LinearOperatorT.)
	SingularValueMatrix	Gets a matrix with the singular values on the diagonal.
	SingularValues	Gets a vector containing the singular values.

	Name	Description
	AddProductToVector	Obsolete. Multiplies a VectorT by this instance and stores the result in a second vector of type DenseVectorT. (Inherited from LinearOperatorT.)
	Decompose	Performs the actual decomposition. (Inherited from DecompositionT.)
	Deconstruct	Deconstructs a singular value decomposition into its component matrices.
	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 matrix. (Overrides LinearOperatorTEstimateConditionNumber.)
	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 matrix. (Overrides LinearOperatorTGetDeterminant.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetInverse	Calculates the inverse matrix.. (Inherited from LinearOperatorT.)
	GetInverse(Boolean)	Calculates the inverse of the factorized matrix. (Overrides LinearOperatorTGetInverse(Boolean).)
	GetObjectData	Populates a SerializationInfo with the data needed to serialize the target object. (Inherited from LinearOperatorT.)
	GetPseudoInverse	Calculates the pseudo-inverse of the factorized matrix.
	GetPseudoInverse(T)	Calculates the pseudo-inverse of the factorized matrix.
	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 DecompositionT.)
	LeastSquaresSolve(MatrixT)	Solves the system of linear equations for the specified right-hand side matrix in the least squares sense. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(DenseMatrixT, Boolean)	Solves the system of linear equations for the specified right-hand side dense matrix in the least squares sense and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(DenseVectorT, Boolean)	Solves the system of linear equations for the specified right-hand side dense vector in the least squares sense and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	LeastSquaresSolveInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides in the least squares sense. (Overrides LinearOperatorTLeastSquaresSolveInto(MatrixT, MatrixT).)
	LeastSquaresSolveInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side in the least squares sense. (Overrides DecompositionTLeastSquaresSolveInto(VectorT, VectorT).)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Multiply(MatrixT)	Applies the linear operator to a matrix. (Inherited from LinearOperatorT.)
	Multiply(VectorT)	Applies the linear operator to a vector. (Inherited from LinearOperatorT.)
	Multiply(TransposeOperation, MatrixT)	Obsolete. Multiplies a matrix on the left by this matrix. (Inherited from LinearOperatorT.)
	Multiply(TransposeOperation, VectorT)	Obsolete. Multiplies a vector on the left by this vector. (Inherited from LinearOperatorT.)
	MultiplyAndAddAsLeftFactorCore	Multiplies the matrix with a vector, adds the scaled result to another scaled vector, and returns the result. (Inherited from DecompositionT.)
	MultiplyAsLeftCore(TransposeOperation, MatrixT, MatrixT)	Multiplies a matrix by the linear operator and returns the result. (Inherited from DecompositionT.)
	MultiplyAsLeftCore(TransposeOperation, VectorT, VectorT)	Multiplies a vector by the linear operator and returns the result. (Inherited from DecompositionT.)
	MultiplyTranspose(MatrixT)	Applies the transpose of the linear operator to a matrix. (Inherited from LinearOperatorT.)
	MultiplyTranspose(VectorT)	Applies the (conjugate) transpose of the linear operator to a vector. (Inherited from LinearOperatorT.)
	Rank	Returns the numerical rank of a matrix. (Inherited from LinearOperatorT.)
	Rank(T)	Returns the numerical rank of a matrix using the specified tolerance. (Overrides LinearOperatorTRank(T).)
	SetRank	Sets the smallest singular values to zero so the matrix has at most the specified rank.
	SetSingular	Sets a flag that indicates the underlying matrix of this decomposition is singular. (Inherited from DecompositionT.)
	Solve(MatrixT)	Solves the system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperatorT.)
	Solve(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	Solve(DenseMatrixT, Boolean)	Solves the system of linear equations for the specified right-hand side dense matrix and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	Solve(DenseVectorT, Boolean)	Solves the system of linear equations for the specified right-hand side dense vector and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	SolveInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperatorT.)
	SolveInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperatorT.)
	SolveInto(TransposeOperation, MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Overrides LinearOperatorTSolveInto(TransposeOperation, MatrixT, MatrixT).)
	SolveInto(TransposeOperation, VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Overrides LinearOperatorTSolveInto(TransposeOperation, VectorT, VectorT).)
	SolveTranspose(MatrixT)	Solves the transposed system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperatorT.)
	SolveTranspose(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	SolveTranspose(DenseMatrixT, Boolean)	Solves the transposed system of linear equations for the specified right-hand side dense matrix and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	SolveTranspose(DenseVectorT, Boolean)	Solves the transposed system of linear equations for the specified right-hand side dense vector and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	SolveTransposeInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperatorT.)
	SolveTransposeInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperatorT.)
	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.

QRDecompositionT 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.

SingularValueDecompositionT inherits from LinearOperatorT. 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(VectorT) method. You can also calculate the determinant, the inverse, and an estimate for the EstimateConditionNumber.

In addition, the SingularValueDecompositionT 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 ?GESDD.

Reference